Perspective: Machine learning potentials for atomistic simulations

Chemical heuristics have been fundamental to the advancement of chemistry and materials science. These heuristics are typically established by scientists using knowledge and creativity to extract patterns from limited datasets. Machine learning offers opportunities to perfect this approach using computers and larger datasets. Here, we discuss the relationships between traditional heuristics and machine learning approaches. We show how traditional rules can be challenged by large-scale statistical assessment and how traditional concepts commonly used as features are feeding the machine learning techniques. We stress the waste involved in relearning chemical rules and the challenges in terms of data size requirements for purely data-driven approaches. Our view is that heuristic and machine learning approaches are at their best when they work together.

<sec>Photoelectron spectroscopy serves as a prevalent characterization technique in the field of materials science. Especially, angle-resolved photoelectron spectroscopy (ARPES) provides a direct method for determining the energy-momentum dispersion relationship and Fermi surface structure of electrons in a material system, therefore ARPES has become a potent tool for investigating many-body interactions and correlated quantum materials. With the emergence of technologies such as time-resolved ARPES and nano-ARPES, the field of photoelectron spectroscopy continues to advance. Meanwhile, the development of synchrotron radiation facilities has led to an increase of high-throughput and high-dimensional experimental data. This highlights the urgency for developing more efficient and accurate data processing methods, as well as extracting deeper physical information. In light of these developments, machine learning will play an increasingly significant role in various fields, including but not limited to ARPES.</sec><sec>This paper reviews the applications of machine learning in photoelectron spectroscopy, mainly including the following three aspects.</sec><sec>1) Data Denoising Machine learning can be utilized for denoising photoelectron spectroscopy data. The denoising process via machine learning algorithms can be divided into two methods. Neither of the two methods need manual data annotation. The first method is to use noise generation algorithms to simulate experimental noise, so as to obtain effective low signal-to-noise ratio data pair to high signal-to-noise ratio data pair. And the second method is to extract noise and clean spectral data.</sec><sec>2) Electronic Structure and Chemical Composition Analysis Machine learning can be used for analyzing electronic structure and chemical composition. (Angle-resolved) photoelectron spectroscopy contains abundant information about material structure. Information such as energy band structure, self-energy, binding energy, and other condensed matter data can be rapidly acquired through machine learning schemes.</sec><sec>3) Prediction of Photoelectron Spectroscopy The electronic structure information obtained by combining first-principles calculation can also predict the photoelectron spectroscopy. The rapid acquisition of photoelectron spectroscopy data through machine learning algorithms also holds significance for material design.</sec><sec>Photoelectron spectroscopy holds significant importance in the study of condensed matter physics. In the context of the development of synchrotron radiation, the construction of an automated data acquisition and analysis system can play a pivotal role in studying condensed matter physics. In addition, adding more physical constraints to the machine learning model will improve the interpretability and accuracy of the model. There exists a close relationship between photoelectron spectroscopy and first-principles calculations of electronic structure properties. The integration of these two through machine learning is anticipated to significantly contribute to the study of electronic structure properties. Furthermore, as machine learning algorithms continue to evolve, the application of more advanced machine learning algorithms in photoelectron spectroscopy research is expected. Building automated data acquisition and analysis systems, designing comprehensive workflows based on machine learning and first-principles methods, and integrating new machine learning techniques will help accelerate the progress of photoelectron spectroscopy experiments and facilitate the analysis of electronic structure properties and microscopic physical mechanisms, thereby advancing the frontier research in quantum materials and condensed matter physics.</sec>

Density functional theory (DFT) stands as the predominant workhorse for electronic structure calculation across physics, chemistry, and materials science. However, its practical application is fundamentally constrained by a computational cost that scales cubically with system size, rendering high-precision studies of complex or large-scale materials prohibitively expensive. This review addresses the pivotal challenge by surveying the rapidly evolving paradigm of integrating machine learning (ML) with first-principles calculations to dramatically accelerate and scale electronic structure prediction. Our primary objective is to provide a comprehensive and critical overview of the methodological advances, physical outcomes, and transformative potential of this interdisciplinary field.<br>The core methodological progression involves a shift from black-box property predictors to symmetry-preserving, transferable models that learn the fundamental Hamiltonian—the central quantity from which diverse electronic properties derive. We detail this evolution, beginning with pioneering applications in molecular systems using graph neural networks (e.g., SchNOrb, DimeNet) to predict energies, wavefunctions, and Hamiltonian matrices with meV-level accuracy. The review then focuses on the critical extension to periodic solids, where preserving symmetries like E(3)-equivariance and handling vast configurational spaces are paramount. We systematically analyze three leading model families that define the state-of-the-art: the DeepH series, which employs local coordinate message passing and E(3)-equivariant networks to achieve sub-meV accuracy and linear scaling; the HamGNN framework, built on rigorous equivariant tensor decomposition, excelling in modeling systems with spin-orbit coupling and charged defects; and the DeePTB approach, which leverages deep learning for tight-binding Hamiltonian parameterization, enabling quantum-accurate simulations of millions of atoms.<br>These methods yield significant physical results and computational breakthroughs. Key outcomes include: 1) Unprecedented accuracy and speed. Models consistently achieve Hamiltonian prediction mean absolute errors (MAE) below 1 meV (e.g., DeepH-E3: ~0.4 meV in graphene; HamGNN: ~1.5 meV in QM9 molecules), coupled with computational speedups of 3 to 5 orders of magnitude compared to conventional DFT. 2) Scale bridging. Successful applications now span from small molecules to defect-containing supercells with over 10,000 atoms (e.g., HamGNN-Q on a 13,824-atom GaAs defect) and even to millions of atoms for optoelectronic property simulations (DeePTB). 3) Expanded application scope. The review highlights how these ML-accelerated tools are revolutionizing research in previously intractable areas: predicting spectroscopic properties of molecules (e.g., DetaNet for NMR/UV-Vis spectra), elucidating electronic structures of topological materials and magnetic moiré systems, computing electron-phonon coupling and carrier mobility with DFT-level accuracy but far greater efficiency (HamEPC framework), and enabling high-throughput screening for materials design.<br>In conclusion, ML-accelerated electronic structure calculation has matured into a powerful paradigm, transitioning from a proof-of-concept to a tool capable of delivering DFT-fidelity results at dramatically reduced cost for systems of realistic scale and complexity. However, challenges remain, including model interpretability ("black-box" nature), transferability to unseen elements, and seamless integration with existing plane-wave DFT databases. Future directions point towards physics-constrained unsupervised learning (e.g., DeepH-zero), development of more universal and element-agnostic architectures, and the creation of closed-loop, artificial intelligence (AI)-driven discovery pipelines. By overcoming current limitations, these methods hold the potential to fundamentally reshape the materials research landscape, accelerating the journey from atomistic simulation to rational material design and discovery.

Amp: A modular approach to machine learning in atomistic simulations

Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors-atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors-using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications.

Theory-Guided Machine Learning Finds Geometric Structure-Property Relationships for Chemisorption on Subsurface Alloys

Recent advances in the development of interatomic potential using neural networks have proven that its accuracy reaches that of first-principles calculations but with considerably reduced computati...

Recent Advances in Topological Quantum Materials by Angle-Resolved Photoemission Spectroscopy

This dissertation contains four projects: transforming electronic structure Hamiltonian to approximating Ising-type Hamiltonian to enable electronic structure calculations by quantum annealing, quantum-assisted restricted Boltzmann machine for electronic structure calculations, hybrid quantum classical neural network for calculating ground state energies of molecules and qubit coupled cluster single and double excitations variational quantum eigensolver for electronic structure. In chapter 1 we present a general introduction of quantum computer, including a brief introduction of two quantum computing model: gate model and quantum annealing model. We also give a general review about electronic structure calculations on quantum computer. In chapter 2, we show an approximating mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. The whole mapping is enabled by first enlarging the qubits space to transform the electronic structure Hamiltonian to a diagonal Hamiltonian. Then introduce ancilla qubits to transform the diagonal Hamiltonian to an Ising-type Hamiltonian. We also design an algorithm to use the transformed Hamiltonian to obtain the approximating ground energy of the original Hamiltonian. The numerical simulation results of the transformed Hamiltonian for H2, He2, HeH+, and LiH molecules match the exact numerical calculations of the original Hamiltonian. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware. In chapter 3, we report a hybrid quantum algorithm employing a restricted Boltzmann machine to obtain accurate molecular potential energy surfaces. By exploiting a quantum algorithm to help optimize the underlying objective function, we obtained an efficient procedure for the calculation of the electronic ground state energy for a small molecule system. Our approach achieves high accuracy for the ground state energy for H2, LiH, H2O at a specific location on its potential energy surface with a finite basis set. With the future availability of larger-scale quantum computers, quantum machine learning techniques are set to become powerful tools to obtain accurate values for electronic structures. In chapter 4, we present a hybrid quantum classical neural network that can be trained to perform electronic structure calculation and generate potential energy curves of simple molecules. The method is based on the combination of parameterized quantum circuit and measurements. With unsupervised training, the neural network can generate electronic potential energy curves based on training at certain bond lengths. To demonstrate the power of the proposed new method, we present results of using the quantum-classical hybrid neural network to calculate ground state potential energy curves of simple molecules such as H2, LiH and BeH2. The results are very accurate and the approach could potentially be used to generate complex molecular potential energy surfaces. In chapter 5, we introduce a new variational quantum eigensolver (VQE) ansatz based on the particle preserving exchange gate to achieve qubit excitations. The proposed VQE ansatz has gate complexity up-bounded to O(n4) where n is the number of qubits of the Hamiltonian. Numerical results of simple molecular systems such as BeH2, H2O, N2, H4 and H6 using the proposed VQE ansatz gives very accurate results within errors about 10-3 Hartree.

Bridging the gap between diffuse x-ray or neutron scattering measurements and predicted structures derived from atom–atom pair potentials in disordered materials, has been a longstanding challenge in condensed matter physics. This perspective gives a brief overview of the traditional approaches employed over the past several decades. Namely, the use of approximate interatomic pair potentials that relate three-dimensional structural models to the measured structure factor and its’ associated pair distribution function. The use of machine learned interatomic potentials has grown in the past few years, and has been particularly successful in the cases of ionic and oxide systems. Recent advances in large scale sampling, along with a direct integration of scattering measurements into the model development, has provided improved agreement between experiments and large-scale models calculated with quantum mechanical accuracy. However, details of local polyhedral bonding and connectivity in meta-stable disordered systems still require improvement. Here we leverage MACE-MP-0; a newly introduced equivariant foundation model and validate the results against high-quality experimental scattering data for the case of molten iron(II) oxide (FeO). These preliminary results suggest that the emerging foundation model has the potential to surpass the traditional limitations of classical interatomic potentials.

Jürgen Hafner started in the early 1970s with pseudopotential calculations on the structures and properties of sp-bonded metals, improving on work done elsewhere [1]. This expanded in four directions: transition metals, molten metals, magnetism and alloys, and combinations of these. As well as electronic structure calculations, he helped to advance the statistical mechanical classical theory of liquids for the molten metals [2]. In magnetism he was one of the pioneers of calculations with non-collinear spins [3, 4]. As well as simple (solid and molten) alloys, he also treated materials with strong chemical interaction such as sulphides and liquids such as arsenic and tellurium [5, 6]. All this fed into two directions which dominated much of his work for many years, namely the theory of glassy metals [7] and that of quasicrystals [8]. One notable result in the latter was to show that it was possible to construct hypothetical materials for which the quasicrystalline state is indeed the lowest energy structure. This displaced the established wisdom of the time that quasicrystals were necessarily metastable forms. In more recent years he has turned to calculations in surface science [9, 10], including catalysis of chemical reactions on surfaces [11, 12].

Predicting the behaviour of a component under irradiation or submitted to an external load often requires understanding the evolution of its microstructure. This usually requires knowledge of the mechanisms taking place at the atomic level, which are introduced in multiscale-type modelling suites. In this context, interatomic potentials are necessary ingredients for most simulation techniques at the atomic level. They have been used for more than 40 years in various areas of materials science and, in particular, in the fields of radiation damage and plasticity. These simulations have shed particular light on the role of solute atoms in the formation of the primary damage or the motion of dislocations. However, ab initio calculations, as well as comparison of the results obtained with different interatomic potentials have indicated some failures in these potentials, which led to the building of new potentials. This article highlights how ab initio calculations, which nowadays constitute the state of the art method to predict atomic properties can (and will) increasingly contribute to the assessment, validation and building of interatomic potentials.

The ever-increasing power of modern supercomputers, along with the availability of highly scalable atomistic simulation codes, has begun to revolutionize predictive modeling of materials. In particular, molecular dynamics (MD) has led to breakthrough advances in diverse fields, including tribology, catalysis, sensing, and nanoparticle self-assembly. Furthermore, recent integration of MD simulations with X-ray characterization has demonstrated promise in real-time 3-D characterization of materials on the atomic scale. The popularity of MD is driven by its applicability at disparate length/time scales, ranging from ab initio MD (hundreds of atoms and tens of picoseconds) to all-atom classical MD (millions of atoms over microseconds), and coarse-grained (CG) models (micrometers and tens of microseconds). Nevertheless, a substantial gap persists between AIMD, which is highly accurate but restricted to extremely small sizes, and those based on classical force fields (atomistic and CG) with limited accuracy but access to larger length/time scales. The accuracy and predictive power of classical MD simulations is dictated by the empirical force fields, and their capability to capture the relevant physics. Here, we discuss some of our recent work on the use of machine learning (ML) to combine the accuracy and flexibility of electronic structure calculations with the speed of classical potentials. Our ML framework attempts to bridge the significant gulf that exists between the handful of research groups that develop new interatomic potential models (often requiring several years of effort), and the increasingly large user community from academia and industry that applies these models. Our data-driven approach represents significant departure from the status quo and involves several steps including generation and manipulation of extensive training data sets through electronic structure calculations, defining novel potential functional forms, employing state-of-the-art ML algorithms to formulate highly optimized training procedures, and subsequently developing user-friendly workflow tools integrating these algorithms on high-performance computers (HPCs). Our ML approach shows marked success in developing force fields for a wide range of materials from metals, oxides, nitrides, and heterointerfaces to two-dimensional (2D) materials.

SIMPLE-NN: An efficient package for training and executing neural-network interatomic potentials

Thermoelectric materials with crystal-amorphicity duality induced by large atomic size mismatch