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The numerical solution of a linear Schr\"odinger equation in the semiclassical regime is very well understood in a torus $\mathbb{T}^d$. A raft of modern computational methods are precise and affordable, while conserving energy and…

Numerical Analysis · Mathematics 2022-01-17 Arieh Iserles , Karolina Kropielnicka , Katharina Schratz , Marcus Webb

Deep learning has deeply changed the paradigms of many research fields. At the heart of chemical and physical sciences is the accurate ab initio calculation of many-body wavefunction, which has become one of the most notable examples to…

Chemical Physics · Physics 2025-04-01 Yubing Qian , Xiang Li , Zhe Li , Weiluo Ren , Ji Chen

We demonstrate a machine learning approach designed to extract hidden chemistry/physics to facilitate new materials discovery. In particular, we propose a novel method for learning latent knowledge from material structure data in which…

Materials Science · Physics 2021-08-03 Tien-Cuong Nguyen , Van-Quyen Nguyen , Van-Linh Ngo , Quang-Khoat Than , Tien-Lam Pham

The hydrogen molecule can be used for determination of physical constants and for improved tests of the hypothetical long range force between hadrons, which requires a sufficiently accurate knowledge of the molecular levels. For this…

Chemical Physics · Physics 2016-05-25 Krzysztof Pachucki , Jacek Komasa

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

Disordered Systems and Neural Networks · Physics 2024-12-24 Yixiong Ren , Jianhui Zhou

Accurately solving the Schr\"odinger equation for intricate systems remains a prominent challenge in physical sciences. A paradigm-shifting approach to address this challenge involves the application of artificial intelligence techniques.…

Quantum Physics · Physics 2024-04-05 Honghui Shang , Chu Guo , Yangjun Wu , Zhenyu Li , Jinlong Yang

Scientific machine learning has become an increasingly important tool in materials science and engineering. It is particularly well suited to tackle material problems involving many variables or to allow rapid construction of surrogates of…

Numerical Analysis · Mathematics 2023-05-25 Ting Wang , Jaroslaw Knap

We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…

Numerical Analysis · Mathematics 2021-08-31 L. Al Sakkaf , U. Al Khawaja

Reliable description of bond breaking remains a major challenge for quantum chemistry due to the multireferential character of the electronic structure in dissociating species. Multireferential methods in particular suffer from large…

Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr\"odinger equation to obtain molecular energies has been demonstrated to scale polynomially with system…

Quantum Physics · Physics 2019-03-27 Hefeng Wang , Sabre Kais , Alán Aspuru-Guzik , Mark R. Hoffmann

In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schr\"odinger equation. The new methodology is based on the requirement of vanishing the…

Numerical Analysis · Mathematics 2008-11-18 Z. A. Anastassi , D. S. Vlachos , T. E. Simos

Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schr\"odinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic…

Nuclear Theory · Physics 2020-05-01 Stefano Gandolfi , Diego Lonardoni , Alessandro Lovato , Maria Piarulli

In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo estimation with the evaluation of a deep neural network. Once…

Numerical Analysis · Mathematics 2021-02-18 Thomas Gerstner , Bastian Harrach , Daniel Roth , Martin Simon

Collisions at high-energy particle colliders are a traditionally fruitful source of exotic particle discoveries. Finding these rare particles requires solving difficult signal-versus-background classification problems, hence machine…

High Energy Physics - Phenomenology · Physics 2015-06-18 Pierre Baldi , Peter Sadowski , Daniel Whiteson

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods.…

Chemical Physics · Physics 2024-12-13 Yaolong Zhang , Bin Jiang , Hua Guo

We consider the linear Schr\"odinger equation and its discretization by split-step methods where the part corresponding to the Laplace operator is approximated by the midpoint rule. We show that the numerical solution coincides with the…

Numerical Analysis · Mathematics 2009-01-12 Arnaud Debussche , Erwan Faou

The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…

Strongly Correlated Electrons · Physics 2011-06-27 Maho Nakata , Mituhiro Fukuda , Katsuki Fujisawa

In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all…

Chemical Physics · Physics 2021-03-15 Julia Westermayr , Michael Gastegger , Philipp Marquetand

In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…

Numerical Analysis · Mathematics 2017-07-20 Sambasiva Rao Chinnamsetty , Michael Griebel , Jan Hamaekers

Deep Learning has enabled many advances in machine learning applications in the last few years. However, since current Deep Learning algorithms require much energy for computations, there are growing concerns about the associated…

Machine Learning · Computer Science 2023-03-06 Vanessa Mehlin , Sigurd Schacht , Carsten Lanquillon