arXiv subjects

Michele Ceriotti

Publications and source records attributed to Michele Ceriotti.

At least 19 recordsLinked to original sources

arXiv2026

Truncated automatic sparse differentiation for machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.

physics.chem-ph↗

arXiv2026

High-quality, high-information datasets for universal atomistic machine learning

The quality, consistency, and information content of training data is often what determines the practical value of machine-learning models for atomistic simulations. Yet, many widely used electronic-structure databases are assembled having materials screening as primary goal rather than robust force-field learning, are limited in their scope to a specific class of chemical compounds, and/or employ inconsistent DFT functionals and settings. Here we introduce MAD-1.6, a highly curated dataset designed explicitly for training broadly applicable atomistic models across the periodic table at high levels of theory. MAD-1.6 extends the MAD dataset with targeted enrichment strategies that improve the coverage of chemical space to 102 elements while keeping the total number of configurations compact. All structures are computed with a single, standardized all-electron DFT workflow using the r$^2$SCAN meta-GGA functional and consistent convergence settings, ensuring uniformity across chemically heterogeneous systems. The dataset encompasses molecules, clusters, bulk crystals, surfaces, and low-dimensional structures, and its quality and consistency are further enhanced by outlier removal using uncertainty quantification. We demonstrate the high accuracy that can be achieved with the proposed dataset by training PET-MAD-1.6, a generally applicable r$^2$SCAN interatomic potential that covers 102 elements in the periodic table and achieves exceptional levels of benchmark accuracy and stability in challenging simulation protocols.

cond-mat.mtrl-sci↗

arXiv2026

Quantum-corrected NMR crystallography at scale

Structure determination by chemical-shift-driven NMR crystallography relies on comparing chemical shieldings measured in solid-state NMR experiments with simulations. However, computational cost limits the accuracy of shielding predictions, that usually rely on low-level electronic-structure approximations and neglect thermal and quantum mechanical nuclear motion, leading to large errors, especially for highly informative hydrogen-bonded protons. To address these limitations, we introduce a quantum-nuclei-corrected (QNC-NMR) approach. We generate inexpensively quantum ensembles using PET-MOLS, a novel machine-learning learning model of the interatomic potential transferable across molecular crystals. Using them as inputs to a chemical-shift model results in a 33 % improvement of the agreement with experiments for hydrogen-bonded protons, without the need for empirical corrections. The ability to sample structures consistent with the experimental conditions enables further refinement of the shielding model by finetuning it against measured shieldings. The favorable scaling with system size allows similar improvements for amorphous materials that are otherwise inaccessible to explicit DFT simulations.

physics.chem-ph↗

arXiv2026

Machine-Learned NMR Shieldings in Molecular Solids with Built-In Hybrid-Functional Molecular Corrections

Fast and accurate chemical shielding estimators are essential for shielding-driven Nuclear Magnetic Resonance (NMR) crystallography. Machine-learning models for shielding predictions have matured significantly and today are primarily limited by the electronic structure reference data they are trained on. Here, we introduce ShiftML4, a shielding-tensor model trained directly on monomer-corrected calculations that approximate PBE0, rather than the PBE reference targeted by earlier ShiftML models. ShiftML4 is trained on a diverse set of structures containing 12 of the most common NMR nuclei in molecular organic solids. On experimental benchmark sets, the 13C isotropic RMSE against experiment is 1.67 ppm, compared with 2.34 ppm for GIPAW-PBE on the same geometries. ShiftML4 gives a similar 1H prediction RMSE to ShiftML3 (0.5 ppm) and improves the 15N RMSE from 7.24 to 6.08 ppm. The model also reduces errors in the shielding-tensor anisotropy, with an RMSE of 4.63 ppm on 13C CSA principal components against 5.85 ppm for GIPAW. The improvements in prediction accuracy are retained on better geometries. Basing shift predictions on structures relaxed with PET-MOLS, a recent machine-learned interatomic potential that reaches approximate hybrid-DFT geometries in seconds, lowers the ShiftML4 errors further to 0.48 ppm (1H), 1.49 ppm (13C) and 3.66 ppm (15N).

physics.chem-ph↗

arXiv2026

Using large language models to probe the limits of atom-centered structural descriptors

Mapping an atomic structure to a compact set of geometric descriptors is an essential step in any machine-learning application to atomic-scale modeling. A powerful and widely-used approach can be understood as a discretization of the histogram of pair distances, triangles, etc., that results in a hierarchy of symmetry-invariant atom-centered descriptors. Unfortunately, the lower rungs on this hierarchy (two, three, four-neighbor clusters) were found to be incomplete, with symmetry-unrelated pairs of structures having exactly the same descriptors. However, all the ``descriptor degeneracies'' reported so far are resolved by considering larger clusters of neighbors to build the descriptors. We report examples of 3D structures that are indistinguishable even if one considers clusters of up to seven neighbors, and to arbitrary order when considering a practical level of discretization of the descriptors, discovered with the assistance of large language models. The key ingredients in their construction can be traced to results that have been known for decades in different communities; the model was able to find the references and recognize their significance for the problem at hand. We believe this experiment exposes an extremely fruitful usage pattern for AI in science: translating results between different communities and application domains, accelerating the process by which serendipitous discoveries in a field become paradigm-shifting breakthroughs in another.

physics.chem-ph↗

arXiv2026

Mechanistic study of mixed lithium halides solid state electrolytes

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

cond-mat.mtrl-sci↗

arXiv2026

Transferable machine learning of excited-state dynamics with extremal pooling

Photochemical processes govern phenomena ranging from solar energy conversion and atmospheric chemistry to vision and photosynthesis. Accurate simulation of these processes requires modeling excited-state potential energy surfaces, often involving chemical reactions, tasks that remain computationally prohibitive for extended systems and long timescales using traditional \textit{ab initio} methods. Machine learning interatomic potentials have revolutionized ground-state simulations, but their extension to excited states faces fundamental challenges: standard architectures assume energy extensivity, an assumption that fails for excited states. Here, we present a size-intensive machine-learning framework for excited-state dynamics based on \textit{extremal pooling} of predicted atomic HOMO and LUMO contributions. Trained exclusively on excitations energies and forces, the architecture learns interpretable atomic-level contributions that encode physical information on the extent of electron localization. We demonstrate this framework on the photoexcited solvated electron in liquid water, a paradigmatic problem in radiation chemistry leading to competing pathways involving both hydrogen-atom dissociation and proton-coupled electron transfer. The model not only reproduces the relevant chain of reactions and product species that form during excitation, but also allows one to explicitly study the dynamics of the solvated electron in quantitative agreement with previously reported Restricted Open-Shell Kohn-Sham calculations, while enabling excited-state simulations of periodic systems at length and time scales inaccessible to the reference electronic-structure method. This work establishes a general strategy for machine learning-driven excited-state dynamics applicable to diverse photochemical systems, from molecular chromophores in solution to extended condensed-phase systems.

physics.chem-ph↗

arXiv2026

Six Open Questions in Machine-Learned Interatomic Potential Foundation Models

Machine-learned interatomic potentials (MLIPs) have had a profound impact on molecular modelling in recent years, promising to resolve the long-standing tension between the scale and accuracy of simulations. There has been a proliferation of new models and designs, and recently the paradigm of ``foundational'' MLIPs has become prevalent. Broadly speaking, foundation models are trained on large diverse datasets and promise to work well for new systems with minimal updates required. However, in such a new and fast moving field, there are many unanswered questions. In this article, we set out to articulate and explore what we see as the most important among these questions. We start by developing a working definition for foundational MLIPs and use this definition to frame the subsequent open questions. Despite the rapid progress in the field of MLIP models, we believe that these are fundamental questions which will continue to define cutting edge research in MLIPs in the years to come.

cond-mat.mtrl-sci↗

arXiv2026

Pushing the limits of unconstrained machine-learned interatomic potentials

Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to fulfill a number of physical laws exactly, from geometric symmetries to energy conservation. Evidence is mounting that relaxing some of these constraints can be beneficial to the efficiency and (somewhat surprisingly) accuracy of MLIPs, even though care should be taken to avoid qualitative failures associated with the breaking of physical symmetries. Given the recent trend of scaling up models to larger numbers of parameters and training samples, a very important question is how unconstrained MLIPs behave in this limit. Here we investigate this issue, showing that -- when trained on large datasets -- unconstrained models can be superior in accuracy and speed when compared to physically constrained models. We assess these models both in terms of benchmark accuracy and in terms of usability in practical scenarios, focusing on static simulation workflows such as geometry optimization and lattice dynamics. We conclude that accurate unconstrained models can be applied with confidence, especially since simple inference-time modifications can be used to recover observables that are consistent with the relevant physical symmetries.

physics.chem-ph↗

arXiv2026

Simultaneous Learning of Static and Dynamic Charges

Long-range interactions and electric response are essential for accurate modeling of condensed-phase systems, but capturing them efficiently remains a challenge for atomistic machine learning. Traditionally, these two phenomena can be represented by static charges, that participate in Coulomb interactions between atoms, and dynamic charges such as atomic polar tensors - aka Born effective charges - describing the response to an external electric field. We critically compare different approaches to learn both types of charges, taking bulk water and water clusters as paradigmatic examples: (1) Learning them independently; (2) Coupling static and dynamic charges based on their physical relationship with a single global coupling constant to account for dielectric screening; (3) Coupled learning with a local, environment-dependent screening factor. In the coupled case, correcting for dielectric screening is essential, yet the common assumption of homogeneous, isotropic screening breaks down in heterogeneous systems such as water clusters. A learned, environment-dependent screening restores high accuracy for the dynamical charges. However, the accuracy gain over independent dynamic predictions is negligible, while the computational cost increases compared to using separate models for static and dynamical charges. This suggests that, despite the formal connection between the two charge types, modeling them independently is the more practical choice for both condensed-phase and isolated cluster systems.

physics.chem-ph↗

arXiv2026

Errors that matter: Uncertainty-aware universal machine-learning potentials calibrated on experiments

Machine-learning models of atomic-scale interactions achieve the accuracy of the quantum mechanical calculations on which they are trained, but at a dramatically lower computational cost. Their predictions can be made trustworthy by uncertainty quantification techniques that estimate the residual error relative to their reference. These errors, however, do not include uncertainty contributions from the approximations inherent in the electronic structure calculations, which are often the main source of discrepancy with empirical observations. We construct an ensemble of ML potentials trained on multiple electronic-structure references and calibrate it against experimental data on cohesive energies, atomization energies, lattice constants and bulk moduli of simple materials and molecules, similar to the uncertainty-aware functional distribution approach. The resulting ensemble of models, which we call PET-UAFD, can be used to simulate matter across a wide range of compositions and thermodynamic conditions. By comparison with experimental measurements of the density and structure of liquids, we demonstrate that, even outside the static properties on which it was calibrated, PET-UAFD enables predictions that are as accurate against experiments as the best available electronic-structure reference and that the spread in the ensemble can be used to assess the reliability of such predictions. We also introduce the PET-EXP protocol that uses shallow ensembles and statistical reweighting techniques to provide accurate estimates of uncertainty relative to experimental measurements at virtually no additional cost over a simulation based on a single conventional ML potential. Ultimately, this approach provides a practical and inexpensive approach to elevate machine-learning potentials from faithful interpolators of approximate theories to genuinely predictive tools anchored in experimental reality.

physics.chem-ph↗

arXiv2026

Roadmap on Advancements of the FHI-aims Software Package

Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precision, and its efficient handling of density functional theory (DFT) with hybrid functionals and van der Waals interactions. It treats molecules, clusters, and extended systems (solids and liquids) on an equal footing. Besides DFT, FHI-aims also includes quantum-chemistry methods, descriptions for excited states and vibrations, and calculations of various types of transport. Recent advancements address the integration of FHI-aims into an increasing number of workflows and various artificial intelligence (AI) methods. This Roadmap describes the state-of-the-art of FHI-aims and advancements that are currently ongoing or planned.

cond-mat.mtrl-sci↗

arXiv2026

Comparing the latent features of universal machine-learning interatomic potentials

The past few years have seen the development of ``universal'' machine-learning interatomic potentials (uMLIPs) capable of approximating the ground-state potential energy surface across a wide range of chemical structures and compositions with reasonable accuracy. While these models differ in the architecture and the dataset used, they share the ability to compress a staggering amount of chemical information into descriptive latent features. Herein, we systematically analyze what the different uMLIPs have learned by quantitatively assessing the relative information content of their latent features with feature reconstruction errors, and observing how the trends are affected by the choice of training set and training protocol. We find that uMLIPs encode the chemical space in significantly distinct ways, with substantial cross-model feature reconstruction errors. When variants of the same model architecture are considered, trends become dependent on the dataset, target, and training protocol of choice. We also observe that fine-tuning of a uMLIP retains a strong pre-training bias in the latent features. Finally, we discuss how atom-level features, which are directly output by MLIPs, can be compressed into global structure-level features via concatenation of progressive cumulants, each adding significantly new information about the variability across the atomic environments within a given system.

physics.chem-ph↗

arXiv2026

Path Integral Methods in Atomistic Modelling: An Introduction

This book provides an introduction to path integral methods and their application to modeling atomistic processes. The book covers both the foundational theory and recently developed simulation techniques. The text provides a self-contained resource and was originally developed for the CECAM schools on Path Integral Methods.

physics.chem-ph↗

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↗