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The Posner molecule (calcium phosphate trimer), has been hypothesized tofunction as a biological quantum information processor due to its supposedlylong-lived entangled $^{31}$P nuclear spin states. This hypothesis waschallenged by our recent finding that the molecule lacks a well-definedrotational axis of symmetry -- an essential assumption in the proposal forPosner-mediated neural processing -- and exists as an asymmetric dynamicalensemble. Following up, we investigate here the spin dynamics of the molecule'sentangled $^{31}$P nuclear spins within the asymmetric ensemble. Oursimulations show that entanglement between two nuclear spins prepared in a Bellstate in separate Posner molecules decays on a sub-second timescale -- muchfaster than previously hypothesized, and not long enough for super-cellularneuronal processing. Calcium phosphate dimers however, are found to besurprisingly resilient to decoherence and are able to preserve entanglednuclear spins for hundreds of seconds, suggesting that neural processing mightoccur through them instead.

A spectral method using associated Legendre functions with algebraic mappingis developed for a linear stability analysis of wake vortices. These functionsserve as Galerkin basis functions, capturing correct analyticity and boundaryconditions for vortices in an unbounded domain. The incompressible Euler orNavier-Stokes equations linearised on a swirling flow are transformed into astandard matrix eigenvalue problem of toroidal and poloidal streamfunctions,solving perturbation velocity eigenmodes with their complex growth rate aseigenvalues. This reduces the problem size for computation and distributescollocation points adjustably clustered around the vortex core. Based on thismethod, strong swirling $q$-vortices with linear perturbation wavenumbers oforder unity are examined. Without viscosity, neutrally stable eigenmodesassociated with the continuous eigenvalue spectrum having critical-layersingularities are successfully resolved. The inviscid critical-layer eigenmodesnumerically tend to appear in pairs, implying their singular degeneracy. Withviscosity, the spectra pertaining to physical regularisation of critical layersstretch out toward an area, referring to potential eigenmodes with wavepacketsfound by Mao & Sherwin (2011). However, the potential eigenmodes exhibit nospatial similarity to the inviscid critical-layer eigenmodes, doubting thatthey truly represent the viscous remnants of the inviscid critical-layereigenmodes. Instead, two distinct continuous curves in the numerical spectraare identified for the first time, named the viscous critical-layer spectrum,where the similarity is noticeable. Moreover, the viscous critical-layereigenmodes are resolved in conformity with the $Re^{-1/3}$ scaling law. Theonset of the two curves is believed to be caused by viscosity breaking thesingular degeneracy.

The computational cost for high energy physics detector simulation in futureexperimental facilities is going to exceed the current available resources. Toovercome this challenge, new ideas on surrogate models using machine learningmethods are being explored to replace computationally expensive components.Additionally, differentiable programming has been proposed as a complementaryapproach, providing controllable and scalable simulation routines. In thisdocument, new and ongoing efforts for surrogate models and differentialprogramming applied to detector simulation are discussed in the context of the2021 Particle Physics Community Planning Exercise (`Snowmass').

Today's world of scientific software for High Energy Physics (HEP) is poweredby x86 code, while the future will be much more reliant on accelerators likeGPUs and FPGAs. The portable parallelization strategies (PPS) project of theHigh Energy Physics Center for Computational Excellence (HEP/CCE) isinvestigating solutions for portability techniques that will allow the codingof an algorithm once, and the ability to execute it on a variety of hardwareproducts from many vendors, especially including accelerators. We think withoutthese solutions, the scientific success of our experiments and endeavors is indanger, as software development could be expert driven and costly to be able torun on available hardware infrastructure. We think the best solution for thecommunity would be an extension to the C++ standard with a very low entry barfor users, supporting all hardware forms and vendors. We are very far from thatideal though. We argue that in the future, as a community, we need to requestand work on portability solutions and strive to reach this ideal.

We present a high-performance coupled electrodynamics–micromagnetics solver for full physical modeling of signals in microelectronic circuitry. The overall strategy couples a finite-difference time-domain approach for Maxwell’s equations to a magnetization model described by the Landau–Lifshitz–Gilbert equation. The algorithm is implemented in the Exascale Computing Project software framework, AMReX, which provides effective scalability on manycore and GPU-based supercomputing architectures. Furthermore, the code leverages ongoing developments of the Exascale Application Code, WarpX, which is primarily being developed for plasma wakefield accelerator modeling. Our temporal coupling scheme provides second-order accuracy in space and time by combining the integration steps for the magnetic field and magnetization into an iterative sub-step that includes a trapezoidal temporal discretization for the magnetization. The performance of the algorithm is demonstrated by the excellent scaling results on NERSC multicore and GPU systems, with a significant (59×) speedup on the GPU using a node-by-node comparison. We demonstrate the utility of our code by performing simulations of an electromagnetic waveguide and a magnetically tunable filter.

WarpX is a general purpose electromagnetic particle-in-cell code that was originally designed to run on many-core CPU architectures. We describe the strategy, based on the AMReX library, followed to allow WarpX to use the GPU-accelerated nodes on OLCF's Summit supercomputer, a strategy we believe will extend to the upcoming machines Frontier and Aurora. We summarize the challenges encountered, lessons learned, and give current performance results on a series of relevant benchmark problems.

We present a high-energy neutrino event generator, called LeptonInjector, alongside an event weighter, called LeptonWeighter. Both are designed for large-volume Cherenkov neutrino telescopes such as IceCube. The neutrino event generator allows for quick and flexible simulation of neutrino events within and around the detector volume, and implements the leading Standard Model neutrino interaction processes relevant for neutrino observatories: neutrino-nucleon deep-inelastic scattering and neutrino-electron annihilation. In this paper, we discuss the event generation algorithm, the weighting algorithm, and the main functions of the publicly available code, with examples. Program summary: Program Titles: LeptonInjector and LeptonWeighter CPC Library link to program files: https://doi.org/10.17632/662gkpjfd9.1 Developer's repository links: https://github.com/icecube/LeptonInjector and https://github.com/icecube/LeptonWeighter Licensing provisions: GNU Lesser General Public License, version 3. Programming Language: C++11 External Routines: • Boost • HDF5 • nuflux (https://github.com/icecube/nuflux) • nuSQuIDS (https://github.com/arguelles/nuSQuIDS) • Photospline (https://github.com/icecube/photospline) • SuiteSparse (https://github.com/DrTimothyAldenDavis/SuiteSparse) Nature of problem: LeptonInjector: Generate neutrino interaction events of all possible topologies and energies throughout and around a detector volume. LeptonWeighter: Reweight Monte Carlo events, generated by a set of LeptonInjector Generators, to any desired physical neutrino flux or cross section. Solution method: LeptonInjector: Projected ranges of generated leptons and the extent of the detector, in terms of column depth, are used to inject events in and around the detector volume. Event kinematics follow distributions provided in cross section files. LeptonWeighter: Event generation probabilities are calculated for each Generator, which are then combined into a generation weight and used to calculate an overall event weight.

The Posner molecule, $\text{Ca}_9(\text{PO}_4)_6$, has long been recognizedto have biochemical relevance in various physiological processes. It has foundrecent attention for its possible role as a biological quantum informationprocessor, whereby the molecule purportedly maintains long-lived nuclear spincoherences among its ${^{31}\text{P}}$ nuclei (presumed to be symmetricallyarranged), allowing it to function as a room temperature qubit. The structureof the molecule has been of much dispute in the literature, although the$\text{S}_6$ point group symmetry has often been assumed and exploited incalculations. Using a variety of simulation techniques (including ab initiomolecular dynamics and structural relaxation), rigorous data analysis tools andby exploring thousands of individual configurations, we establish that themolecule predominantly assumes low symmetry structures ($\text{C}_\text{s}$ and$\text{C}_\text{i}$) at room temperature, as opposed to the higher symmetryconfigurations explored previously. Our findings have important implications onthe viability of this molecule as a qubit.

We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system's behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.

We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system's behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.

ArQTiC is an open-source, full-stack software package built for thesimulations of materials on quantum computers. It currently can simulatematerials that can be modeled by any Hamiltonian derived from a generic,one-dimensional, time-dependent Heisenberg Hamiltonain. ArQTiC includes modulesfor generating quantum programs for real- and imaginary-time evolution, quantumcircuit optimization, connection to various quantum backends via the cloud, andpost-processing of quantum results. By enabling users to seamlessly perform andanalyze materials simulations on quantum computers by simply providing aminimal input text file, ArQTiC opens this field to a broader community ofscientists from a wider range of scientific domains.

Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-1/2 J1 − J2 Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

Abstract: Transfer learning refers to the use of knowledge gained while solving a machine learning task and applying it to the solution of a closely related problem. Such an approach has enabled scientific breakthroughs in computer vision and natural language processing where the weights learned in state-of-the-art models can be used to initialize models for other tasks which dramatically improve their performance and save computational time. Here we demonstrate an unsupervised learning approach augmented with basic physical principles that achieves fully transferrable learning for problems in statistical physics across different physical regimes. By coupling a sequence model based on a recurrent neural network to an extensive deep neural network, we are able to learn the equilibrium probability distributions and inter-particle interaction models of classical statistical mechanical systems. Our approach, distribution-consistent learning, DCL, is a general strategy that works for a variety of canonical statistical mechanical models (Ising and Potts) as well as disordered interaction potentials. Using data collected from a single set of observation conditions, DCL successfully extrapolates across all temperatures, thermodynamic phases, and can be applied to different length-scales. This constitutes a fully transferrable physics-based learning in a generalizable approach.

The Hartree-Fock-Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree-Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size Nb. We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-Type Hamiltonian, the cost of PEXSI is at most (Nb2) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with Nb up to 2.88 × 106, and the wall clock time is less than 100 s using 17 280 CPU cores. This enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

Explicit electromagnetic Particle-In-Cell (PIC) codes are typically limitedby the Courant- Friedrichs-Lewy (CFL) condition, which implies that thetimestep multiplied by the speed of light must be smaller than the smallestcell size. In the case of boosted-frame PIC simulations of plasma-basedacceleration, this limitation can be a major hinderance as the cells are oftenvery elongated along the longitudinal direction and the timestep is thuslimited by the small, transverse cell size. This entails many small-timestepPIC iterations, and can limit the potential speed-up of the boosted-frametechnique. Here, by using a CFL-free analytical spectral solver, and bymitigating additional numerical instabilities that arise at large timestep, weshow that it is possible to overcome traditional limitations on the timestepand thereby realize the full potential of the boosted-frame technique over amuch wider range of parameters.

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an end-to-end machine learning model that automatically generates descriptors that capture a complex representation of a material's structure and chemistry. This approach builds on computational topology techniques (namely, persistent homology) and word embeddings from natural language processing. It automatically encapsulates geometric and chemical information directly from the material system. We demonstrate our approach on multiple nanoporous metal-organic framework datasets by predicting methane and carbon dioxide adsorption across different conditions. Our results show considerable improvement in both accuracy and transferability across targets compared to models constructed from the commonly-used, manually-curated features, consistently achieving an average 25-30% decrease in root-mean-squared-deviation and an average increase of 40-50% in R2 scores. A key advantage of our approach is interpretability: Our model identifies the pores that correlate best to adsorption at different pressures, which contributes to understanding atomic-level structure-property relationships for materials design.

Maintaining computational load balance is important to the performantbehavior of codes which operate under a distributed computing model. This isespecially true for GPU architectures, which can suffer from memoryoversubscription if improperly load balanced. We present enhancements totraditional load balancing approaches and explicitly target GPU architectures,exploring the resulting performance. A key component of our enhancements is theintroduction of several GPU-amenable strategies for assessing compute work.These strategies are implemented and benchmarked to find the most optimal datacollection methodology for in-situ assessment of GPU compute work. For thefully kinetic particle-in-cell code WarpX, which supports MPI+CUDA parallelism,we investigate the performance of the improved dynamic load balancing via astrong scaling-based performance model and show that, for a laser-ionacceleration test problem run with up to 6144 GPUs on Summit, the enhanceddynamic load balancing achieves from 62%--74% (88% when running on 6 GPUs) ofthe theoretically predicted maximum speedup; for the 96-GPU case, we find thatdynamic load balancing improves performance relative to baselines without loadbalancing (3.8x speedup) and with static load balancing (1.2x speedup). Ourresults provide important insights into dynamic load balancing and performanceassessment, and are particularly relevant in the context of distributed memoryapplications ran on GPUs.

The electronic transport behaviour of materials determines their suitability for technological applications. We develop a computationally efficient method for calculating carrier scattering rates of solid-state semiconductors and insulators from first principles inputs. The present method extends existing polar and non-polar electron-phonon coupling, ionized impurity, and piezoelectric scattering mechanisms formulated for isotropic band structures to support highly anisotropic materials. We test the formalism by calculating the electronic transport properties of 23 semiconductors, including the large 48 atom CH3NH3PbI3 hybrid perovskite, and comparing the results against experimental measurements and more detailed scattering simulations. The Spearman rank coefficient of mobility against experiment (rs = 0.93) improves significantly on results obtained using a constant relaxation time approximation (rs = 0.52). We find our approach offers similar accuracy to state-of-the art methods at approximately 1/500th the computational cost, thus enabling its use in high-throughput computational workflows for the accurate screening of carrier mobilities, lifetimes, and thermoelectric power.

The arrival of direct electron detectors (DED) with high frame-rates in thefield of scanning transmission electron microscopy has enabled manyexperimental techniques that require collection of a full diffraction patternat each scan position, a field which is subsumed under the name fourdimensional-scanning transmission electron microscopy (4D-STEM). DED framerates approaching 100 kHz require data transmission rates and data storagecapabilities that exceed commonly available computing infrastructure. Currentcommercial DEDs allow the user to make compromises in pixel bit depth, detectorbinning or windowing to reduce the per-frame file size and allow higher framerates. This change in detector specifications requires decisions to be madebefore data acquisition that may reduce or lose information that could havebeen advantageous during data analysis. The 4D Camera, a DED with 87 kHzframe-rate developed at Lawrence Berkeley National Laboratory, reduces the rawdata to a linear-index encoded electron event representation (EER). Here weshow with experimental data from the 4D Camera that linear-index encoded EERand its direct use in 4D-STEM phase contrast imaging methods enables real-time,interactive phase-contrast from large-area 4D-STEM datasets. We detail thecomputational complexity advantages of the EER and the necessary computationalsteps to achieve real-time interactive ptychography and center-of-massdifferential phase contrast using commonly available hardware accelerators.

In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the fluctuating immersed-boundary approach that treats a solute as discrete Lagrangian particles that interact with Eulerian hydrodynamic and electrostatic fields. In both algorithms the immersed-boundary method of Peskin is used for particle-field coupling. Hydrodynamic interactions are taken to be overdamped, with thermal noise incorporated using the fluctuating Stokes equation, including a "dry diffusion"Brownian motion to account for scales not resolved by the coarse-grained model of the solvent. Long-range electrostatic interactions are computed by solving the Poisson equation, with short-range corrections included using an immersed-boundary variant of the classical particle-particle particle-mesh technique. Also included is a short-range repulsive force based on the Weeks-Chandler-Andersen potential. This methodology is validated by comparison to Debye-Hückel theory for ion-ion pair correlation functions, and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In each case, good agreement is observed, provided that hydrodynamic interactions at the typical ion-ion separation are resolved by the fluid grid.

We present a new, high-performance coupled electrodynamics-micromagneticssolver for full physical modeling of signals in microelectronic circuitry. Theoverall strategy couples a finite-difference time-domain (FDTD) approach forMaxwell's equations to a magnetization model described by theLandau-Lifshitz-Gilbert (LLG) equation. The algorithm is implemented in theExascale Computing Project software framework, AMReX, which provides effectivescalability on manycore and GPU-based supercomputing architectures.Furthermore, the code leverages ongoing developments of the ExascaleApplication Code, WarpX, primarily developed for plasma wakefield acceleratormodeling. Our novel temporal coupling scheme provides second-order accuracy inspace and time by combining the integration steps for the magnetic field andmagnetization into an iterative sub-step that includes a trapezoidaldiscretization for the magnetization. The performance of the algorithm isdemonstrated by the excellent scaling results on NERSC multicore and GPUsystems, with a significant (59x) speedup on the GPU using a node-by-nodecomparison. We demonstrate the utility of our code by performing simulations ofan electromagnetic waveguide and a magnetically tunable filter.

We present a greedy algorithm for computing selected eigenpairs of a largesparse matrix $H$ that can exploit localization features of the eigenvector.When the eigenvector to be computed is localized, meaning only a small numberof its components have large magnitudes, the proposed algorithm identifies thelocation of these components in a greedy manner, and obtains approximations tothe desired eigenpairs of $H$ by computing eigenpairs of a submatrix extractedfrom the corresponding rows and columns of $H$. Even when the eigenvector isnot completely localized, the approximate eigenvectors obtained by the greedyalgorithm can be used as good starting guesses to accelerate the convergence ofan iterative eigensolver applied to $H$. We discuss a few possibilities forselecting important rows and columns of $H$ and techniques for constructinggood initial guesses for an iterative eigensolver using the approximateeigenvectors returned from the greedy algorithm. We demonstrate theeffectiveness of this approach with examples from nuclear quantum many-bodycalculations and many-body localization studies of quantum spin chains.

The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. In this work, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ^{*} depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ^{*} scales weakly with system size, i.e., the dependence of ℓ^{*} on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim_{L→∞}(ℓ^{*}/L)=0. In particular, for (2+1)-dimensional interfaces ℓ^{*} is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. This weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

We present a benchmark test suite and an automated machine learning procedure for evaluating supervised machine learning (ML) models for predicting properties of inorganic bulk materials. The test suite, Matbench, is a set of 13 ML tasks that range in size from 312 to 132k samples and contain data from 10 density functional theory-derived and experimental sources. Tasks include predicting optical, thermal, electronic, thermodynamic, tensile, and elastic properties given a material’s composition and/or crystal structure. The reference algorithm, Automatminer, is a highly-extensible, fully automated ML pipeline for predicting materials properties from materials primitives (such as composition and crystal structure) without user intervention or hyperparameter tuning. We test Automatminer on the Matbench test suite and compare its predictive power with state-of-the-art crystal graph neural networks and a traditional descriptor-based Random Forest model. We find Automatminer achieves the best performance on 8 of 13 tasks in the benchmark. We also show our test suite is capable of exposing predictive advantages of each algorithm—namely, that crystal graph methods appear to outperform traditional machine learning methods given ~104 or greater data points. We encourage evaluating materials ML algorithms on the Matbench benchmark and comparing them against the latest version of Automatminer.

Machine learning has emerged as a novel tool for the efficient prediction of material properties, and claims have been made that machine-learned models for the formation energy of compounds can approach the accuracy of Density Functional Theory (DFT). The models tested in this work include five recently published compositional models, a baseline model using stoichiometry alone, and a structural model. By testing seven machine learning models for formation energy on stability predictions using the Materials Project database of DFT calculations for 85,014 unique chemical compositions, we show that while formation energies can indeed be predicted well, all compositional models perform poorly on predicting the stability of compounds, making them considerably less useful than DFT for the discovery and design of new solids. Most critically, in sparse chemical spaces where few stoichiometries have stable compounds, only the structural model is capable of efficiently detecting which materials are stable. The nonincremental improvement of structural models compared with compositional models is noteworthy and encourages the use of structural models for materials discovery, with the constraint that for any new composition, the ground-state structure is not known a priori. This work demonstrates that accurate predictions of formation energy do not imply accurate predictions of stability, emphasizing the importance of assessing model performance on stability predictions, for which we provide a set of publicly available tests.

Laser-ion acceleration with ultra-short pulse, petawatt-class lasers is dominated by non-thermal, intra-pulse plasma dynamics. The presence of multiple ion species or multiple charge states in targets leads to characteristic modulations and even mono-energetic features, depending on the choice of target material. As spectral signatures of generated ion beams are frequently used to characterize underlying acceleration mechanisms, thermal, multi-fluid descriptions require revision for predictive capabilities and control in next-generation particle beam sources. We present an analytical model with explicit inter-species interactions, supported by extensive ab initio simulations. This enables us to derive important ensemble properties from the spectral distribution resulting from these multi-species effects for arbitrary mixtures. We further propose a potential experimental implementation with a novel cryogenic target, delivering jets with variable mixtures of hydrogen and deuterium. Free from contaminants and without strong influence of hardly controllable processes such as ionization dynamics, this would allow a systematic realization of our predictions for the multi-species effect.

Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. In this work, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets. Program summary: Program title: ELSI Interface CPC Library link to program files: http://dx.doi.org/10.17632/473mbbznrs.1 Licensing provisions: BSD 3-clause Programming language: Fortran 2003, with interface to C/C++ External routines/libraries: BLACS, BLAS, BSEPACK (optional), EigenExa (optional), ELPA, FortJSON, LAPACK, libOMM, MPI, MAGMA (optional), MUMPS (optional), NTPoly, ParMETIS (optional), PETSc (optional), PEXSI, PT-SCOTCH (optional), ScaLAPACK, SLEPc (optional), SuperLU_DIST Nature of problem: Solving the electronic structure from given Hamiltonian and overlap matrices in electronic structure calculations. Solution method: ELSI provides a unified software interface to facilitate the use of various electronic structure solvers including cubic scaling dense eigensolvers, linear scaling density matrix methods, and other approaches.

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets. Program summary: Program title: ELSI Interface CPC Library link to program files: http://dx.doi.org/10.17632/473mbbznrs.1 Licensing provisions: BSD 3-clause Programming language: Fortran 2003, with interface to C/C++ External routines/libraries: BLACS, BLAS, BSEPACK (optional), EigenExa (optional), ELPA, FortJSON, LAPACK, libOMM, MPI, MAGMA (optional), MUMPS (optional), NTPoly, ParMETIS (optional), PETSc (optional), PEXSI, PT-SCOTCH (optional), ScaLAPACK, SLEPc (optional), SuperLU_DIST Nature of problem: Solving the electronic structure from given Hamiltonian and overlap matrices in electronic structure calculations. Solution method: ELSI provides a unified software interface to facilitate the use of various electronic structure solvers including cubic scaling dense eigensolvers, linear scaling density matrix methods, and other approaches.

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H2, Li2, and BeH2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

Local causal states are latent representations that capture organized patternand structure in complex spatiotemporal systems. We expand their functionality,framing them as spacetime autoencoders. Previously, they were only consideredas maps from observable spacetime fields to latent local causal state fields.Here, we show that there is a stochastic decoding that maps back from thelatent fields to observable fields. Furthermore, their Markovian propertiesdefine a stochastic dynamic in the latent space. Combined with stochasticdecoding, this gives a new method for forecasting spacetime fields.

All computation is physically embedded. Reflecting this, a growing body ofresults embraces rate equations as the underlying mechanics of thermodynamiccomputation and biological information processing. Strictly applying theimplied continuous-time Markov chains, however, excludes a universe of naturalcomputing. We show that expanding the toolset to continuous-time hidden Markovchains substantially removes the constraints. The general point is madeconcrete by our analyzing two eminently-useful computations that are impossibleto describe with a set of rate equations over the memory states. We design andanalyze a thermodynamically-costless bit flip, providing a first counterexampleto rate-equation modeling. We generalize this to a costless Fredkin gate---akey operation in reversible computing that is computation universal. Goingbeyond rate-equation dynamics is not only possible, but necessary if stochasticthermodynamics is to become part of the paradigm for physical informationprocessing.

Modelling long-time convective flows in the interiors of stars is extremely challenging using conventional compressible hydrodynamics codes due to the acoustic timestep limitation. Many of these flows are in the low Mach number regime, which allows us to exploit the relationship between acoustic and advective time scales to develop a more computationally efficient approach. MAESTROeX is an open source low Mach number stellar hydrodynamics code that allows much larger timesteps to be taken, therefore enabling systems to be modelled for much longer periods of time. This is particularly important for the problem of convection in the cores of rotating massive stars prior to core collapse. To fully capture the dynamics, it is necessary to model these systems in three dimensions at high resolution over many rotational periods. We present an overview of MAESTROeX's current capabilities, describe ongoing work to incorporate the effects of rotation and discuss how we are optimising the code to run on GPUs.

We describe recent developments to the Castro astrophysics simulation code, focusing on new features that enable our simulations of X-ray bursts. Two highlights of Castro's ongoing development are the new integration technique to couple hydrodynamics and reactions to high order and GPU offloading. We discuss how these features will help offset some of the computational expense in X-ray burst models.

While cloud-resolving models can explicitly simulate the details of small-scale storm formation and morphology, these details are often ignored by climate models for lack of computational resources. Here, we explore the potential of generative modeling to cheaply recreate small-scale storms by designing and implementing a Variational Autoencoder (VAE) that performs structural replication, dimensionality reduction, and clustering of high-resolution vertical velocity fields. Trained on ∼6 · 106 samples spanning the globe, the VAE successfully reconstructs the spatial structure of convection, performs unsupervised clustering of convective organization regimes, and identifies anomalous storm activity, confirming the potential of generative modeling to power stochastic parameterizations of convection in climate models.

We present a new mesoscale model for ionic liquids based on a low Mach number fluctuating hydrodynamics formulation for multicomponent charged species. The low Mach number approach eliminates sound waves from the fully compressible equations leading to a computationally efficient incompressible formulation. The model uses a Gibbs free-energy functional that includes enthalpy of mixing, interfacial energy, and electrostatic contributions. These lead to a new fourth-order term in the mass equations and a reversible stress in the momentum equations. We calibrate our model using parameters for [DMPI+][F6P-], an extensively studied room temperature ionic liquid (RTIL), and numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double-layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic flows.

Materials Cloud is a platform designed to enable open and seamless sharing of resources for computational science, driven by applications in materials modelling. It hosts (1) archival and dissemination services for raw and curated data, together with their provenance graph, (2) modelling services and virtual machines, (3) tools for data analytics, and pre-/post-processing, and (4) educational materials. Data is citable and archived persistently, providing a comprehensive embodiment of entire simulation pipelines (calculations performed, codes used, data generated) in the form of graphs that allow retracing and reproducing any computed result. When an AiiDA database is shared on Materials Cloud, peers can browse the interconnected record of simulations, download individual files or the full database, and start their research from the results of the original authors. The infrastructure is agnostic to the specific simulation codes used and can support diverse applications in computational science that transcend its initial materials domain.

Three-dimensional phase contrast imaging of multiply-scattering samples inX-ray and electron microscopy is extremely challenging, due to small numericalapertures, the unavailability of wavefront shaping optics, and the highlynonlinear inversion required from intensity-only measurements. In this work, wepresent a new algorithm using the scattering matrix formalism to solve thescattering from a non-crystalline medium from scanning diffractionmeasurements, and recover the illumination aberrations. Our method will enable3D imaging and materials characterization at high resolution for a wide rangeof materials.

Nanomagnets with giant magnetic anisotropy energy and long coherence time aredesired for various technological innovations such as quantum informationprocession and storage. Based on the first-principles calculations and modelanalyses, we demonstrate that a single uranium atom substituting Al on theAl2O3(0001) surface may have high structural stability and large magneticanisotropy energy up to 48 meV per uranium atom. As the magnetization residesin the localized f-shell and is not much involved in chemical bonding withneighbors, long coherence time up to ~1.6 mS can be achieved for the quantumspin states. These results suggest a new strategy for the search of ultrasmallmagnetic units for diverse applications in the quantum information era.

We show how to bound and calculate the likelihood of dynamical large deviations using evolutionary reinforcement learning. An agent, a stochastic model, propagates a continuous-time Monte Carlo trajectory and receives a reward conditioned upon the values of certain path-extensive quantities. Evolution produces progressively fitter agents, potentially allowing the calculation of a piece of a large-deviation rate function for a particular model and path-extensive quantity. For models with small state spaces, the evolutionary process acts directly on rates, and for models with large state spaces, the process acts on the weights of a neural network that parameterizes the model's rates. This approach shows how path-extensive physics problems can be considered within a framework widely used in machine learning.

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

Classical turning surfaces of Kohn-Sham potentials, separatingclassically-allowed regions (CARs) from classically-forbidden regions (CFRs),provide a useful and rigorous approach to understanding many chemicalproperties of molecules. Here we calculate such surfaces for severalparadigmatic solids. Our study of perfect crystals at equilibrium geometriessuggests that CFRs are absent in metals, rare in covalent semiconductors, butcommon in ionic and molecular crystals. A CFR can appear at a monovacancy in ametal. In all materials, CFRs appear or grow as the internuclear distances areuniformly expanded. Calculations with several approximate density functionalsand codes confirm these behaviors. A classical picture of conduction suggeststhat CARs should be connected in metals, and disconnected in wide-gapinsulators. This classical picture is confirmed in the limits of extremeuniform compression of the internuclear distances, where all materials becomemetals without CFRs, and extreme expansion, where all materials becomeinsulators with disconnected and widely-separated CARs around the atoms.

To address the unprecedented scale of HL-LHC data, the Exa.TrkX project isinvestigating a variety of machine learning approaches to particle trackreconstruction. The most promising of these solutions, graph neural networks(GNN), process the event as a graph that connects track measurements (detectorhits corresponding to nodes) with candidate line segments between the hits(corresponding to edges). Detector information can be associated with nodes andedges, enabling a GNN to propagate the embedded parameters around the graph andpredict node-, edge- and graph-level observables. Previously, message-passingGNNs have shown success in predicting doublet likelihood, and we here reportupdates on the state-of-the-art architectures for this task. In addition, theExa.TrkX project has investigated innovations in both graph construction, andembedded representations, in an effort to achieve fully learned end-to-endtrack finding. Hence, we present a suite of extensions to the original model,with encouraging results for hitgraph classification. In addition, we exploreincreased performance by constructing graphs from learned representations whichcontain non-linear metric structure, allowing for efficient clustering andneighborhood queries of data points. We demonstrate how this framework fits inwith both traditional clustering pipelines, and GNN approaches. The embeddedgraphs feed into high-accuracy doublet and triplet classifiers, or can be usedas an end-to-end track classifier by clustering in an embedded space. A set ofpost-processing methods improve performance with knowledge of the detectorphysics. Finally, we present numerical results on the TrackML particle trackingchallenge dataset, where our framework shows favorable results in both seedingand track finding.

CFD is widely used in physical system design and optimization, where it isused to predict engineering quantities of interest, such as the lift on a planewing or the drag on a motor vehicle. However, many systems of interest areprohibitively expensive for design optimization, due to the expense ofevaluating CFD simulations. To render the computation tractable, reduced-orderor surrogate models are used to accelerate simulations while respecting theconvergence constraints provided by the higher-fidelity solution. This paperintroduces CFDNet -- a physical simulation and deep learning coupled framework,for accelerating the convergence of Reynolds Averaged Navier-Stokessimulations. CFDNet is designed to predict the primary physical properties ofthe fluid including velocity, pressure, and eddy viscosity using a singleconvolutional neural network at its core. We evaluate CFDNet on a variety ofuse-cases, both extrapolative and interpolative, where test geometries areobserved/not-observed during training. Our results show that CFDNet meets theconvergence constraints of the domain-specific physics solver whileoutperforming it by 1.9 - 7.4x on both steady laminar and turbulent flows.Moreover, we demonstrate the generalization capacity of CFDNet by testing itsprediction on new geometries unseen during training. In this case, the approachmeets the CFD convergence criterion while still providing significant speedupsover traditional domain-only models.

To directly simulate rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well-established enhanced-sampling techniques do exist to obtain the thermodynamic functions for such systems. However, developing methods for obtaining the kinetics of long timescale processes from simulation at atomic detail is comparatively less developed an area. Milestoning and the weighted ensemble (WE) method are two different stratification strategies; both have shown promise for computing long timescales of complex biomolecular processes. Nevertheless, both require a significant investment of computational resources. We have combined WE and milestoning to calculate observables in orders-of-magnitude less central processing unit and wall-clock time. Our weighted ensemble milestoning method (WEM) uses WE simulation to converge the transition probability and first passage times between milestones, followed by the utilization of the theoretical framework of milestoning to extract thermodynamic and kinetic properties of the entire process. We tested our method for a simple one-dimensional double-well potential, for an eleven-dimensional potential energy surface with energy barrier, and on the biomolecular model system alanine dipeptide. We were able to recover the free energy profiles, time correlation functions, and mean first passage times for barrier crossing events at a significantly small computational cost. WEM promises to extend the applicability of molecular dynamics simulation to slow dynamics of large systems that are well beyond the scope of present day brute-force computations.

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. The routinely used single-shot GW approximation (G0W0) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.