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This paper revisits the principle of uniform convergence in statistical learning, discusses how it acts as the foundation behind machine learning, and attempts to gain a better understanding of the essential problem that current deep…

Computer Vision and Pattern Recognition · Computer Science 2022-09-07 Lei Zhang , Heung-Yeung Shum

In many scientific and data-driven applications, machine learning models are increasingly used as measurement instruments, rather than merely as predictors of predefined labels. When the measurement function is learned from data, the…

Machine Learning · Computer Science 2026-01-27 Indrė Žliobaitė

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this…

We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using…

Materials Science · Physics 2013-02-25 Albert P. Bartok , Michael J. Gillan , Frederick R. Manby , Gabor Csanyi

This chapter gives an overview of the core concepts of machine learning (ML) -- the use of algorithms that learn from data, identify patterns, and make predictions or decisions without being explicitly programmed -- that are relevant to…

Data Analysis, Statistics and Probability · Physics 2025-12-15 Javier M. Duarte , Uros Seljak , Kazu Terao

Materials characterization and property measurements are a cornerstone of material science, providing feedback from synthesis to applications. Traditionally, a single sample is used to derive information on a single point in composition…

Obtaining microscopic structure-property relationships for grain boundaries are challenging because of the complex atomic structures that underlie their behavior. This has led to recent efforts to obtain these relationships with machine…

Recent advances in scanning transmission electron and scanning tunneling microscopies allow researchers to measure materials structural and electronic properties, such as atomic displacements and charge density modulations, at an Angstrom…

Accurate and fast prediction of materials properties is central to the digital transformation of materials design. However, the vast design space and diverse operating conditions pose significant challenges for accurately modeling arbitrary…

Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information,…

Computational Physics · Physics 2020-08-21 Juan Carrasquilla

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…

Machine Learning · Computer Science 2024-05-08 Yongquan Qu , Mohamed Aziz Bhouri , Pierre Gentine

Electronic density of states (DOS) plays a crucial role in determining and understanding materials properties. We investigate the machine learnability of additive atomic contributions to electronic DOS, focusing on atom-projected DOS rather…

Materials Science · Physics 2025-08-26 A. Aryanpour , Ali Sadeghi

Exciting advances have been made in artificial intelligence (AI) during the past decades. Among them, applications of machine learning (ML) and deep learning techniques brought human-competitive performances in various tasks of fields,…

Computational Physics · Physics 2018-07-17 Quan Zhou , Peizhe Tang , Shenxiu Liu , Jinbo Pan , Qimin Yan , Shou-Cheng Zhang

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

Machine Learning · Computer Science 2024-05-01 Fabio A. González , Alejandro Gallego , Santiago Toledo-Cortés , Vladimir Vargas-Calderón

This review aims to draw attention to two issues of concern when we set out to make machine learning work in the chemical and materials domain, i.e., statistical loss function metrics for the validation and benchmarking of data-derived…

Chemical Physics · Physics 2021-01-26 Gaurav Vishwakarma , Aditya Sonpal , Johannes Hachmann

Coarse graining techniques play an essential role in accelerating molecular simulations of systems with large length and time scales. Theoretically grounded bottom-up models are appealing due to their thermodynamic consistency with the…

Computational Physics · Physics 2022-11-01 Blake R. Duschatko , Jonathan Vandermause , Nicola Molinari , Boris Kozinsky

Predictive materials synthesis is the primary bottleneck in realizing new functional and quantum materials. Strategies for synthesis of promising materials are currently identified by time-consuming trial and error approaches and there are…

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years,…

Machine Learning · Computer Science 2023-09-13 Marco Eckhoff , Markus Reiher

Within the past few years, we have witnessed the rising of quantum machine learning (QML) models which infer electronic properties of molecules and materials, rather than solving approximations to the electronic Schrodinger equation. The…

Chemical Physics · Physics 2018-07-17 Bing Huang , Nadine O. Symonds , O. Anatole von Lilienfeld

Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for learned simulations of…