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Computer simulations are invaluable tools for scientific discovery. However, accurate simulations are often slow to execute, which limits their applicability to extensive parameter exploration, large-scale data analysis, and uncertainty…

Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…

Materials Science · Physics 2025-01-08 Alfonso Annarelli , Dario Alfè , Andrea Zen

Quantum nanostructures offer crucial applications in electronics, photonics, materials, drugs, etc. For accurate design and analysis of nanostructures and materials, simulations of the Schrodinger or Schrodinger-like equation are always…

Computational Physics · Physics 2025-07-09 Martin Veresko , Yu Liu , Daqing Hou , Ming-Cheng Cheng

This work presents a direct and highly accurate method to solve ordinary differential equations, in particular the Schr\"odinger equation in one dimension, through the direct substitution of a power series solution to obtain a purely…

Quantum Physics · Physics 2014-09-25 Fabio E. R. Campolim

Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…

Quantum Physics · Physics 2025-06-26 Shi Jin , Nana Liu , Wei Wei

By decomposing the important sampled imaginary time Schr\"odinger evolution operator to fourth order with positive coefficients, we derived a number of distinct fourth order Diffusion Monte Carlo algorithms. These sophisticated algorithms…

Nuclear Theory · Physics 2009-11-06 Harald A. Forbert , Siu A. Chin

Solving the electronic Schr\"odinger equation for strongly correlated systems remains one of the grand challenges in quantum chemistry. Here we demonstrate that Transformer architectures can be adapted to capture the complex grammar of…

Quantum Physics · Physics 2025-10-01 Huan Ma , Bowen Kan , Honghui Shang , Jinlong Yang

We propose a novel gray-box modeling algorithm for physical systems governed by stochastic differential equations (SDE). The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms…

Machine Learning · Statistics 2023-03-22 Tushar , Souvik Chakraborty

In particle physics the simulation of particle transport through detectors requires an enormous amount of computational resources, utilizing more than 50% of the resources of the CERN Worldwide Large Hadron Collider Grid. This challenge has…

High Energy Physics - Experiment · Physics 2021-03-26 Florian Rehm , Sofia Vallecorsa , Kerstin Borras , Dirk Krücker

The rise and fall of artificial neural networks is well documented in the scientific literature of both computer science and computational chemistry. Yet almost two decades later, we are now seeing a resurgence of interest in deep learning,…

Machine Learning · Statistics 2018-08-15 Garrett B. Goh , Nathan O. Hodas , Abhinav Vishnu

The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts…

Computational Physics · Physics 2020-08-26 M. Gastegger , A. McSloy , M. Luya , K. T. Schütt , R. J. Maurer

Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…

Quantum Physics · Physics 2017-09-07 Ilkka Ruokosenmäki , Tapio T. Rantala

When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness…

Machine Learning · Computer Science 2024-09-05 Hartmut Maennel , Oliver T. Unke , Klaus-Robert Müller

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning…

Disordered Systems and Neural Networks · Physics 2019-12-02 Ce Wang , Hui Zhai , Yi-Zhuang You

We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for…

High Energy Physics - Phenomenology · Physics 2020-12-30 M. C. Gordillo , F. De Soto , J. Segovia

The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The…

Computational Physics · Physics 2011-01-28 Jindrich Kolorenc , Lubos Mitas

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

Machine Learning · Computer Science 2022-10-14 Philipp Holl , Vladlen Koltun , Nils Thuerey

In 2011, the fundamental gap conjecture for Schr\"odinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schr\"odinger equation with a convex potential and relative error \epsilon.…

Quantum Physics · Physics 2013-09-26 Anargyros Papageorgiou , Iasonas Petras

Total energies of crystal structures can be calculated to high precision using quantum-based density functional theory (DFT) methods, but the calculations can be time consuming and scale badly with system size. Cluster expansions of total…

Materials Science · Physics 2015-12-31 Qin Gao , Sanxi Yao , Jeff Schneider , Michael Widom

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…

High Energy Physics - Phenomenology · Physics 2020-10-21 Matthew D. Klimek , Maxim Perelstein