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The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message-passing architectures. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. This work introduces higher-rank irreducible Cartesian tensors as an alternative to spherical tensors, addressing the above limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical models.

Dynamics of a polymer chain in solution gets significantly affected by the temperature and the frictional forces arising due to solvent viscosity. Here, using an explicit solvent framework for polymer simulation with the liberty to tune the solvent viscosity, we study the nonequilibrium dynamics of a flexible homopolymer when it is suddenly quenched from an extended coil state in good solvent to poor solvent conditions. Results from our extensive simulations reveal that depending on the temperature $T$ and solvent viscosity, one encounters long-lived sausage-like intermediates following the usual pearl-necklace intermediates. Use of shape factors of polymers allows us to disentangle these two distinct stages of the overall collapse process, and the corresponding relaxation times. The relaxation time $\tau_s$ of the sausage stage, which is the rate-limiting stage of the overall collapse process, follows an anti-Arrhenius behavior in the high-$T$ limit, and the Arrhenius behavior in the low-$T$ limit. Furthermore, the variation of $\tau_s$ with the solvent viscosity provides evidence of internal friction of the polymer, that modulates the overall collapse significantly, analogous to what is observed for relaxation rates of proteins during their folding. This suggests that the origin of internal friction in proteins is plausibly intrinsic to its polymeric backbone rather than other specifications., Comment: 14 pages, 10 captioned figures

This letter presents a measurement campaign carried out in an FR2 urban outdoor environment in a live experimental network deployment. The radio propagation analysis from a physical perspective at 26 GHz is essential for the correct deployment and dimensioning of future communication networks. This study performs a walk test emulating realistic conditions under which a pedestrian may be affected, summarizing and evaluating some of the typical effects encountered in a communications scenario such as penetration losses in a building, losses due to vegetation or the human body, or diffraction/scattering propagation around corners in street canyon-like environments. The operational conditions of the 5G network, the urban micro-cell scenario, and the use of omnidirectional antennas on the UE side validate the channel conditions from a perspective closer to a realistic scenario for a pedestrian within a FR2 live network., Comment: Published in IEEE Wireless Communications Letters

Aging in phase-ordering kinetics of the $d=3$ Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator $C_\text{ag}$ is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent $\lambda$. Previous work indicated that the lower Fisher-Huse bound of $\lambda\geq d/2 = 1.5$ is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for $\lambda$ we obtain at late times does \emph{not} disagree with this bound. By conducting systematic fits to the data of $C_\text{ag}$ using different ansaetze for the leading correction term, we find $\lambda = 1.58(14)$ with most of error attributed to the systematic uncertainty regarding the ansaetze. This result is in contrast to the recent report that below the roughening transition universality might be violated., Comment: 9 pages, 7 figures

Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs. Recently, deep graph networks have been employed as efficient, data-driven surrogate models for predicting properties of complex systems represented as graphs. These models rely on a local and iterative message passing strategy that should, in principle, capture long-range information without explicitly modeling the corresponding interactions. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. This work proposes a general framework that learns to mitigate these limitations: within a variational inference framework, we endow message passing architectures with the ability to freely adapt their depth and filter messages along the way. With theoretical and empirical arguments, we show that this simple strategy better captures long-range interactions, by surpassing the state of the art on five node and graph prediction datasets suited for this problem. Our approach consistently improves the performances of the baselines tested on these tasks. We complement the exposition with qualitative analyses and ablations to get a deeper understanding of the framework's inner workings.

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning (AL), which uses either biased or unbiased molecular dynamics (MD) simulations to generate candidate pools, aims to address this objective. Existing biased and unbiased MD simulations, however, are prone to miss either rare events or extrapolative regions -- areas of the configurational space where unreliable predictions are made. Simultaneously exploring both regions is necessary for developing uniformly accurate MLIPs. In this work, we demonstrate that MD simulations, when biased by the MLIP's energy uncertainty, effectively capture extrapolative regions and rare events without the need to know \textit{a priori} the system's transition temperatures and pressures. Exploiting automatic differentiation, we enhance bias-forces-driven MD simulations by introducing the concept of bias stress. We also employ calibrated ensemble-free uncertainties derived from sketched gradient features to yield MLIPs with similar or better accuracy than ensemble-based uncertainty methods at a lower computational cost. We use the proposed uncertainty-driven AL approach to develop MLIPs for two benchmark systems: alanine dipeptide and MIL-53(Al). Compared to MLIPs trained with conventional MD simulations, MLIPs trained with the proposed data-generation method more accurately represent the relevant configurational space for both atomic systems.

The performance of Hamiltonian Monte Carlo crucially depends on its parameters, in particular the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune these parameters based on a loss function which promotes the fast exploration of phase-space. For this, we make use of a fully-differentiable set-up and use backpropagation for optimization. An attention-like loss is defined which allows for the gradient driven learning of the distribution of integration steps. We also highlight the importance of jittering for a smooth loss-surface. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein common as a test-case for simulation methods. We find a good correspondence between our loss and the autocorrelation times, resulting in well-tuned parameters for Hamiltonian Monte Carlo.

One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent $\alpha = 1/2$ is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with $\alpha<1/2$ was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations of lattice sizes up to $L=2048$ employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law -- but surprisingly, at still later times domains even grow superdiffusively, i.e., with $\alpha > 1/2$. We argue that this new problem is possibly caused by sponge-like structures emerging at early times., Comment: 13 pages, 10 figures

We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising model with nonconserved order parameter and a Lennard-Jones system both in two dimensions. The measured runtimes support an average complexity $O(N\log N)$, where $N$ is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than $10^4$. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions.

We investigate the nonequilibrium dynamics following a quench to zero temperature of the non-conserved Ising model with power-law decaying long-range interactions $\propto 1/r^{d+\sigma}$ in $d=2$ spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent $\alpha$, the persistence exponent $\theta$, and the fractal dimension $d_f$. It is found that the growth exponent $\alpha\approx 3/4$ is independent of $\sigma$ and different from $\alpha=1/2$ as expected for nearest-neighbor models. In the large $\sigma$ regime of the tunable interactions only the fractal dimension $d_f$ of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponent $\theta$ this is a direct consequence of the different growth exponents $\alpha$ as can be understood from the relation $d-d_f=\theta/\alpha$; they just differ by the ratio of the growth exponents $\approx 3/2$. This relation has been proposed for annihilation processes and later numerically tested for the $d=2$ nearest-neighbor Ising model. We confirm this relation for all $\sigma$ studied, reinforcing its general validity.

Methods for accurate prediction of radio signal quality parameters are crucial for optimization of mobile networks, and a necessity for future autonomous driving solutions. The power-distance relation of current empirical models struggles with describing the specific local geo-statistics that influence signal quality parameters. The use of empirical models commonly results in an over- or under-estimation of the signal quality parameters and require additional calibration studies. In this paper, we present a novel model-aided deep learning approach for path loss prediction, which implicitly extracts radio propagation characteristics from top-view geographical images of the receiver location. In a comprehensive evaluation campaign, we apply the proposed method on an extensive real-world data set consisting of five different scenarios and more than 125.000 individual measurements. It is found that 1) the novel approach reduces the average prediction error by up to 53% in comparison to ray-tracing techniques, 2) A distance of 250-300 meters spanned by the images offer the necessary level of detail, 3) Predictions with a root-mean-squared error of approximately 6 dB is achieved across inherently different data sources.

Path-loss modelling in deep-indoor scenarios is a difficult task. On one hand, the theoretical formulae solely dependent on transmitter-receiver distance are too simple; on the other hand, discovering all significant factors affecting the loss of signal power in a given situation may often be infeasible. In this paper, we experimentally investigate the influence of deep-indoor features such as indoor depth, indoor distance and distance to the closest tunnel corridor and the effect on received power using NB-IoT. We describe a measurement campaign performed in a system of long underground tunnels, and we analyse linear regression models involving the engineered features. We show that the current empirical models for NB-IoT signal attenuation are inaccurate in a deep-indoor scenario. We observe that 1) indoor distance and penetration depth do not explain the signal attenuation well and increase the error of the prediction by 2-12 dB using existing models, and 2) a promising feature of average distance to the nearest corridor is identified., Comment: 6 pages, 6 figures, submitted to Globecom2020 conference, Selected Areas in Communications Symposium, Track on Internet of Things and Smart Connected Communities

Met-enkephalin, one of the smallest opiate peptides and an important neurotransmitter, is a widely used benchmarking problem in the field of molecular simulation. Through its range of possible low-temperature conformations separated by free-energy barriers it was previously found to be hard to thermalize using straight canonical molecular dynamics simulations. Here, we demonstrate how one can use the recently proposed population annealing molecular dynamics scheme to overcome these difficulties. We show how the use of multi-histogram reweighting allows one to accurately estimate the density of states of the system and hence derive estimates such as the potential energy as quasi continuous functions of temperature. We further investigate the free-energy surface as a function of end-to-end distance and radius-of-gyration and observe two distinct basins of attraction.

Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse in computer simulations. Primary focus of these approaches is to understand various dynamic scaling laws related to coarsening and aging during the collapse in space dimension $d=3$, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overview of those results, we also present new preliminary data for $d=2$., Comment: 18 pages, 14 figures

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with $\lambda=1.25$ in the effectively short-range regime, while for stronger long-range interactions the data are consistent with $\lambda=d/2=1$. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as sub-aging.

We study the equilibrium dynamics of a single polymer chain under good solvent condition. Special emphasis is laid on varying the drag force experienced by the chain while it moves. To this end we model the solvent in a mesoscopic manner by employing the Lowe-Andersen approach of dissipative particle dynamics which is known to reproduce hydrodynamic effects. Our approach captures the correct static behavior in equilibrium. Regarding the dynamics, we investigate the scaling of the self-diffusion coefficient $D$ with respect to the length of the polymer $N$, yielding results that are compatible with the Zimm scaling $D \sim N^{-3/5}$., Comment: Conference proceedings of the conference: Computer Simulations in Physics and beyond (CSP2018) submitted to Journal of Physics: Conference Series

We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions erform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

We present comparative results from simulations of a lattice and an off-lattice model of a homopolymer, in the context of kinetics of the collapse transition. Scaling laws related to the collapse time, cluster coarsening and aging behavior are compared. Although in both models the cluster growth is independent of temperature, the related exponents turn out to be different. Conversely, the aging and associated scaling properties are found to be universal, with the nonequilibrium autocorrelation exponent obeying a recently derived bound., Comment: 6 pages, 3 figures, conference; accepted for publication in J. Phys.: Conf. Ser

We present results for the nonequilibrium dynamics of collapse for a model flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds between the monomers. Results from our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a nonuniversal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a temperature independent growth, which can be described by a universal nonequilibrium finite-size scaling function with a non-universal metric factor. We also examine the related aging phenomenon, probed by a suitable two-time density-density autocorrelation function showing a simple power-law scaling with respect to the growing cluster size. Unlike the cluster-growth exponent $\alpha_c $, the nonequilibrium autocorrelation exponent $\lambda_C$ governing the aging during the collapse, however, is independent of the bond type and strictly follows the bounds proposed by two of us in Phys. Rev. E 93, 032506 (2016) at all temperatures., Comment: 14 pages, 12 figures, accepted for publication in Journal of Chemical Physics