arXiv subjects

Jigyasa Nigam

Publications and source records attributed to Jigyasa Nigam.

11 recordsLinked to original sources

arXiv2026

Reconstructing local environments from concise atomistic representations

Symmetry-based representations of local atomic structure, such as the power spectrum or bispectrum, are routinely used to characterize the structural diversity of datasets and as input features for atomistic machine learning. Although these descriptors systematically incorporate increasingly complex geometric correlations, it remains unclear if a given feature can be mapped back to a discrete point cloud, whether such a reconstruction is unique, and how changes in the descriptor are reflected in the underlying atomic geometry. The choice and discretization of the radial and angular bases, as well as the high dimensionality of the resulting feature vectors -- which may contain hundreds or thousands of components -- make this interpretation even more challenging. In this work, we investigate the inverse problem of recovering atomic structures from local invariant descriptors. We show that accurate reconstructions can be obtained from remarkably compact descriptors of different correlation orders, each comprising only a few tens of features. Even representations that are formally incomplete or locally ill-conditioned can be inverted to accurate geometric reconstructions of atomic environments across molecular and material datasets. Our reconstruction framework provides a general algorithmic means of identifying approximate degeneracies of invariant descriptors and recovering distinct atomic environments that cannot be distinguished by a given representation. Finally, by reconstructing atomic configurations from descriptors, we examine how perturbations in invariant descriptors of different correlation orders translate into structural distortions.

physics.comp-ph↗

arXiv2026

Learning Lattice Parameters from Powder X-Ray Diffraction Data Using Invariants

We present a machine learning (ML) method to determine unit cell parameters from powder X-Ray diffraction (XRD) data using a novel invariant lattice representation. In ML, the data representation used can have a substantial impact on the prediction quality. Previous approaches have directly predicted lattice parameters ($a,b,c,α,β,γ$) from XRD inputs. However, these parameters depend strongly on the unit cell reduction or convention used. In this work, we construct an invariant representation of the reciprocal lattice that is independent of primitive cell convention, based on the bispectrum--a descriptor built from spherical harmonic projections of lattice points. The calculation of the lattice bispectrum is differentiable, and we demonstrate how to invert it using a dynamic programming approach. We show that when fixing ML model architecture, using the lattice bispectrum as the ML target rather than the unit cell parameters leads to more accurate lattice parameter predictions. For example, using the MP-20 dataset, the bispectrum reduces length mean absolute percentage error (MAPE) from 11.18% to 2.44% and angle MAPE from 12.74% to 3.07% compared to direct prediction with the same model architecture. We additionally benchmark our approach against pre-existing XRD to crystal structure models such as Crystalyze and assess its performance on the experimental RRUFF dataset. Beyond unit cell representation, we anticipate this invariant lattice representation could serve more broadly as a geometry-aware target for other crystallographic machine learning tasks such as structure generation.

physics.comp-ph↗

arXiv2026

Machine learning of electronic structure and atomistic properties from the external potential

Electronic structure calculations remain a major bottleneck in atomistic simulations and, not surprisingly, have attracted significant attention in machine learning (ML). Most existing approaches learn a direct map from molecular geometries, typically represented as graphs or encoded local environments, to molecular properties or use ML as a surrogate for electronic structure theory by targeting quantities such as Fock or density matrices expressed in an atomic orbital (AO) basis. Inspired by the Hohenberg-Kohn theorem, in this work, we propose an operator-centered framework in which the external (nuclear) potential, expressed in an AO basis, serves as the model input. From this operator, we construct hierarchical, body-ordered representations of atomic configurations that closely mirror the principles underlying several popular atom-centered descriptors. At the same time, the matrix-valued nature of the external potential provides a natural connection to equivariant message-passing neural networks. In particular, we show that successive products of the external potential provide a scalable route to equivariant message passing and enable an efficient description of long-range effects. We demonstrate that this approach can be used to model molecular properties, such as energies and dipole moments, from the external potential, or learn effective operator-to-operator maps, including mappings to the Fock matrix and the reduced density matrix from which multiple molecular observables can be simultaneously derived.

physics.chem-ph↗

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↗

arXiv2024

Expanding Density-Correlation Machine Learning Representations for Anisotropic Coarse-Grained Particles

Physics-based, atom-centered machine learning (ML) representations have been instrumental to the effective integration of ML within the atomistic simulation community. Many of these representations build off the idea of atoms as having spherical, or isotropic, interactions. In many communities, there is often a need to represent groups of atoms, either to increase the computational efficiency of simulation via coarse-graining or to understand molecular influences on system behavior. In such cases, atom-centered representations will have limited utility, as groups of atoms may not be well-approximated as spheres. In this work, we extend the popular Smooth Overlap of Atomic Positions (SOAP) ML representation for systems consisting of non-spherical anisotropic particles or clusters of atoms. We show the power of this anisotropic extension of SOAP, which we deem \AniSOAP, in accurately characterizing liquid crystal systems and predicting the energetics of Gay-Berne ellipsoids and coarse-grained benzene crystals. With our study of these prototypical anisotropic systems, we derive fundamental insights into how molecular shape influences mesoscale behavior and explain how to reincorporate important atom-atom interactions typically not captured by coarse-grained models. Moving forward, we propose \AniSOAP as a flexible, unified framework for coarse-graining in complex, multiscale simulation.

physics.comp-ph↗

arXiv2023

Completeness of Atomic Structure Representations

In this paper, we address the challenge of obtaining a comprehensive and symmetric representation of point particle groups, such as atoms in a molecule, which is crucial in physics and theoretical chemistry. The problem has become even more important with the widespread adoption of machine-learning techniques in science, as it underpins the capacity of models to accurately reproduce physical relationships while being consistent with fundamental symmetries and conservation laws. However, some of the descriptors that are commonly used to represent point clouds -- most notably those based on discretized correlations of the neighbor density, that underpin most of the existing ML models of matter at the atomic scale -- are unable to distinguish between special arrangements of particles in three dimensions. This makes it impossible to machine learn their properties. Atom-density correlations are provably complete in the limit in which they simultaneously describe the mutual relationship between all atoms, which is impractical. We present a novel approach to construct descriptors of \emph{finite} correlations based on the relative arrangement of particle triplets, which can be employed to create symmetry-adapted models with universal approximation capabilities, which have the resolution of the neighbor discretization as the sole convergence parameter. Our strategy is demonstrated on a class of atomic arrangements that are specifically built to defy a broad class of conventional symmetric descriptors, showcasing its potential for addressing their limitations.

physics.chem-ph↗

arXiv2023

Electronic excited states from physically-constrained machine learning

Data-driven techniques are increasingly used to replace electronic-structure calculations of matter. In this context, a relevant question is whether machine learning (ML) should be applied directly to predict the desired properties or be combined explicitly with physically-grounded operations. We present an example of an integrated modeling approach, in which a symmetry-adapted ML model of an effective Hamiltonian is trained to reproduce electronic excitations from a quantum-mechanical calculation. The resulting model can make predictions for molecules that are much larger and more complex than those that it is trained on, and allows for dramatic computational savings by indirectly targeting the outputs of well-converged calculations while using a parameterization corresponding to a minimal atom-centered basis. These results emphasize the merits of intertwining data-driven techniques with physical approximations, improving the transferability and interpretability of ML models without affecting their accuracy and computational efficiency, and providing a blueprint for developing ML-augmented electronic-structure methods.

physics.chem-ph↗

arXiv2022

Unified theory of atom-centered representations and message-passing machine-learning schemes

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, that are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), that are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes, that gather information on the relationship between neighboring atoms using "message-passing" ideas, cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provides a coherent foundation to systematize our understanding of both atom-centered and message-passing, invariant and equivariant machine-learning schemes.

stat.ML↗

arXiv2021

Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most cases, the models rely on a description of atom-centered environments, and are suitable to learn atomic properties, or global observables that can be decomposed into atomic contributions. Many quantities that are relevant for quantum mechanical calculations, however -- most notably the single-particle Hamiltonian matrix when written in an atomic-orbital basis -- are not associated with a single center, but with two (or more) atoms in the structure. We discuss a family of structural descriptors that generalize the very successful atom-centered density correlation features to the N-centers case, and show in particular how this construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian written in an atom-centered orbital basis. These N-centers features are fully equivariant -- not only in terms of translations and rotations, but also in terms of permutations of the indices associated with the atoms -- and are suitable to construct symmetry-adapted machine-learning models of new classes of properties of molecules and materials.

physics.chem-ph↗

arXiv2020

Multi-scale approach for the prediction of atomic scale properties

Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables -- such as the cohesive energy, the electron density, or a variety of response properties -- as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects, ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics, to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.

physics.comp-ph↗

arXiv2020

Recursive evaluation and iterative contraction of $N$-body equivariant features

Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible $N$-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different orders (generalizations of $N$-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically-improvable, symmetry adapted representations for atomistic machine learning.

physics.chem-ph↗