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Machine learning interatomic potentials (MLIPs) have become a workhorse of modern atomistic simulations, and recently published universal MLIPs, pre-trained on large datasets, have demonstrated remarkable accuracy and generalizability. However, the computational cost of MLIPs limits their applicability to chemically disordered systems requiring large simulation cells or to sample-intensive statistical methods. Here, we report the use of continuous and differentiable alchemical degrees of freedom in atomistic materials simulations, exploiting the fact that graph neural network MLIPs represent discrete elements as real-valued tensors. The proposed method introduces alchemical atoms with corresponding weights into the input graph, alongside modifications to the message-passing and readout mechanisms of MLIPs, and allows smooth interpolation between the compositional states of materials. The end-to-end differentiability of MLIPs enables efficient calculation of the gradient of energy with respect to the compositional weights. Leveraging these gradients, we propose methodologies for optimizing the composition of solid solutions towards target macroscopic properties and conducting alchemical free energy simulations to quantify the free energy of vacancy formation and composition changes. The approach offers an avenue for extending the capabilities of universal MLIPs in the modeling of compositional disorder and characterizing the phase stabilities of complex materials systems.

Generating a data set that is representative of the accessible configuration space of a molecular system is crucial for the robustness of machine learned interatomic potentials (MLIP). However, the complexity of molecular systems, characterized by intricate potential energy surfaces (PESs) with numerous local minima and energy barriers, presents a significant challenge. Traditional methods of data generation, such as random sampling or exhaustive exploration, are either intractable or may not capture rare, but highly informative configurations. In this study, we propose a method that leverages uncertainty as the collective variable (CV) to guide the acquisition of chemically-relevant data points, focusing on regions of the configuration space where ML model predictions are most uncertain. This approach employs a Gaussian Mixture Model-based uncertainty metric from a single model as the CV for biased molecular dynamics simulations. The effectiveness of our approach in overcoming energy barriers and exploring unseen energy minima, thereby enhancing the data set in an active learning framework, is demonstrated on the alanine dipeptide benchmark system., Comment: 13 pages, 4 figures, 10 pages of Supplementary Information

In molecular dynamics simulations, rare events, such as protein folding, are typically studied using enhanced sampling techniques, most of which are based on the definition of a collective variable (CV) along which acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. This new data can be used to improve the accuracy of classifier-based methods. Alternatively, a regression-based learning scheme for CV models can be adopted by leveraging the interpolation progress parameter.

The Speech Wikimedia Dataset is a publicly available compilation of audio with transcriptions extracted from Wikimedia Commons. It includes 1780 hours (195 GB) of CC-BY-SA licensed transcribed speech from a diverse set of scenarios and speakers, in 77 different languages. Each audio file has one or more transcriptions in different languages, making this dataset suitable for training speech recognition, speech translation, and machine translation models., Comment: Data-Centric Machine Learning Workshop at the International Machine Learning Conference 2023 (ICML)

The reactivity of silicates in an aqueous solution is relevant to various chemistries ranging from silicate minerals in geology, to the C-S-H phase in cement, nanoporous zeolite catalysts, or highly porous precipitated silica. While simulations of chemical reactions can provide insight at the molecular level, balancing accuracy and scale in reactive simulations in the condensed phase is a challenge. Here, we demonstrate how a machine-learning reactive interatomic potential can accurately capture silicate-water reactivity. The model was trained on a new dataset comprising 400,000 energies and forces of molecular clusters at the $\omega$-B97XD def2-TVZP level. To ensure the robustness of the model, we introduce a new and general active learning strategy based on the attribution of the model uncertainty, that automatically isolates uncertain regions of bulk simulations to be calculated as small-sized clusters. Our trained potential is found to reproduce static and dynamic properties of liquid water and solid crystalline silicates, despite having been trained exclusively on cluster data. Furthermore, we utilize enhanced sampling simulations to recover the self-ionization reactivity of water accurately, and the acidity of silicate oligomers, and lastly study the silicate dimerization reaction in a water solution at neutral conditions and find that the reaction occurs through a flanking mechanism., Comment: 26 pages, 4 figures, 1 supplementary figure

Green hydrogen production is crucial for a sustainable future, but current catalysts for the oxygen evolution reaction (OER) suffer from slow kinetics, despite many efforts to produce optimal designs, particularly through the calculation of descriptors for activity. In this study, we develop a dataset of density functional theory calculations of bulk and surface perovskite oxides, and adsorption energies of OER intermediates, which includes compositions up to quaternary and facets up to (555). We demonstrate that per-site properties of perovskite oxides such as Bader charge or band center can be tuned through element substitution and faceting, and develop a machine learning model that accurately predicts these properties directly from the local chemical environment. We leverage these per-site properties to identify promising perovskites with high theoretical OER activity. The identified design principles and promising new materials provide a roadmap for closing the gap between current artificial catalysts and biological enzymes.

Autonomous or self-driving networks are expected to provide a solution to the myriad of extremely demanding new applications in the Future Internet. The key to handle complexity is to perform tasks like network optimization and failure recovery with minimal human supervision. For this purpose, the community relies on the development of new Machine Learning (ML) models and techniques. However, ML can only be as good as the data it is fitted with. Datasets provided to the community as benchmarks for research purposes, which have a relevant impact in research findings and directions, are often assumed to be of good quality by default. In this paper, we show that relatively minor modifications on the same benchmark dataset (UGR'16, a flow-based real-traffic dataset for anomaly detection) cause significantly more impact on model performance than the specific ML technique considered. To understand this finding, we contribute a methodology to investigate the root causes for those differences, and to assess the quality of the data labelling. Our findings illustrate the need to devote more attention into (automatic) data quality assessment and optimization techniques in the context of autonomous networks.

Cu-exchanged zeolites rely on mobile solvated Cu+ cations for their catalytic activity, but the role of framework composition on transport is not fully understood. Ab initio molecular dynamics simulations can provide quantitative atomistic insight but are too computationally expensive to explore large length- and time-scales or diverse compositions. We report a machine-learning interatomic potential that accurately reproduces ab initio results and effectively generalizes to allow multi-nanosecond simulations of large supercells and diverse chemical compositions. Biased and unbiased simulations of [Cu(NH3)2]+ mobility show that aluminum pairing in eight-membered rings accelerates local hopping, and demonstrate that increased NH3 concentration enhances long-range diffusion. The probability of finding two [Cu(NH3)2]+ complexes in the same cage - key for SCR-NOx reaction - increases with Cu content and Al content, but does not correlate with the long-range mobility of Cu+. Supporting experimental evidence was obtained from reactivity tests of Cu-CHA catalysts with controlled chemical composition.

Understanding material surfaces and interfaces is vital in applications like catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can in principle predict the structure of material surfaces as a function of thermodynamic variables. However, accurate energy simulations are prohibitive when coupled to the vast phase space that must be statistically sampled. Here, we present a bi-faceted computational loop to predict surface phase diagrams of multi-component materials that accelerates both the energy scoring and statistical sampling methods. Fast, scalable, and data-efficient machine learning interatomic potentials are trained on high-throughput density-functional theory calculations through closed-loop active learning. Markov-chain Monte Carlo sampling in the semi-grand canonical ensemble is enabled by using virtual surface sites. The predicted surfaces for GaN(0001), Si(111), and SrTiO3(001) are in agreement with past work and suggest that the proposed strategy can model complex material surfaces and discover previously unreported surface terminations., Comment: 30 pages main, 15 figures/tables, 5 pages supplementary

Neural networks (NNs) often assign high confidence to their predictions, even for points far out-of-distribution, making uncertainty quantification (UQ) a challenge. When they are employed to model interatomic potentials in materials systems, this problem leads to unphysical structures that disrupt simulations, or to biased statistics and dynamics that do not reflect the true physics. Differentiable UQ techniques can find new informative data and drive active learning loops for robust potentials. However, a variety of UQ techniques, including newly developed ones, exist for atomistic simulations and there are no clear guidelines for which are most effective or suitable for a given case. In this work, we examine multiple UQ schemes for improving the robustness of NN interatomic potentials (NNIPs) through active learning. In particular, we compare incumbent ensemble-based methods against strategies that use single, deterministic NNs: mean-variance estimation, deep evidential regression, and Gaussian mixture models. We explore three datasets ranging from in-domain interpolative learning to more extrapolative out-of-domain generalization challenges: rMD17, ammonia inversion, and bulk silica glass. Performance is measured across multiple metrics relating model error to uncertainty. Our experiments show that none of the methods consistently outperformed each other across the various metrics. Ensembling remained better at generalization and for NNIP robustness; MVE only proved effective for in-domain interpolation, while GMM was better out-of-domain; and evidential regression, despite its promise, was not the preferable alternative in any of the cases. More broadly, cost-effective, single deterministic models cannot yet consistently match or outperform ensembling for uncertainty quantification in NNIPs., Comment: 27 pages, 4 figures, Supporting Information (22 pages)

The structural tunability and compositional diversity of multicomponent perovskite oxides have enabled their various applications, including catalysis and electronics. The cation ordering in these oxides, ranging from disordered (i.e., high-entropy) to ordered (e.g., rocksalt), profoundly influences their properties. While computational design tools can typically predict properties associated with a particular ordering, inferring which ordering -- if any -- will be observed in synthesized oxides remains challenging. Here, we leveraged first-principles simulations and machine learning to develop data-driven, physics-informed descriptors of experimental ordering in multicomponent perovskites and compared them with traditional physicochemical descriptors, e.g., ionic radii and oxidation states. The fitted low-dimensional classification models correctly rank up to 93% of compositions in an experimental dataset of 190 perovskites between cation-ordered and disordered, offering a rigorous benchmark between theory and experiments. Furthermore, these descriptors accelerate high-throughput virtual screening of multicomponent oxides by predicting their dominant ordering to avoid costly, exhaustive simulations of cation arrangements.

The description of chemical processes at the molecular level is often facilitated by use of reaction coordinates, or collective variables (CVs). The CV measures the progress of the reaction and allows the construction of profiles that track the evolution of a specific property as the reaction progresses. Whereas CVs are routinely used, especially alongside enhanced sampling techniques, links between profiles and thermodynamic state functions and reaction rate constants are not rigorously exploited. Here, we report a unified treatment of such reaction profiles. Tractable expressions are derived for the free-energy, internal-energy, and entropy profiles as functions of only the CV.We demonstrate the ability of this treatment to extract quantitative insight from the entropy and internal-energy profiles of various real-world physicochemical processes, including intramolecular organic reactions, ionic transport in superionic electrolytes, and molecular transport in nanoporous materials., Comment: 24 pages, 5 figures, 3 tables

Afterpulsing is a factor limiting the distance over which discrete-variable quantum key distribution systems are secure, and a common feature in single-photon detectors. The relevance of this phenomenon stems from its stochastic, self-interacting nature and the fact that its rate rises with the number of avalanche events, which increases the quantum bit error rate. Here we introduce an effective analytic model, including dead-time and afterpulsing corrections, where afterpulsing correction depends on dead-time value. This model is useful to evaluate the performance of prepare and measure quantum key distribution protocols (standard and decoy versions) that use gated single photon detectors. The model provides an expression to numerically optimize the secret key rate over the full distance range for secure communication, enabling in this way the calculation of quantum bit error rate and secure key rate. In the conventional procedure, the dead-time value is fixed regardless of distance, limiting the distance range of the channel due to remaining afterpulsing effects, which are more relevant at higher operating frequencies. Here we demonstrate that optimizing the dead-time values increases the distance range of the channel to share secret keys., Comment: 13 pages, 9 figures

Deep generative models have emerged as an exciting avenue for inverse molecular design, with progress coming from the interplay between training algorithms and molecular representations. One of the key challenges in their applicability to materials science and chemistry has been the lack of access to sizeable training datasets with property labels. Published patents contain the first disclosure of new materials prior to their publication in journals, and are a vast source of scientific knowledge that has remained relatively untapped in the field of data-driven molecular design. Because patents are filed seeking to protect specific uses, molecules in patents can be considered to be weakly labeled into application classes. Furthermore, patents published by the US Patent and Trademark Office (USPTO) are downloadable and have machine-readable text and molecular structures. In this work, we train domain-specific generative models using patent data sources by developing an automated pipeline to go from USPTO patent digital files to the generation of novel candidates with minimal human intervention. We test the approach on two in-class extracted datasets, one in organic electronics and another in tyrosine kinase inhibitors. We then evaluate the ability of generative models trained on these in-class datasets on two categories of tasks (distribution learning and property optimization), identify strengths and limitations, and suggest possible explanations and remedies that could be used to overcome these in practice., Comment: Digital Discovery (2023)

Coarse-graining (CG) accelerates molecular simulations of protein dynamics by simulating sets of atoms as singular beads. Backmapping is the opposite operation of bringing lost atomistic details back from the CG representation. While machine learning (ML) has produced accurate and efficient CG simulations of proteins, fast and reliable backmapping remains a challenge. Rule-based methods produce poor all-atom geometries, needing computationally costly refinement through additional simulations. Recently proposed ML approaches outperform traditional baselines but are not transferable between proteins and sometimes generate unphysical atom placements with steric clashes and implausible torsion angles. This work addresses both issues to build a fast, transferable, and reliable generative backmapping tool for CG protein representations. We achieve generalization and reliability through a combined set of innovations: representation based on internal coordinates; an equivariant encoder/prior; a custom loss function that helps ensure local structure, global structure, and physical constraints; and expert curation of high-quality out-of-equilibrium protein data for training. Our results pave the way for out-of-the-box backmapping of coarse-grained simulations for arbitrary proteins., Comment: 18 pages

Light-activated drugs are a promising way to localize biological activity and minimize side effects. However, their development is complicated by the numerous photophysical and biological properties that must be simultaneously optimized. To accelerate the design of photoactive drugs, we describe a procedure that combines ligand-protein docking with chemical property prediction based on machine learning (ML). We apply this procedure to 58 proteins and 9,000 photo-drug candidates based on azobenzene cis-trans isomerism. We find that most proteins display a preference for trans isomers over cis, and that the binding affinities of nominally active/inactive pairs are in fact highly correlated. These findings have significant value for photopharmacology research, and reinforce the need for virtual screening to identify compounds with rare desirable properties. Further, we combine our procedure with quantum chemical validation to identify promising candidates for the photoactive inhibition of PARP1, an enzyme that is over-expressed in cancer cells. The top compounds are predicted to have long-lived active forms, differential bioactivity, and absorption in the near-infrared therapeutic window.

High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such relations for design. However, to build these connections, materials data must be translated into a numerical form, called a representation, that can be processed by a machine learning model. Datasets in materials science vary in format (ranging from images to spectra), size, and fidelity. Predictive models vary in scope and property of interests. Here, we review context-dependent strategies for constructing representations that enable the use of materials as inputs or outputs of machine learning models. Furthermore, we discuss how modern ML techniques can learn representations from data and transfer chemical and physical information between tasks. Finally, we outline high-impact questions that have not been fully resolved and thus, require further investigation., Comment: 20 pages, 5 figures, To Appear in Annual Review of Materials Research 53

Simulating rare events, such as the transformation of a reactant into a product in a chemical reaction typically requires enhanced sampling techniques that rely on heuristically chosen collective variables (CVs). We propose using differentiable simulations (DiffSim) for the discovery and enhanced sampling of chemical transformations without a need to resort to preselected CVs, using only a distance metric. Reaction path discovery and estimation of the biasing potential that enhances the sampling are merged into a single end-to-end problem that is solved by path-integral optimization. This is achieved by introducing multiple improvements over standard DiffSim such as partial backpropagation and graph mini-batching making DiffSim training stable and efficient. The potential of DiffSim is demonstrated in the successful discovery of transition paths for the Muller-Brown model potential as well as a benchmark chemical system - alanine dipeptide.

Li$_{10}$Ge(PS$_6$)$_2$ (LGPS) is a highly concentrated solid electrolyte, in which Coulombic repulsion between neighboring cations is hypothesized as the underlying reason for concerted ion hopping, a mechanism common among superionic conductors such as Li$_7$La$_3$Zr$_2$O$_{12}$ (LLZO) and Li$_{1.3}$Al$_{0.3}$Ti$_{1.7}$(PO$_4$)$_3$ (LATP). While first principles simulations using molecular dynamics (MD) provide insight into the Li$^+$ transport mechanism, historically, there has been a gap in the temperature ranges studied in simulations and experiments. Here, we used a neural network (NN) potential trained on density functional theory (DFT) simulations, to run up to 40-nanosecond long MD simulations at DFT-like accuracy to characterize the ion conduction mechanisms across a range of temperatures that includes previous simulations and experimental studies. We have confirmed a Li$^+$ sublattice phase transition in LGPS around 400 K, below which the \textit{ab}-plane diffusivity $D^*_{ab}$ is drastically reduced. Concomitant with the sublattice phase transition near 400 K, there is less cation-cation (cross) correlation, as characterized by Haven ratios closer to 1, and the vibrations in the system are more harmonic at lower temperature. Intuitively, at high temperature, the collection of vibrational modes may be sufficient to drive concerted ion hops. However, near room temperature, the vibrational modes available may be insufficient to overcome electrostatic repulsion, thus resulting in less correlated ion motion and comparatively slower ion conduction. Such phenomena of a sublattice phase transition, below which concerted hopping plays a less significant role, may be extended to other highly concentrated solid electrolytes such as LLZO and LATP.

Molecular dynamics (MD) simulation techniques are widely used for various natural science applications. Increasingly, machine learning (ML) force field (FF) models begin to replace ab-initio simulations by predicting forces directly from atomic structures. Despite significant progress in this area, such techniques are primarily benchmarked by their force/energy prediction errors, even though the practical use case would be to produce realistic MD trajectories. We aim to fill this gap by introducing a novel benchmark suite for learned MD simulation. We curate representative MD systems, including water, organic molecules, a peptide, and materials, and design evaluation metrics corresponding to the scientific objectives of respective systems. We benchmark a collection of state-of-the-art (SOTA) ML FF models and illustrate, in particular, how the commonly benchmarked force accuracy is not well aligned with relevant simulation metrics. We demonstrate when and how selected SOTA methods fail, along with offering directions for further improvement. Specifically, we identify stability as a key metric for ML models to improve. Our benchmark suite comes with a comprehensive open-source codebase for training and simulation with ML FFs to facilitate future work., Comment: 31 pages, 18 figures

Learning pair interactions from experimental or simulation data is of great interest for molecular simulations. We propose a general stochastic method for learning pair interactions from data using differentiable simulations (DiffSim). DiffSim defines a loss function based on structural observables, such as the radial distribution function, through molecular dynamics (MD) simulations. The interaction potentials are then learned directly by stochastic gradient descent, using backpropagation to calculate the gradient of the structural loss metric with respect to the interaction potential through the MD simulation. This gradient-based method is flexible and can be configured to simulate and optimize multiple systems simultaneously. For example, it is possible to simultaneously learn potentials for different temperatures or for different compositions. We demonstrate the approach by recovering simple pair potentials, such as Lennard-Jones systems, from radial distribution functions. We find that DiffSim can be used to probe a wider functional space of pair potentials compared to traditional methods like Iterative Boltzmann Inversion. We show that our methods can be used to simultaneously fit potentials for simulations at different compositions and temperatures to improve the transferability of the learned potentials., Comment: 12 pages, 10 figures

Historically, materials informatics has relied on human-designed descriptors of materials structures. In recent years, graph neural networks (GNNs) have been proposed for learning representations of crystal structures from data end-to-end producing vectorial embeddings that are optimized for downstream prediction tasks. However, a systematic scheme is lacking to analyze and understand the limits of GNNs for capturing crystal structures. In this work, we propose to use human-designed descriptors as a bank of human knowledge to test whether black-box GNNs can capture the knowledge of crystal structures. We find that current state-of-the-art GNNs cannot capture the periodicity of crystal structures well, and we analyze the limitations of the GNN models that result in this failure from three aspects: local expressive power, long-range information, and readout function. We propose an initial solution, hybridizing descriptors with GNNs, to improve the prediction of GNNs for materials properties, especially phonon internal energy and heat capacity with 90% lower errors, and we analyze the mechanisms for the improved prediction. All the analysis can be extended easily to other deep representation learning models, human-designed descriptors, and systems such as molecules and amorphous materials.

Molecular photoswitches are the foundation of light-activated drugs. A key photoswitch is azobenzene, which exhibits trans-cis isomerism in response to light. The thermal half-life of the cis isomer is of crucial importance, since it controls the duration of the light-induced biological effect. Here we introduce a computational tool for predicting the thermal half-lives of azobenzene derivatives. Our automated approach uses a fast and accurate machine learning potential trained on quantum chemistry data. Building on well-established earlier evidence, we argue that thermal isomerization proceeds through rotation mediated by intersystem crossing, and incorporate this mechanism into our automated workflow. We use our approach to predict the thermal half-lives of 19,000 azobenzene derivatives. We explore trends and tradeoffs between barriers and absorption wavelengths, and open-source our data and software to accelerate research in photopharmacology.

Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) that discriminates between R and P, one can define a free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. The FEP is not a true free energy, however, it is common to treat the FEP as the free-energy analog of the minimum energy path on the PES and to take the activation free energy, $\Delta F^\ddagger_\mathrm{RP}$, as the difference between the maximum of the FEP at the transition state and the minimum at R. We show that this approximation can result in large errors. Since the FEP depends on the CV, it is therefore not unique, and different, discriminating CVs can yield different activation free energies for the same reaction. We derive an exact expression for the activation free energy that avoids this ambiguity with respect to the choice of CV. We find $\Delta F^\ddagger_\mathrm{RP}$ to be a combination of the probability of the system being in the reactant state, the probability density at the transition state surface, and the thermal de~Broglie wavelength associated with the transition from R to P. We then evaluate the activation free energies based on our formalism for simple analytic models and realistic chemical systems. The analytic models show that the widespread FEP-based approximation applies only at low temperatures for CVs for which the effective mass of the associated pseudo-particle is small. Most chemical reactions of practical interest involve polyatomic molecules with complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV, typically through heuristics. We study the influence of the choice of CV and find that, while the reaction free energy is largely unaffected, $\Delta F^\ddagger_\mathrm{RP}$ is quite sensitive., Comment: 19 pages, 11 figures

We address the problem of defending predictive models, such as machine learning classifiers (Defender models), against membership inference attacks, in both the black-box and white-box setting, when the trainer and the trained model are publicly released. The Defender aims at optimizing a dual objective: utility and privacy. Both utility and privacy are evaluated with an external apparatus including an Attacker and an Evaluator. On one hand, Reserved data, distributed similarly to the Defender training data, is used to evaluate Utility; on the other hand, Reserved data, mixed with Defender training data, is used to evaluate membership inference attack robustness. In both cases classification accuracy or error rate are used as the metric: Utility is evaluated with the classification accuracy of the Defender model; Privacy is evaluated with the membership prediction error of a so-called "Leave-Two-Unlabeled" LTU Attacker, having access to all of the Defender and Reserved data, except for the membership label of one sample from each. We prove that, under certain conditions, even a "na\"ive" LTU Attacker can achieve lower bounds on privacy loss with simple attack strategies, leading to concrete necessary conditions to protect privacy, including: preventing over-fitting and adding some amount of randomness. However, we also show that such a na\"ive LTU Attacker can fail to attack the privacy of models known to be vulnerable in the literature, demonstrating that knowledge must be complemented with strong attack strategies to turn the LTU Attacker into a powerful means of evaluating privacy. Our experiments on the QMNIST and CIFAR-10 datasets validate our theoretical results and confirm the roles of over-fitting prevention and randomness in the algorithms to protect against privacy attacks., Comment: 10 pages, 4 figures, accepted for presentation at the Third AAAI Workshop on Privacy-Preserving Artificial Intelligence (PPAI-22), February 2022

Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes accurate backmapping, i.e., restoring fine-grained (FG) coordinates from CG coordinates, a long-standing challenge. Inspired by the recent progress in generative models and equivariant networks, we propose a novel model that rigorously embeds the vital probabilistic nature and geometric consistency requirements of the backmapping transformation. Our model encodes the FG uncertainties into an invariant latent space and decodes them back to FG geometries via equivariant convolutions. To standardize the evaluation of this domain, we provide three comprehensive benchmarks based on molecular dynamics trajectories. Experiments show that our approach always recovers more realistic structures and outperforms existing data-driven methods with a significant margin., Comment: 23 pages, 11 figures

Analyzing the atomic structure of glassy materials is a tremendous challenge both experimentally and computationally, and the lack of direct, detailed insights into glass structure hinders our ability to navigate structure-property relationships. For instance, the structural origin of the density anomaly in silica glasses - the negative thermal expansion coefficient - is still poorly understood. Simulations based on molecular dynamics (MD) produce atomically resolved structures, but quantifying the role of disorder in the density anomaly is challenging. Here, we propose to use a a graph-theoretical approach to assess topological differences between disordered structural arrangements from MD trajectories of silica glasses. A graph similarity metric quantifies the similarity between the covalent networks and can characterize the nature of the disordered solid, by comparing to reference crystalline solids, or with glasses in different thermodynamic states . This approach involves casting all-atom glass configurations as networks, and subsequently applying a graph-similarity metric (D-measure). Calculated D-measure values are then taken as the topological distances between two configurations. By measuring the topological distances of silica glass configurations across a range of temperatures, distinct structural features could be observed at temperatures higher than the fictive temperature. In addition, we compared topological distances between local atomic environments in the glass and crystalline silica phases. This approach suggests that more coesite-like and quartz-like local structures emerge in silica glasses when the density is at a minimum during the heating process., Comment: 12 pages, 7 figures, supporting information