arXiv subjects

Anton Bochkarev

Publications and source records attributed to Anton Bochkarev.

14 recordsLinked to original sources

arXiv2026

Fast contracted Clebsch--Gordan tensor products for equivariant graph neural networks

We present an $\mathcal{O}(L^3)$ algorithm for evaluating contracted Clebsch--Gordan tensor products in $\mathrm{O}(3)$-equivariant machine learning potentials at fixed Canonical Polyadic (CP) rank. Mapping the angular integral to a structured Gauss--Legendre and Fourier tensor-product grid decouples the radial channel contractions from the angular transforms. The antisymmetric parity-odd Clebsch--Gordan channels, unreachable by the symmetric pointwise product on a scalar $S^2$ grid, are recovered through the surface-curl pairing $\hat r \cdot [\nabla_{S^2} A \times \nabla_{S^2} B]$, the spherical Poisson bracket, which supplies the $L=1$ angular momentum on the grid while preserving rotational equivariance. The construction extends to parity-aware equivariant message passing in atomic-cluster-expansion-style architectures and is verified by direct numerical quadrature. The full uncontracted Clebsch--Gordan tensor product remains subject to the $\mathcal{O}(L^4)$ output-size lower bound. A benchmark shows wall-clock scaling empirically as $L^2$ across the practical $l_{\max}$ range. For the on-site contraction this is pre-asymptotic, giving way to $L^3$ at large $l_{\max}$. For message passing it is structural and the runtime is memory-bandwidth bound on $L^2$-sized grid tensors.

physics.comp-ph↗

arXiv2026

AI-Driven Expansion and Application of the Alexandria Database

We present a novel multi-stage workflow for computational materials discovery that achieves a 99% success rate in identifying compounds within 100 meV/atom of thermodynamic stability, with a threefold improvement over previous approaches. By combining the Matra-Genoa generative model, Orb-v2 universal machine learning interatomic potential, and ALIGNN graph neural network for energy prediction, we generated 119 million candidate structures and added 1.3 million DFT-validated compounds to the ALEXANDRIA database, including 74 thousand new stable materials. The expanded ALEXANDRIA database now contains 5.8 million structures with 175 thousand compounds on the convex hull. Predicted structural disorder rates (37-43%) match experimental databases, unlike other recent AI-generated datasets. Analysis reveals fundamental patterns in space group distributions, coordination environments, and phase stability networks, including sub-linear scaling of convex hull connectivity. We release the complete dataset, including sAlex25 with 14 million out-of-equilibrium structures containing forces and stresses for training universal force fields. We demonstrate that fine-tuning a GRACE model on this data improves benchmark accuracy. All data, models, and workflows are freely available under Creative Commons licenses.

cond-mat.mtrl-sci↗

arXiv2026

Perspective: Towards sustainable exploration of chemical spaces with machine learning

Artificial intelligence is transforming molecular and materials science, but its growing computational and data demands raise critical sustainability challenges. In this Perspective, we examine resource considerations across the AI-driven discovery pipeline--from quantum-mechanical (QM) data generation and model training to automated, self-driving research workflows--building on discussions from the ``SusML workshop: Towards sustainable exploration of chemical spaces with machine learning'' held in Dresden, Germany. In this context, the availability of large quantum datasets has enabled rigorous benchmarking and rapid methodological progress, while also incurring substantial energy and infrastructure costs. We highlight emerging strategies to enhance efficiency, including general-purpose machine learning (ML) models, multi-fidelity approaches, model distillation, and active learning. Moreover, incorporating physics-based constraints within hierarchical workflows, where fast ML surrogates are applied broadly and high-accuracy QM methods are used selectively, can further optimize resource use without compromising reliability. Equally important is bridging the gap between idealized computational predictions and real-world conditions by accounting for synthesizability and multi-objective design criteria, which is essential for practical impact. Finally, we argue that sustainable progress will rely on open data and models, reusable workflows, and domain-specific AI systems that maximize scientific value per unit of computation, enabling efficient and responsible discovery of technological materials and therapeutics.

cs.LG↗

arXiv2026

Hydrogen uptake and hydride formation in Al$_x$CoCrFeNi high-entropy alloys: First-principles, universal-potential, and experimental study

Hydrogen uptake in complex multicomponent alloys, including high-entropy alloys (HEAs), governs both hydrogen storage capacity and resistance to hydrogen-induced degradation. We combine high-pressure experiments, density-functional theory (DFT), and a GRACE universal interatomic potential to investigate hydrogen absorption in Al$_{0.3}$CoCrFeNi and Al$_3$CoCrFeNi HEAs. In H$_2$ as a pressure-transmitting medium, the FCC Al$_{0.3}$CoCrFeNi alloy forms hydrides at ambient temperature above 3 GPa, whereas the Al-rich B2 Al$_3$CoCrFeNi alloy shows no evidence of hydride formation even upon heating at pressures up to 50 GPa. Experiments and calculations show that aluminum suppresses hydrogen uptake by increasing solution energies and destabilizing interstitial sites. The universal potential, employed in the calculations and pretrained on large DFT databases, closely reproduces DFT energetics and demonstrates transferability from the dilute limit to the hydride-forming regime. Simulations further disentangle the roles of local ordering, volume changes, composition, and crystal structure. Overall, our results indicate that hydrogen solubility in Al-containing HEAs is governed primarily by composition, with Al-driven B2 ordering as a strong secondary effect.

cond-mat.mtrl-sci↗

arXiv2026

Exploring the extremes: atomic basis for multi-elemental materials science under complex thermodynamic conditions

Modern materials science has historically been founded on combining restricted subsets of the periodic table, favoring high-purity, few-element systems. However, the demands of an emerging circular economy, together with the need to understand materials behavior under planetary and industrial extremes, increasingly require mastering Mendeleev materials - chemically and structurally complex systems that span large portions of the periodic table. In these regimes, current universal machine-learning interatomic potentials often fail, largely due to systematic gaps in traditional training datasets that heavily emphasize low-energy, near-equilibrium structures. We address this limitation by introducing a chemistry-agnostic, information-entropy-maximization protocol for data generation. By decoupling structural sampling from thermodynamic bias, our approach provides a robust physical prior for atomic interactions across the entire periodic table, including regimes far from equilibrium and under extreme conditions. Training a Graph Atomic Cluster Expansion (GRACE) model on the resulting statistically maximized entropy (SMAX) dataset yields markedly improved robustness across a range of stringent benchmarks. These include large-strain phase transformations in tin, defect evolution in tungsten-based alloys, and catalytic reaction barrier prediction. More broadly, our approach establishes a scalable and principled methodology for navigating the vast chemical and configurational space relevant to future materials design. It enables a paradigm of discovery by simulation in which unbiased sampling protocols autonomously resolve emergent structures in multi-elemental mixtures-such as systems containing the nine most abundant elements in the Earth's crust-without reliance on a priori chemical assumptions.

cond-mat.mtrl-sci↗

arXiv2026

Graph atomic cluster expansion for foundational machine learning interatomic potentials

Foundational machine learning interatomic potentials that can accurately and efficiently model a vast range of materials are critical for accelerating atomistic discovery. We introduce universal potentials based on the graph atomic cluster expansion (GRACE) framework, trained on several of the largest available materials datasets. Through comprehensive benchmarks, we demonstrate that the GRACE models establish a new Pareto front for accuracy versus efficiency among foundational interatomic potentials. We further showcase their exceptional versatility by adapting them to specialized tasks and simpler architectures via fine-tuning and knowledge distillation, achieving high accuracy while preventing catastrophic forgetting. This work establishes GRACE as a robust and adaptable foundation for the next generation of atomistic modeling, enabling high-fidelity simulations across the periodic table.

cond-mat.mtrl-sci↗

arXiv2025

Efficient local atomic cluster expansion for BaTiO$_3$ close to equilibrium

Barium titanate (BTO) is a representative perovskite oxide that undergoes three first-order ferroelectric phase transitions related to exceptional functional properties. In this work, we develop two atomic cluster expansion (ACE) models for BTO to reproduce fundamental properties of bulk as well as defective BTO phases. The two ACE models do not target full transferability but rather aim to examine the influence of implicit and explicit treatment of long-range Coulomb interactions. We demonstrate that both models describe equally well the temperature induced phase transitions as well as polarization switching due to applied electric field. Even though the parametrizations are based on a limited number of configurations that are mostly not far away from the equilibrium, the ACE models are able to capture also properties of important crystal defects, such as oxygen vacancies, stacking faults and domain walls. A systematic comparison shows that the phase transitions as well as the fundamental properties of the investigated defects can be described with similar accuracy with or without explicit treatment of charges and Coulomb interactions allowing for efficient short-range machine learning potentials.

cond-mat.mtrl-sci↗

arXiv2024

Charge-constrained Atomic Cluster Expansion

The atomic cluster expansion (ACE) efficiently parameterizes complex energy surfaces of pure elements and alloys. Due to the local nature of the many-body basis, ACE is inherently local or semilocal for graph ACE. Here, we employ descriptor-constrained density functional theory for parameterizing ACE with charge or other degrees of freedom, thereby transfering the variational property of the density functional to ACE. The descriptors can be of scalar, vectorial or tensorial nature. From the simplest case of scalar atomic descriptors we directly obtain charge-dependent ACE with long-range electrostatic interactions between variable charges. We observe that the variational properties of the charges greatly help in training, avoiding the need for charge-constrained DFT calculations.

cond-mat.mtrl-sci↗

arXiv2024

Graph Atomic Cluster Expansion for semilocal interactions beyond equivariant message passing

The Atomic Cluster Expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the Atomic Cluster Expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph Atomic Cluster Expansion for a number of small molecules, clusters and a general-purpose model for carbon. We further show that the graph Atomic Cluster Expansion scales linearly with number of neighbors and layer depth of the graph basis functions.

cond-mat.mtrl-sci↗

arXiv2023

Atomic cluster expansion for quantum-accurate large-scale simulations of carbon

We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parameterized from an exhaustive set of important carbon structures at extended volume and energy range, computed using density functional theory (DFT). Rigorous validation reveals that ACE predicts accurately a broad range of properties of both crystalline and amorphous carbon phases while being several orders of magnitude more computationally efficient than available machine learning models. We demonstrate the predictive power of ACE on three distinct applications, brittle crack propagation in diamond, evolution of amorphous carbon structures at different densities and quench rates and nucleation and growth of fullerene clusters under high pressure and temperature conditions.

cond-mat.mtrl-sci↗

arXiv2023

Non-collinear Magnetic Atomic Cluster Expansion for Iron

The Atomic Cluster Expansion (ACE) provides a formally complete basis for the local atomic environment. ACE is not limited to representing energies as a function of atomic positions and chemical species, but can be generalized to vectorial or tensorial properties and to incorporate further degrees of freedom (DOF). This is crucial for magnetic materials with potential energy surfaces that depend on atomic positions and atomic magnetic moments simultaneously. In this work, we employ the ACE formalism to develop a non-collinear magnetic ACE parametrization for the prototypical magnetic element Fe. The model is trained on a broad range of collinear and non-collinear magnetic structures calculated using spin density functional theory. We demonstrate that the non-collinear magnetic ACE is able to reproduce not only ground state properties of various magnetic phases of Fe but also the magnetic and lattice excitations that are essential for a correct description of the finite temperature behavior and properties of crystal defects.

cond-mat.mtrl-sci↗

arXiv2022

Active learning strategies for atomic cluster expansion models

The atomic cluster expansion (ACE) was proposed recently as a new class of data-driven interatomic potentials with a formally complete basis set. Since the development of any interatomic potential requires a careful selection of training data and thorough validation, an automation of the construction of the training dataset as well as an indication of a model's uncertainty are highly desirable. In this work, we compare the performance of two approaches for uncertainty indication of ACE models based on the D-optimality criterion and ensemble learning. While both approaches show comparable predictions, the extrapolation grade based on the D-optimality (MaxVol algorithm) is more computationally efficient. In addition, the extrapolation grade indicator enables an active exploration of new structures, opening the way to the automated discovery of rare-event configurations. We demonstrate that active learning is also applicable to explore local atomic environments from large-scale MD simulations.

cond-mat.mtrl-sci↗

arXiv2022

Multilayer atomic cluster expansion for semi-local interactions

Traditionally, interatomic potentials assume local bond formation supplemented by long-range electrostatic interactions when necessary. This ignores intermediate range multi-atom interactions that arise from the relaxation of the electronic structure. Here, we present the multilayer atomic cluster expansion (ml-ACE) that includes collective, semi-local multi-atom interactions naturally within its remit. We demonstrate that ml-ACE significantly improves fit accuracy compared to a local expansion on selected examples and provide physical intuition to understand this improvement.

cond-mat.mtrl-sci↗

arXiv2021

Performant implementation of the atomic cluster expansion (PACE): Application to copper and silicon

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code \verb+PACE+ that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in \verb+PACE+ shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

cond-mat.mtrl-sci↗