Thomas D. Swinburne

Previous density functional theory (DFT) calculations for random solid solution (RSS) CoCrNi predict negative intrinsic stacking-fault energy (ISFE) at 0 K, contrary to experimental observations of finite stacking-fault widths. Two explanations have been proposed: finite-temperature stabilization of the RSS state, suggested by harmonic approximations showing increasing ISFE with temperature, and local chemical order (LCO), which shifts the ISFE to positive values at 0 K. Here, we compute temperature-dependent generalized stacking-fault free energies for RSS and LCO CoCrNi using a near-quantum-accuracy machine learning interatomic potential and the fully anharmonic projected average force integrator. Unlike harmonic approximations, our anharmonic calculations show that the RSS ISFE decreases with temperature and remains negative, indicating that RSS stacking faults are not thermally stabilized at elevated temperatures. By contrast, LCO maintains positive ISFE over 0-1000 K. Molecular dynamics simulations further confirm unbounded dislocation dissociation in RSS CoCrNi but finite stacking-fault widths in the LCO state.

Previous density functional theory (DFT) calculations for random solid solution (RSS) CoCrNi predict negative intrinsic stacking-fault energy (ISFE) at 0 K, contrary to experimental observations of finite stacking-fault widths. Two explanations have been proposed: finite-temperature stabilization of the RSS state, suggested by harmonic approximations showing increasing ISFE with temperature, and local chemical order (LCO), which shifts the ISFE to positive values at 0 K. Here, we compute temperature-dependent generalized stacking-fault free energies for RSS and LCO CoCrNi using a near-quantum-accuracy machine learning interatomic potential and the fully anharmonic projected average force integrator. Unlike harmonic approximations, our anharmonic calculations show that the RSS ISFE decreases with temperature and remains negative, indicating that RSS stacking faults are not thermally stabilized at elevated temperatures. By contrast, LCO maintains positive ISFE over 0-1000 K. Molecular dynamics simulations further confirm unbounded dislocation dissociation in RSS CoCrNi but finite stacking-fault widths in the LCO state.

Abstract Machine-learned interatomic potentials can offer near first-principles accuracy but are computationally expensive, limiting their application to large-scale molecular dynamics simulations. Inspired by quantum mechanics/molecular mechanics methods, we present ML-MIX, a CPU- and GPU-compatible package to accelerate simulations by spatially mixing interatomic potentials of different complexities, allowing deployment of modern MLIPs even under restricted computational budgets. We demonstrate our method for ACE, UF3, SNAP and MACE potential architectures and demonstrate how linear ‘cheap’ potentials can be distilled from a given ‘expensive’ potential, allowing close matching in relevant regions of configuration space. The functionality of ML-MIX is demonstrated through tests on point defects in Si, Fe and W-He, in which speedups of up to 11× over ~8000 atoms are demonstrated, without sacrificing accuracy. The scientific potential of ML-MIX is demonstrated via two case studies in W, measuring the mobility of $$b=\frac{1}{2}\langle 111\rangle$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> <mml:mo>〈</mml:mo> <mml:mn>111</mml:mn> <mml:mo>〉</mml:mo> </mml:mrow> </mml:math> screw dislocations with ACE/ACE mixing and the implantation of He with MACE/SNAP mixing. The latter returns He reflection coefficients which (for the first time) match experimental observations up to an He incident energy of 80 eV—demonstrating the benefits of deploying state-of-the-art models on large, realistic systems.

Vibrational free energy estimation is a cornerstone of atomic simulation, essential to predict finite-temperature material properties. Expressing the free energy as a function of interatomic potential parameters is actively sought in modern workflows for uncertainty quantification or inverse design. However, to achieve meV/atom accuracy, existing schemes conduct slow, sequential sampling with fixed potential parameters. We present a solution, an efficient model-agnostic free energy estimator which is meV/atom accurate over a broad, multi-element parameter range. For a broad class of machine learning potentials we show the free energy is the Legendre transform of an entropy function, accurately estimated via score-matching. Sampling requires 10× less effort than a single traditional estimate, tensor compression ensures lightweight storage, and inference is instantaneous. We demonstrate targeting of phase boundaries in back-propagation, fine-tuning the α − γ transition temperature in a Fe model from 2030 K to 1063 K. Extensions to a range of high-dimensional integration tasks are discussed. A new technique for ML-driven atomic simulations produces differentiable free energy estimates, allowing computational phase diagram predictions to be fine-tuned against experimental data and equipped with robust uncertainty quantification.

Atomistic simulations of matter, especially those that leverage first-principles (ab initio) electronic structure theory, provide a microscopic view of the world, underpinning much of our understanding of chemistry and materials science. Over the last decade or so, machine-learned force fields have transformed atomistic modeling by enabling simulations of ab initio quality over unprecedented time and length scales. However, early machine-learning (ML) force fields have largely been limited by (i) the substantial computational and human effort required to develop and validate potentials for each particular system of interest and (ii) a general lack of transferability from one chemical system to the next. Here, we show that it is possible to create a general-purpose atomistic ML model, trained on a public dataset of moderate size, that is capable of running stable molecular dynamics for a wide range of molecules and materials. We demonstrate the power of the MACE-MP-0 model-and its qualitative and at times quantitative accuracy-on a diverse set of problems in the physical sciences, including properties of solids, liquids, gases, chemical reactions, interfaces, and even the dynamics of a small protein. The model can be applied out of the box as a starting or "foundation" model for any atomistic system of interest and, when desired, can be fine-tuned on just a handful of application-specific data points to reach ab initio accuracy. Establishing that a stable force-field model can cover almost all materials changes atomistic modeling in a fundamental way: experienced users obtain reliable results much faster, and beginners face a lower barrier to entry. Foundation models thus represent a step toward democratizing the revolution in atomic-scale modeling that has been brought about by ML force fields.

The activation entropy of dislocation glide, a key process controlling the strength of many metals, is often assumed to be constant or linked to enthalpy through the empirical Meyer-Neldel law-both of which are simplified approximations. In this study, we take a more direct approach by calculating the activation Gibbs energy for kink-pair nucleation on screw dislocations of two body-centered cubic metals, iron and tungsten. To ensure reliability, we develop machine learning interatomic potentials for both metals, carefully trained on dislocation data from density functional theory. Our findings reveal that dislocations undergo harmonic transitions between Peierls valleys, with an activation entropy that remains largely constant, regardless of temperature or applied stress. We use these results to parameterize a thermally-activated model of yield stress, which consistently matches experimental data in both iron and tungsten. Our work challenges recent studies using classical potentials, which report highly varying activation entropies, and suggests that simulations relying on classical potentials-widely used in materials modeling-could be significantly influenced by overestimated entropic effects. The authors use atomistic calculations with machine-learned interatomic potentials to show that dislocation motion in metals like iron and tungsten involves a nearly constant activation entropy, challenging prior models and improving strength predictions.

This study completes a long-standing effort to understand experimental measurements of self-diffusion in non-magnetic body-centered cubic (bcc) metals and proposes a complete workflow to estimate it. Over the past decade, consensus has emerged attributing anomalous non-Arrhenius behavior to anharmonicity of atomic interactions. This work advances two issues: (i) free-energy contributions from small vacancy clusters are quantitatively accounted for, showing di-vacancy effects to be negligible; and (ii) quantitative agreement with experiment requires interatomic interactions beyond standard exchange-correlation functionals, such as recent meta-Generalized Gradient Approximations (meta-GGAs). The developed workflow enables automated, systematic investigations of diffusion and complex energetic landscapes, providing a foundation for predictive phase stability by connecting atomic vibrations with defect-driven phase diagrams.

Abstract The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of settings, which has brought renewed interest in robust means to quantify uncertainties. In many practical settings where model complexity is constrained (e.g., due to performance considerations), misspecification — the inability of any one choice of model parameters to exactly match all training data — is a key contributor to errors that is often disregarded. Here, we employ a recent misspecification-aware regression technique to quantify parameter uncertainties, which is then propagated to a broad range of phase and defect properties in tungsten. The propagation is performed through both brute-force resampling and implicit Taylor expansion. The propagated misspecification uncertainties robustly quantify and bound errors on a broad range of material properties. We demonstrate application to recent foundational machine learning interatomic potentials, accurately predicting and bounding errors in MACE-MPA-0 energy predictions across the diverse materials project database.

Machine-learned interatomic potentials can offer near first-principles accuracy but are computationally expensive, limiting their application to large-scale molecular dynamics simulations. Inspired by quantum mechanics/molecular mechanics methods we present ML-MIX, a CPU- and GPU-compatible LAMMPS package to accelerate simulations by spatially mixing interatomic potentials of different complexities allowing deployment of modern MLIPs even under restricted computational budgets. We demonstrate our method for ACE, UF3, SNAP and MACE potential architectures and demonstrate how linear 'cheap' potentials can be distilled from a given 'expensive' potential, allowing close matching in relevant regions of configuration space. The functionality of ML-MIX is demonstrated through tests on point defects in Si, Fe and W-He, in which speedups of up to 11x over ~ 8,000 atoms are demonstrated, without sacrificing accuracy. The scientific potential of ML-MIX is demonstrated via two case studies in W, measuring the mobility of b = 1/2 111 screw dislocations with ACE/ACE mixing and the implantation of He with MACE/SNAP mixing. The latter returns He reflection coefficients which (for the first time) match experimental observations up to an He incident energy of 80 eV - demonstrating the benefits of deploying state-of-the-art models on large, realistic systems.

We present a new method to evaluate vibrational free energies of atomic systems without a priori specification of an interatomic potential. Our model-agnostic approach leverages descriptors, high-dimensional feature vectors of atomic structure. The entropy of a high-dimensional density, the descriptor density of states, is accurately estimated with conditional score matching. Casting interatomic potentials into a form extensive in descriptor features, we show free energies emerge as the Legendre-Fenchel conjugate of the descriptor entropy, avoiding all high-dimensional integration. The score matching campaign requires less resources than fixed-model sampling and is highly parallel, reducing wall time to a few minutes, with tensor compression schemes allowing lightweight storage. Our model-agnostic estimator returns differentiable free energy predictions over a broad range of potential parameters in microseconds of CPU effort, allowing rapid forward and back propagation of potential variations through finite temperature simulations, long desired for uncertainty quantification and inverse design. We test predictions against thermodynamic integration calculations over a broad range of models for BCC, FCC and A15 phases of W, Mo and Fe at high homologous temperatures. Predictions pass the stringent accuracy threshold of 1-2 meV/atom (1/40-1/20 kcal/mol) for phase prediction with propagated score uncertainties robustly bounding errors. We also demonstrate targeted fine-tuning, reducing the alpha-gamma transition temperature in a non-magnetic machine learning model of Fe from 2030 K to 1063 K through back-propagation, with no additional sampling. Applications to liquids and fine-tuning foundational models are discussed along with the many problems in computational science which estimate high-dimensional integrals.

The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of settings, which has brought renewed interest in robust means to quantify uncertainties on simulation results. In many practical settings, encompassing both classical and a large class of machine learning potentials, the dominant form of uncertainty is currently not due to lack of training data but to misspecification, namely the inability of any one choice of model parameters to exactly match all ab initio training data. However, Bayesian inference, the most common formal tool used to quantify uncertainty, is known to ignore misspecification and thus significantly underestimates parameter uncertainties. Here, we employ a recent misspecification-aware regression technique to quantify parameter uncertainties, which is then propagated to a broad range of phase and defect properties in tungsten via brute force resampling or implicit differentiation. The propagated misspecification uncertainties robustly envelope errors to direct \textit{ab initio} calculation of material properties outside of the training dataset, an essential requirement for any quantitative multi-scale modeling scheme. Finally, we demonstrate application to recent foundational machine learning interatomic potentials, accurately predicting and bounding errors in MACE-MPA-0 energy predictions across the diverse materials project database. Perspectives for the approach in multiscale simulation workflows are discussed.

Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging inverse problems such as fine-tuning or targeted design. Here, the implicit derivative of functions defined as a fixed point is used to Taylor-expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. The implicit expansion accurately predicts lattice distortion and defect formation energies and volumes with classical and machine-learning potentials, enabling high-dimensional uncertainty propagation without prohibitive overhead. We then show how the implicit derivative can be used to solve challenging inverse problems, minimizing an implicit loss to fine-tune potentials and stabilize solute-induced structural rearrangements at dislocations in tungsten.

Abstract Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, this loss ignores model form error, or misspecification, meaning parameter uncertainties are significantly underestimated and vanish in the large data limit. As misspecification is the main source of uncertainty for surrogate models of low-noise calculations, such as those arising in atomistic simulation, predictive uncertainties are systematically underestimated. We analyze the true generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show that posterior parameter distributions must cover every training point to avoid a divergence in the generalization error and design a compatible ansatz which incurs minimal overhead for linear models. The approach is demonstrated on model problems before application to thousand-dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors in terms of parameter uncertainties, allowing this important source of uncertainty to be incorporated in multi-scale computational workflows.

Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging inverse problems such as fine-tuning or targeted design. Here, the implicit derivative of functions defined as a fixed point is used to Taylor expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a novel sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. The implicit expansion accurately predicts lattice distortion and defect formation energies and volumes with classical and machine-learning potentials, enabling high-dimensional uncertainty propagation without prohibitive overhead. We then show how the implicit derivative can be used to solve challenging inverse problems, minimizing an implicit loss to fine-tune potentials and stabilize solute-induced structural rearrangements at dislocations in tungsten.

The recently introduced mean-field anharmonic bond model has shown remarkable accuracy in predicting finite temperature free energies for certain potential models of fcc crystals without thermodynamic sampling. In this work, we extend the model to treat modern machine learning potentials in both isochoric and isobaric ensembles while preserving existing vibrational correlations and ensuring thermodynamic self-consistency. Testing against molecular dynamics simulations of bulk fcc Al and Cu, we find free energies with an accuracy of a few meV/atom up to the melting temperature under typical operating pressures, with similar accuracy for thermal expansion. Our sampling-free estimation is universally superior to the quasiharmonic approximation for less than ten percent of the computational cost and many orders of magnitude more efficient than thermodynamic integration. We discuss applications of the method in modern computational materials science workflows. Published by the American Physical Society 2024

Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian regression are thus significantly underestimated and vanish in the large data limit. This is particularly problematic when building models of low-noise, or near-deterministic, calculations, as the main source of uncertainty is neglected. We analyze the generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show posterior distributions must cover every training point to avoid a divergent generalization error and design an ansatz that respects this constraint, which for linear models incurs minimal overhead. This is demonstrated on model problems before application to thousand dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors where existing schemes fail, allowing this important source of uncertainty to be incorporated in computational workflows.

KIM REVIEW, Volume 2, Article 01, 2024

Atomic simulations of materials require significant resources to generate, store, and analyze. Here, descriptor functions are proposed as a general, metric latent space for atomic structures, ideal for use in large-scale simulations. Descriptors can regress a broad range of properties, including character-dependent dislocation densities, stress states, or radial distribution functions. A vector autoregressive model can generate trajectories over yield points, resample from new initial conditions and forecast trajectory futures. A forecast confidence, essential for practical application, is derived by propagating forecasts through the Mahalanobis outlier distance, providing a powerful tool to assess coarse-grained models. Application to nanoparticles and yielding of nanoscale dislocation networks confirms low uncertainty forecasts are accurate and resampling allows for the propagation of smooth property distributions. Yielding is associated with a collapse in the intrinsic dimension of the descriptor manifold, which is discussed in relation to the yield surface.

Atomic simulations of material microstructure require significant resources to generate, store and analyze. Here, atomic descriptor functions are proposed as a general latent space to compress atomic microstructure, ideal for use in large-scale simulations. Descriptors can regress a broad range of properties, including character-dependent dislocation densities, stress states or radial distribution functions. A vector autoregressive model can generate trajectories over yield points, resample from new initial conditions and forecast trajectory futures. A forecast confidence, essential for practical application, is derived by propagating forecasts through the Mahalanobis outlier distance, providing a powerful tool to assess coarse-grained models. Application to nanoparticles and yielding of dislocation networks confirms low uncertainty forecasts are accurate and resampling allows for the propagation of smooth microstructure distributions. Yielding is associated with a collapse in the intrinsic dimension of the descriptor manifold, which is discussed in relation to the yield surface.

It is generally considered that the elementary building blocks of defects in face-centred cubic (fcc) metals, e.g., interstitial dumbbells, coalesce directly into ever larger 2D dislocation loops, implying a continuous coarsening process. Here, we reveal that, prior to the formation of dislocation loops, interstitial atoms in fcc metals cluster into compact 3D inclusions of A15 Frank-Kasper phase. After reaching the critical size, A15 nano-phase inclusions act as a source of prismatic or faulted dislocation loops, dependent on the energy landscape of the host material. Using cutting-edge atomistic simulations we demonstrate this scenario in Al, Cu, and Ni. Our results explain the enigmatic 3D cluster structures observed in experiments combining diffuse X-ray scattering and resistivity recovery. Formation of compact nano-phase inclusions in fcc structure, along with previous observations in bcc structure, suggests that the fundamental mechanisms of interstitial defect formation are more complex than historically assumed and require a general revision. Interstitial-mediated formation of compact 3D precipitates can be a generic phenomenon, which should be further explored in systems with different crystallographic lattices.

Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

In this study, we employed molecular dynamics simulations, both traditional and machine learned, to emulate spherical nanoindentation experiments of crystalline W matrices at different temperatures and loading rates using different approaches, such as EAM, EAM with Ziegler, Biersack, and Littmark corrections, modified EAM, analytic bond-order approach, and a recently developed machine-learned tabulated Gaussian approximation potential (tabGAP) framework for describing the W-W interaction and plastic deformation mechanisms. Results showed similarities between the recorded load-displacement curves and dislocation densities, for different interatomic potentials and crystal orientations at low and room temperature. However, we observe concrete differences in the early stages of elastic-to-plastic deformation transition, revealing different mechanisms for dislocation nucleation and dynamics during loading, especially at higher temperatures. This is attributed to the particular features of orientation dependence in crystal plasticity mechanisms and, characteristically, the stacking fault and dislocation glide energies information in the interatomic potentials, with tabGAP being the one with the most well-trained results compared to density functional theory calculations and experimental data.