arXiv subjects

Gabor Csanyi

Publications and source records attributed to Gabor Csanyi.

At least 19 recordsLinked to original sources

arXiv2026

How reproducible are first-principles simulations of liquid water?

Liquid water is fundamentally important, and its accurate computer simulation has been the driving force for myriad methodological developments. Ab initio molecular dynamics with forces obtained from density functional theory (DFT) is now a standard tool widely used by researchers. However, we reveal that previous studies of liquid water using the same widely-used density functional (revPBE-D3) exhibit significant discrepancies with one another, varying by over 20% in the diffusion coefficient and 10% in the density, raising fundamental questions about reproducibility. By combining modern long-range machine-learning interatomic potentials that enable robust statistical sampling with carefully converged DFT training data, we resolve these discrepancies, achieving consensus across six diverse community codes. Our predictions differ markedly from previous literature: we show that most previous results overestimate the density and underestimate the diffusion coefficient of revPBE-D3 water due to basis set incompleteness and pseudopotential inconsistencies, coupled with limitations in statistical sampling (in some cases). These benchmark values provide a reliable reference for validating current and future implementations of DFT-based ab initio molecular dynamics. Reaching agreement establishes confidence and credibility and serves as a prerequisite for the systematic assessment of new density functionals and numerical approximations.

physics.chem-ph↗

arXiv2025

Optimizing Data Distribution and Kernel Performance for Efficient Training of Chemistry Foundation Models: A Case Study with MACE

Chemistry Foundation Models (CFMs) that leverage Graph Neural Networks (GNNs) operating on 3D molecular graph structures are becoming indispensable tools for computational chemists and materials scientists. These models facilitate the understanding of matter and the discovery of new molecules and materials. In contrast to GNNs operating on a large homogeneous graphs, GNNs used by CFMs process a large number of geometric graphs of varying sizes, requiring different optimization strategies than those developed for large homogeneous GNNs. This paper presents optimizations for two critical phases of CFM training: data distribution and model training, targeting MACE - a state-of-the-art CFM. We address the challenge of load balancing in data distribution by formulating it as a multi-objective bin packing problem. We propose an iterative algorithm that provides a highly effective, fast, and practical solution, ensuring efficient data distribution. For the training phase, we identify symmetric tensor contraction as the key computational kernel in MACE and optimize this kernel to improve the overall performance. Our combined approach of balanced data distribution and kernel optimization significantly enhances the training process of MACE. Experimental results demonstrate a substantial speedup, reducing per-epoch execution time for training from 12 to 2 minutes on 740 GPUs with a 2.6M sample dataset.

cs.DC↗

arXiv2025

A practical guide to machine learning interatomic potentials -- Status and future

The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3-10+ years.

cond-mat.mtrl-sci↗

arXiv2025

Many-Body Coarse-Grained Molecular Dynamics with the Atomic Cluster Expansion

Molecular dynamics (MD) simulations provide detailed insight into atomic-scale mechanisms but are inherently restricted to small spatio-temporal scales. Coarse-grained molecular dynamics (CGMD) techniques allow simulations of much larger systems over extended timescales. In theory, these techniques can be quantitatively accurate, but common practice is to only target qualitatively correct behaviour of coarse-grained models. Recent advances in applying machine learning methodology in this setting are now being applied to create also quantitatively accurate CGMD models. We demonstrate how the Atomic Cluster Expansion parameterization (Drautz, 2019) can be used in this task to construct highly efficient, interpretable and accurate CGMD models. We focus in particular on exploring the role of many-body effects.

physics.comp-ph↗

arXiv2024

Computing solvation free energies of small molecules with experimental accuracy

Free energies play a central role in characterising the behaviour of chemical systems and are among the most important quantities that can be calculated by molecular dynamics simulations. Solvation free energies in various organic solvents, in particular, are well-studied physicochemical properties of drug-like molecules and are commonly used to assess and optimise the accuracy of nonbonded parameters in empirical forcefields, and also as a fast-to-compute surrogate of performance for protein-ligand binding free energy estimation. Machine learned potentials (MLPs) show great promise as more accurate alternatives to empirical forcefields, but are not readily decomposed into physically motivated functional forms, which has thus far rendered them incompatible with standard alchemical free energy methods that manipulate individual pairwise interaction terms. However, since the accuracy of free energy calculations is highly sensitive to the forcefield, this is a key area in which MLPs have the potential to address the shortcomings of empirical forcefields. In this work, we introduce an efficient alchemical free energy protocol that enables calculations of rigorous free energy differences in condensed phase systems modelled entirely by MLPs. Using a pretrained, transferrable, alchemically equipped MLP model, we demonstrate sub-chemical accuracy for the solvation free energies of a wide range of organic molecules.

physics.chem-ph↗

arXiv2023

Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Science

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems from amorphous carbon, universal materials modelling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimisation to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient, and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.

physics.chem-ph↗

arXiv2022

Ranking the information content of distance measures

Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of these features. Using the fewest features but still retaining sufficient information about the system is crucial in many statistical learning approaches, particularly when data are sparse. We introduce a statistical test that can assess the relative information retained when using two different distance measures, and determine if they are equivalent, independent, or if one is more informative than the other. This in turn allows finding the most informative distance measure out of a pool of candidates. The approach is applied to find the most relevant policy variables for controlling the Covid-19 epidemic and to find compact yet informative representations of atomic structures, but its potential applications are wide ranging in many branches of science.

stat.ML↗

arXiv2021

Atomic Cluster Expansion: Completeness, Efficiency and Stability

The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems. Our presentation extends the derivation by proposing a precomputation algorithm that yields immediate guarantees that a complete basis is obtained. We provide a fast recursive algorithm for efficient evaluation and illustrate its performance in numerical tests. Finally, we discuss generalisations and open challenges, particularly from a numerical stability perspective, around basis optimisation and parameter estimation, paving the way towards a comprehensive analysis of the convergence to a high-fidelity reference model.

math.NA↗

arXiv2020

Gaussian Process States: A data-driven representation of quantum many-body physics

We present a novel, non-parametric form for compactly representing entangled many-body quantum states, which we call a `Gaussian Process State'. In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way the non-local physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a `universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size. We develop two numerical approaches which can learn this form directly: a fragmentation approach, and direct variational optimization, and apply these schemes to the Fermionic Hubbard model. We find competitive or superior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.

cond-mat.str-el↗

arXiv2020

An Experimentally Driven Automated Machine Learned lnter-Atomic Potential for a Refractory Oxide

Understanding the structure and properties of refractory oxides are critical for high temperature applications. In this work, a combined experimental and simulation approach uses an automated closed loop via an active-learner, which is initialized by X-ray and neutron diffraction measurements, and sequentially improves a machine-learning model until the experimentally predetermined phase space is covered. A multi-phase potential is generated for a canonical example of the archetypal refractory oxide, HfO2, by drawing a minimum number of training configurations from room temperature to the liquid state at ~2900oC. The method significantly reduces model development time and human effort.

cond-mat.mtrl-sci↗

arXiv2019

Regularised Atomic Body-Ordered Permutation-Invariant Polynomials for the Construction of Interatomic Potentials

We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are constructed to preserve the symmetry of the potential energy function with respect to rotations and permutations. In contrast to kernel based and artificial neural network models, the explicit decomposition of the total energy as a sum of atomic body-ordered terms allows to keep the dimensionality of the fit reasonably low, up to just 10 for the 5-body terms. The explainability of the potential is aided by this decomposition, as the low body-order components can be studied and interpreted independently. Moreover, although polynomial basis functions are thought to extrapolate poorly, we show that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.

physics.comp-ph↗

arXiv2018

Machine learning a general purpose interatomic potential for silicon

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational cost and its scaling. Techniques based on machine learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations has remained a challenging goal. Here we present a Gaussian Approximation Potential for silicon that achieves this milestone, accurately reproducing density functional theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations that would be extremely expensive with a first principles electronic structure method, such as finite temperature phase boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential's accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material, and serves as a template for the development of such models in the future.

cond-mat.mtrl-sci↗

arXiv2018

Preconditioners for the geometry optimisation and saddle point search of molecular systems

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to construct a sparse preconditioner matrix. The construction requires only the computation of the gradient of the corresponding molecular mechanical terms that are already available in popular force field software packages. For molecular crystals, the preconditioner can be combined straightforwardly with the exponential preconditioner recently introduced for periodic systems. The efficiency is demonstrated on several systems using empirical, semiempirical and ab initio potential energy surfaces.

physics.chem-ph↗

arXiv2017

Machine Learning Unifies the Modelling of Materials and Molecules

Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model, based on a local description of chemical environments and Bayesian statistical learning, provides a unified framework to predict atomic-scale properties. It captures the quantum mechanical effects governing the complex surface reconstructions of silicon, predicts the stability of different classes of molecules with chemical accuracy, and distinguishes active and inactive protein ligands with more than 99% reliability. The universality and the systematic nature of our framework provides new insight into the potential energy surface of materials and molecules.

cond-mat.mtrl-sci↗

arXiv2017

Achieving DFT accuracy with a machine-learning interatomic potential: thermomechanics and defects in bcc ferromagnetic iron

We show that the Gaussian Approximation Potential machine learning framework can describe complex magnetic potential energy surfaces, taking ferromagnetic iron as a paradigmatic challenging case. The training database includes total energies, forces, and stresses obtained from density-functional theory in the generalized-gradient approximation, and comprises approximately 150,000 local atomic environments, ranging from pristine and defected bulk configurations to surfaces and generalized stacking faults with different crystallographic orientations. We find the structural, vibrational and thermodynamic properties of the GAP model to be in excellent agreement with those obtained directly from first-principles electronic-structure calculations. There is good transferability to quantities, such as Peierls energy barriers, which are determined to a large extent by atomic configurations that were not part of the training set. We observe the benefit and the need of using highly converged electronic-structure calculations to sample a target potential energy surface. The end result is a systematically improvable potential that can achieve the same accuracy of density-functional theory calculations, but at a fraction of the computational cost.

cond-mat.mtrl-sci↗

arXiv2016

A universal preconditioner for simulating condensed phase materials

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

cond-mat.mtrl-sci↗

arXiv2013

Machine learning for predictive condensed-phase simulation

We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chemistry, and predict energies and forces in molecular aggregates ranging from clusters to solid and liquid phases. The widely used electronic-structure methods based on density-functional theory (DFT) give poor accuracy for molecular materials like water, and we show how our techniques can be used to generate systematically improvable corrections to DFT. The resulting corrected DFT scheme gives remarkably accurate predictions for the relative energies of small water clusters and of different ice structures, and greatly improves the description of the structure and dynamics of liquid water.

cond-mat.mtrl-sci↗

arXiv2013

Nonsmooth geometry and collapse of flexible structures under smooth loads

While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.

math-ph↗