arXiv subjects

Michele Ceriotti

Publications and source records attributed to Michele Ceriotti.

At least 37 records · Page 2Linked to original sources

arXiv2026

How unconstrained machine-learning models learn physical symmetries

The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases, models are built using constrained mathematical forms that ensure that symmetries are enforced exactly. However, unconstrained models that do not obey rotational symmetries are often found to have competitive performance, and to be able to \emph{learn} to a high level of accuracy an approximate equivariant behavior with a simple data augmentation strategy. In this paper, we introduce rigorous metrics to measure the symmetry content of the learned representations in such models, and assess the accuracy by which the outputs fulfill the equivariant condition. We apply these metrics to two unconstrained, transformer-based models operating on decorated point clouds (a graph neural network for atomistic simulations and a PointNet-style architecture for particle physics) to investigate how symmetry information is processed across architectural layers and is learned during training. Based on these insights, we establish a rigorous framework for diagnosing spectral failure modes in ML models. Enabled by this analysis, we demonstrate that one can achieve superior stability and accuracy by strategically injecting the minimum required inductive biases, preserving the high expressivity and scalability of unconstrained architectures while guaranteeing physical fidelity.

cs.LG↗

arXiv2026

Learning Long-Range Representations with Equivariant Messages

Machine learning interatomic potentials trained on first-principles reference data are becoming valuable tools for computational physics, biology, and chemistry. Equivariant message-passing neural networks, including transformers, achieve state-of-the-art accuracy but rely on cutoff-based graphs, limiting their ability to capture long-range effects such as electrostatics or dispersion, as well as electron delocalization. While long-range correction schemes based on inverse power laws of interatomic distances have been proposed, they are unable to communicate higher-order geometric information and are thus limited in applicability. To address this shortcoming, we propose the use of equivariant, rather than scalar, charges for long-range interactions, and design a graph neural network architecture, LOREM, around this long-range message passing mechanism. We consider several datasets specifically designed to highlight non-local physical effects, and compare short-range message passing with different receptive fields to invariant and equivariant long-range message passing. Even though most approaches work for careful dataset-specific choices of their model hyperparameters, LOREM works consistently without such changes, with excellent benchmark performance.

physics.chem-ph↗

arXiv2026

Learning the action for long-time-step simulations of molecular dynamics

The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational efficiency -- especially in cases such as molecular dynamics that span wildly different time scales. Using machine-learning (ML) algorithms to predict trajectories allows one to greatly extend the integration time step, at the cost of introducing artifacts such as lack of energy conservation and loss of equipartition between different degrees of freedom of a system. We propose learning data-driven structure-preserving (symplectic and time-reversible) maps to generate long time-step classical dynamics and show that this method is equivalent to learning the mechanical action of the system of interest. These models can be learned based on short reference trajectories, and be transferred across thermodynamic conditions and chemical composition. We show that an action-derived ML integrator eliminates the pathological behavior of non-structure-preserving ML predictors, and that the method can be applied iteratively, serving as a correction to computationally cheaper direct predictors.

physics.chem-ph↗

arXiv2026

Tracking the Lithiation State of Li$_x$Si from Machine-Learned XPS Binding Energies

X-ray Photoelectron Spectroscopy (XPS) is a powerful technique to probe chemical states and interfacial processes in battery materials, but a quantitative interpretation is often hindered by the complex, heterogeneous microstructures that form during operation and dominate electrochemical cycling. Silicon based anodes represent a paradigmatic example in Li batteries, as (de)lithiation proceeds through the formation of strongly disordered Li$_x$Si phases and crystal-amorphous transformations that are hard to characterize. Here, we introduce a computational framework that combines machine-learning (ML) prediction of core-level binding energies to large-scale atomistic simulations -- Grand Canonical Monte Carlo (GCMC) complemented with molecular dynamics (MD), driven by a ML potential -- for a systematic sampling of lithiation states and local atomic environments. This approach yields stoichiometry maps that match the characteristic experimental trends observed in operando and ex situ XPS measurements, including the distinctive Si $2p$ spectroscopic signatures associated with the crystal-to-amorphous disordering driving early delithiation.

cond-mat.mtrl-sci↗

arXiv2026

How to Train a Shallow Ensemble

Shallow ensembles provide a convenient strategy for uncertainty quantification in machine learning interatomic potentials, that is computationally efficient because the different ensemble members share a large part of the model weights. In this work, we systematically investigate training strategies for shallow ensembles to balance calibration performance with computational cost. We first demonstrate that explicit optimization of a negative log-likelihood (NLL) loss improves calibration with respect to approaches based on ensembles of randomly initialized models, or on a last-layer Laplace approximation. However, models trained solely on energy objectives yield miscalibrated force estimates. We show that explicitly modeling force uncertainties via an NLL objective is essential for reliable calibration, though it typically incurs a significant computational overhead. To address this, we validate an efficient protocol: full-model fine-tuning of a shallow ensemble originally trained with a probabilistic energy loss, or one sampled from the Laplace posterior. This approach results in negligible reduction in calibration quality compared to training from scratch, while reducing training time by up to 96%. We evaluate this protocol across a diverse range of materials, including amorphous carbon, ionic liquids (BMIM), liquid water (H$_2$O), barium titanate (BaTiO$_3$), and a model tetrapeptide (Ac-Ala3-NHMe), establishing practical guidelines for reliable uncertainty quantification in atomistic machine learning.

physics.chem-ph↗

arXiv2026

FlashMD: long-stride, universal prediction of molecular dynamics

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of such a long-stride MD approach. We validate FlashMD's accuracy in reproducing equilibrium and time-dependent properties, using both system-specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

physics.chem-ph↗

arXiv2026

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↗

arXiv2026

Resolving the Body-Order Paradox of Machine Learning Interatomic Potentials

In many cases, the predictions of machine learning interatomic potentials (MLIPs) can be interpreted as a sum of body-ordered contributions, which is explicit when the model is directly built on neighbor density correlation descriptors, and implicit when the model captures the correlations through non-linear functions of low body-order terms. In both cases, the "effective body-orderedness" of MLIPs remains largely unexplained: how do the models decompose the total energy into body-ordered contributions, and how does their body-orderedness affect the accuracy and learning behavior? In answering these questions, we first discuss the complexities in imposing the many-body expansion on ab initio calculations at the atomic limit. Next, we train a curated set of MLIPs on datasets of hydrogen clusters and reveal the inherent tendency of the ML models to deduce their own, effective body-order trends, which are dependent on the model type and dataset makeup. Finally, we present different trends in the convergence of the body-orders and generalizability of the models, providing useful insights for the development of future MLIPs.

physics.chem-ph↗

arXiv2025

Metatensor and metatomic: foundational libraries for interoperable atomistic machine learning

Incorporation of machine learning (ML) techniques into atomic-scale modeling has proven to be an extremely effective strategy to improve the accuracy and reduce the computational cost of simulations. It also entails conceptual and practical challenges, as it involves combining very different mathematical foundations, as well as software ecosystems that are very well developed in their own right, but do not share many commonalities. To address these issues and facilitate the adoption of ML in atomistic simulations, we introduce two dedicated software libraries. The first one, metatensor, provides multi-platform and multi-language storage and manipulation of arrays with many potentially sparse indices, designed from the ground up for atomistic ML applications. By combining the actual values with metadata that describes their nature and that facilitates the handling of geometric information and gradients with respect to the atomic positions, metatensor provides a common framework to enable data sharing between ML software -- typically written in Python -- and established atomistic modeling tools -- typically written in Fortran, C or C++. The second library, metatomic, provides an interface to store an atomistic ML model and metadata about this model in a portable way, facilitating the implementation, training and distribution of models, and their use across different simulation packages. We showcase a growing ecosystem of tools, including low-level libraries, training utilities, and interfaces with existing software packages that demonstrate the effectiveness of metatensor and metatomic in bridging the gap between traditional simulation software and modern ML frameworks.

physics.chem-ph↗

arXiv2025

The dark side of the forces: assessing non-conservative force models for atomistic machine learning

The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, has revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned this physically constrained approach, suggesting that directly predicting the forces yields a better trade-off between accuracy and computational efficiency, and that energy conservation can be learned during training. This work investigates the applicability of such non-conservative models in microscopic simulations. We identify and demonstrate several fundamental issues, from ill-defined convergence of geometry optimization to instability in various types of molecular dynamics. Given the difficulty in monitoring and correcting the lack of energy conservation, direct forces should be used with great care. We show that the best approach to exploit the acceleration they afford is to use them in conjunction with conservative forces. A model can be pre-trained efficiently on direct forces, then fine-tuned using backpropagation. At evaluation time, both force types can be used together to avoid unphysical effects while still benefitting almost entirely from the computational efficiency of direct forces.

physics.chem-ph↗

arXiv2025

A deep learning model for chemical shieldings in molecular organic solids including anisotropy

Nuclear Magnetic Resonance (NMR) chemical shifts are powerful probes of local atomic and electronic structure that can be used to resolve the structures of powdered or amorphous molecular solids. Chemical shift driven structure elucidation depends critically on accurate and fast predictions of chemical shieldings, and machine learning (ML) models for shielding predictions are increasingly used as scalable and efficient surrogates for demanding ab initio calculations. However, the prediction accuracies of current ML models still lag behind those of the DFT reference methods they approximate, especially for nuclei such as $^{13}$C and $^{15}$N. Here, we introduce ShiftML3.0, a deep-learning model that improves the accuracy of predictions of isotropic chemical shieldings in molecular solids, and does so while also predicting the full shielding tensor. On experimental benchmark sets, we find root-mean-squared errors with respect to experiment for ShiftML3.0 that approach those of DFT reference calculations, with RMSEs of 0.53 ppm for $^{1}$H, 2.4 ppm for $^{13}$C, and 7.2 ppm for $^{15}$N, compared to DFT values of 0.49 ppm, 2.3 ppm, and 5.8 ppm, respectively.

physics.chem-ph↗

arXiv2025

A foundation model for atomistic materials chemistry

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 ML force fields have largely been limited by: (i) the substantial computational and human effort of developing and validating 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 get reliable results much faster, and beginners face a lower barrier to entry. Foundation models thus represent a step towards democratising the revolution in atomic-scale modeling that has been brought about by ML force fields.

physics.chem-ph↗

arXiv2025

Representing spherical tensors with scalar-based machine-learning models

Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of 3D point clouds are able to approximate structure-property relations in a way that is fully consistent with the structure of the rotation group, by combining intermediate representations that are themselves spherical tensors. The symmetry constraints however make this approach computationally demanding and cumbersome to implement, which motivates increasingly popular unconstrained architectures that learn approximate symmetries as part of the training process. In this work, we explore a third route to tackle this learning problem, where equivariant functions are expressed as the product of a scalar function of the point cloud coordinates and a small basis of tensors with the appropriate symmetry. We also propose approximations of the general expressions that, while lacking universal approximation properties, are fast, simple to implement, and accurate in practical settings.

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↗

arXiv2025

scicode-widgets: Bringing Computational Experiments to the Classroom with Jupyter Widgets

"Computational experiments" use code and interactive visualizations to convey mathematical and physical concepts in an intuitive way, and are increasingly used to support ex cathedra lecturing in scientific and engineering disciplines. Jupyter notebooks are particularly well-suited to implement them, but involve large amounts of ancillary code to process data and generate illustrations, which can distract students from the core learning outcomes. For a more engaging learning experience that only exposes relevant code to students, allowing them to focus on the interplay between code, theory and physical insights, we developed scicode-widgets (released as scwidgets), a Python package to build Jupyter-based applications. The package facilitates the creation of interactive exercises and demonstrations for students in any discipline in science, technology and engineering. Students are asked to provide pedagogically meaningful contributions in terms of theoretical understanding, coding ability, and analytical skills. The library provides the tools to connect custom pre- and post-processing of students' code, which runs seamlessly "behind the scenes", with the ability to test and verify the solution, as well as to convert it into live interactive visualizations driven by Jupyter widgets.

physics.ed-ph↗

arXiv2025

Massive Atomic Diversity: a compact universal dataset for atomistic machine learning

The development of machine-learning models for atomic-scale simulations has benefited tremendously from the large databases of materials and molecular properties computed in the past two decades using electronic-structure calculations. More recently, these databases have made it possible to train universal models that aim at making accurate predictions for arbitrary atomic geometries and compositions. The construction of many of these databases was however in itself aimed at materials discovery, and therefore targeted primarily to sample stable, or at least plausible, structures and to make the most accurate predictions for each compound - e.g. adjusting the calculation details to the material at hand. Here we introduce a dataset designed specifically to train machine learning models that can provide reasonable predictions for arbitrary structures, and that therefore follows a different philosophy. Starting from relatively small sets of stable structures, the dataset is built to contain massive atomic diversity (MAD) by aggressively distorting these configurations, with near-complete disregard for the stability of the resulting configurations. The electronic structure details, on the other hand, are chosen to maximize consistency rather than to obtain the most accurate prediction for a given structure, or to minimize computational effort. The MAD dataset we present here, despite containing fewer than 100k structures, has already been shown to enable training universal interatomic potentials that are competitive with models trained on traditional datasets with two to three orders of magnitude more structures. We describe in detail the philosophy and details of the construction of the MAD dataset. We also introduce a low-dimensional structural latent space that allows us to compare it with other popular datasets and that can be used as a general-purpose materials cartography tool.

cond-mat.mtrl-sci↗

arXiv2025

Reconstructions and Dynamics of $β$-Lithium Thiophosphate Surfaces

Lithium thiophosphate (LPS) is a promising solid electrolyte for next-generation lithium-ion batteries due to its superior energy storage, high ionic conductivity, and low-flammability components. Despite its potential, the high reactivity of LPS with common contaminants such as atmospheric water, preparation solvents, and electrode materials poses significant challenges for commercialization. The lack of understanding regarding the structure, morphology, and chemical behavior of LPS's surface slows down the search for solutions to these issues. Here, we utilize a machine learning interatomic potential to achieve a fundamental, atomistic understanding of the mechanical and chemical properties of the $β$-Li$_3$PS$_4$ surfaces. Employing molecular dynamics simulations, we identify relevant surface complexions formed by surface reconstructions, determine their surface energies and compute the Wulff shape of $β$-LPS. The most stable complexions exhibit properties distinctly different from the bulk, including amorphization, increased density, decreased conductivity and large deformation of the structure building blocks. We demonstrate that these surfaces are not static, but undergo significant dynamical activity which is clearly identified by an analysis featuring a time-averaged structural descriptor. Finally, we examine the changes of the electronic structure induced by the surface complexions, which provides us with details on changes in surface reactivity and active sites, underlining the importance to investigate surface complexions under realistic conditions.

cond-mat.mtrl-sci↗

arXiv2025

Exploring the design space of machine-learning models for quantum chemistry with a fully differentiable framework

Traditional atomistic machine learning (ML) models serve as surrogates for quantum mechanical (QM) properties, predicting quantities such as dipole moments and polarizabilities, directly from compositions and geometries of atomic configurations. With the emergence of ML approaches to predict the "ingredients" of a QM calculation, such as the ground state charge density or the effective single-particle Hamiltonian, it has become possible to obtain multiple properties through analytical physics-based operations on these intermediate ML predictions. We present a framework to seamlessly integrate the prediction of an effective electronic Hamiltonian, for both molecular and condensed-phase systems, with PySCFAD, a differentiable QM workflow that facilitates its indirect training against functions of the Hamiltonian, such as electronic energy levels, dipole moments, polarizability, etc. We then use this framework to explore various possible choices within the design space of hybrid ML/QM models, examining the influence of incorporating multiple targets on model performance and learning a reduced-basis ML Hamiltonian that can reproduce targets computed from a much larger basis. Our benchmarks evaluate the accuracy and transferability of these hybrid models, compare them against predictions of atomic properties from their surrogate models, and provide indications to guide the design of the interface between the ML and QM components of the model.

physics.chem-ph↗