arXiv subjects

Sergey Pozdnyakov

Publications and source records attributed to Sergey Pozdnyakov.

8 recordsLinked to original sources

arXiv2025

Mechanistic study of mixed lithium halides solid state electrolytes

Lithium halides with the general formula Li$_x$M$_y$X$_6$, where M indicates metal ions and X halide anions are very actively studied as solid-state electrolytes, because of relatively low cost, high stability and Li conductivity. The structure and properties of these halide-based solid electrolytes (HSE) can be tuned by alloying, e.g. using different halides and/or transition metals simultaneously. The large chemical space is difficult to sample by experiments, making simulations based on broadly applicable machine-learning interatomic potentials (MLIPs) a promising approach to elucidate structure-property relations, and facilitate the design of better-performing compositions. Here we focus on the Li$_3$YCl$_{6x}$Br$_{6(1-x)}$ system, for which reliable experimental data exists, and use the recently-developed PET-MAD universal MLIP to investigate the structure of the alloy, the interplay of crystalline lattice, volume and chemical composition, and its effect on Li conductivity. We find that the distribution of Cl and Br atoms is only weakly correlated, and that the primary effect of alloying is to modulate the lattice parameter -- although it can also trigger transition between different lattice symmetries. By comparing constant-volume and constant-pressure simulations, we disentangle the effect of lattice parameter and chemical composition on the conductivity, finding that the two effects compensate each other, reducing the overall dependency of conductivity on alloy composition. An extended study of the effect of metal substitution, enabled by the semi-quantitative accuracy of the universal model, shows that the effect of metal-site alloying is small, indicating that alloying can be used to optimize cost, or electrochemical stability, without major impact on bulk conductivity.

cond-mat.mtrl-sci↗

arXiv2025

Lookup multivariate Kolmogorov-Arnold Networks

High-dimensional linear mappings, or linear layers, dominate both the parameter count and the computational cost of most modern deep-learning models. We introduce a general-purpose drop-in replacement, lookup multivariate Kolmogorov-Arnold Networks (lmKANs), which deliver a substantially better trade-off between capacity and inference cost. Our construction expresses a general high-dimensional mapping through trainable low-dimensional multivariate functions. These functions can carry dozens or hundreds of trainable parameters each, and yet it takes only a few multiplications to compute them because they are implemented as spline lookup tables. Empirically, lmKANs reduce inference FLOPs by up to 6.0x while matching the flexibility of MLPs in general high-dimensional function approximation. In another feedforward fully connected benchmark, on the tabular-like dataset of randomly displaced methane configurations, lmKANs enable more than 10x higher H100 throughput at equal accuracy. Within frameworks of Convolutional Neural Networks, lmKAN-based CNNs cut inference FLOPs at matched accuracy by 1.6-2.1x and by 1.7x on the CIFAR-10 and ImageNet-1k datasets, respectively. Our code, including dedicated CUDA kernels, is available online at https://github.com/schwallergroup/lmkan.

cs.LG↗

arXiv2025

A universal machine learning model for the electronic density of states

In the last few years several ``universal'' interatomic potentials have appeared, using machine-learning approaches to predict energy and forces of atomic configurations with arbitrary composition and structure, with an accuracy often comparable with that of the electronic-structure calculations they are trained on. Here we demonstrate that these generally-applicable models can also be built to predict explicitly the electronic structure of materials and molecules. We focus on the electronic density of states (DOS), and develop PET-MAD-DOS, a rotationally unconstrained transformer model built on the Point Edge Transformer (PET) architecture, and trained on the Massive Atomistic Diversity (MAD) dataset. We demonstrate our model's predictive abilities on samples from diverse external datasets, showing also that the DOS can be further manipulated to obtain accurate band gap predictions. A fast evaluation of the DOS is especially useful in combination with molecular simulations probing matter in finite-temperature thermodynamic conditions. To assess the accuracy of PET-MAD-DOS in this context, we evaluate the ensemble-averaged DOS and the electronic heat capacity of three technologically relevant systems: lithium thiophosphate (LPS), gallium arsenide (GaAs), and a high entropy alloy (HEA). By comparing with bespoke models, trained exclusively on system-specific datasets, we show that our universal model achieves semi-quantitative agreement for all these tasks. Furthermore, we demonstrate that fine-tuning can be performed using a small fraction of the bespoke data, yielding models that are comparable to, and sometimes better than, fully-trained bespoke models.

physics.chem-ph↗

arXiv2025

PET-MAD, a lightweight universal interatomic potential for advanced materials modeling

Machine-learning interatomic potentials (MLIPs) have greatly extended the reach of atomic-scale simulations, offering the accuracy of first-principles calculations at a fraction of the cost. Leveraging large quantum mechanical databases and expressive architectures, recent ''universal'' models deliver qualitative accuracy across the periodic table but are often biased toward low-energy configurations. We introduce PET-MAD, a generally applicable MLIP trained on a dataset combining stable inorganic and organic solids, systematically modified to enhance atomic diversity. Using a moderate but highly-consistent level of electronic-structure theory, we assess PET-MAD's accuracy on established benchmarks and advanced simulations of six materials. Despite the small training set and lightweight architecture, PET-MAD is competitive with state-of-the-art MLIPs for inorganic solids, while also being reliable for molecules, organic materials, and surfaces. It is stable and fast, enabling the near-quantitative study of thermal and quantum mechanical fluctuations, functional properties, and phase transitions out of the box. It can be efficiently fine-tuned to deliver full quantum mechanical accuracy with a minimal number of targeted calculations.

cond-mat.mtrl-sci↗

arXiv2022

Fast general two- and three-body interatomic potential

We introduce a new class of machine learning interatomic potentials - fast General Two- and Three-body Potential (GTTP), which is as fast as conventional empirical potentials and require computational time that remains constant with increasing fitting flexibility. GTTP does not contain any assumptions about the functional form of two- and three-body interactions. These interactions can be modeled arbitrarily accurately, potentially by thousands of parameters not affecting resulting computational cost. Time complexity is O(1) per every considered pair or triple of atoms. The fitting procedure is reduced to simple linear regression on ab initio calculated energies and forces and leads to effective two- and three-body potential, reproducing quantum many-body interactions as accurately as possible. Our potential can be made continuously differentiable any number of times at the expense of increased computational time. We made a number of performance tests on one-, two- and three-component systems. The flexibility of the introduced approach makes the potential transferable in terms of size and type of atomic systems. We show that trained on randomly generated structures with just 8 atoms in the unit cell, it significantly outperforms common empirical interatomic potentials in the study of large systems, such as grain boundaries in polycrystalline materials.

physics.comp-ph↗

arXiv2022

Unified theory of atom-centered representations and message-passing machine-learning schemes

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, that are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), that are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes, that gather information on the relationship between neighboring atoms using "message-passing" ideas, cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provides a coherent foundation to systematize our understanding of both atom-centered and message-passing, invariant and equivariant machine-learning schemes.

stat.ML↗

arXiv2022

Optimal radial basis for density-based atomic representations

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations can be seen as an expansion of the symmetrized correlations of the atom density, and differ mainly by the choice of basis. Considerable effort has been dedicated to the optimization of the basis set, typically driven by heuristic considerations on the behavior of the regression target. Here we take a different, unsupervised viewpoint, aiming to determine the basis that encodes in the most compact way possible the structural information that is relevant for the dataset at hand. For each training dataset and number of basis functions, one can determine a unique basis that is optimal in this sense, and can be computed at no additional cost with respect to the primitive basis by approximating it with splines. We demonstrate that this construction yields representations that are accurate and computationally efficient, particularly when constructing representations that correspond to high-body order correlations. We present examples that involve both molecular and condensed-phase machine-learning models.

stat.ML↗

arXiv2020

Recursive evaluation and iterative contraction of $N$-body equivariant features

Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible $N$-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different orders (generalizations of $N$-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically-improvable, symmetry adapted representations for atomistic machine learning.

physics.chem-ph↗