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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

We introduce a machine learning method in which energy solutions from the Schrodinger equation are predicted using symmetry adapted atomic orbitals features and a graph neural-network architecture. \textsc{OrbNet} is shown to outperform…

A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schr\"odinger equation by solving its integration (or contraction) to the 2-electron space -- a contracted Schr\"odinger equation (CSE) -- on a quantum computer.…

Quantum Physics · Physics 2022-05-05 Scott E. Smart , David A. Mazziotti

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…

Quantum Physics · Physics 2009-10-30 I. E. Lagaris , A. Likas , D. I. Fotiadis

We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schr\"odinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical.…

Computational Physics · Physics 2020-07-21 Jiequn Han , Linfeng Zhang , Weinan E

This paper analyzes local convergence of the block Newton (BN) method introduced in [5, 6] for one-dimensional shallow neural network approximation to functions and diffusion-reaction problems. The BN method consists of the 2x2 block…

Numerical Analysis · Mathematics 2026-03-13 Zhiqiang Cai , Anastassia Doktorova , Robert D. Falgout , César Herrera

In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schr\"odinger equation, which is widely used in fiber-optic communications. The landscape and minimizers of the…

Numerical Analysis · Mathematics 2021-07-20 Yiran Wang , Zhen Li

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a…

The purpose of this paper is to present a method of solving the Shr\"odinger Equation (SE) by Genetic Algorithms and Grammatical Evolution. The method forms generations of trial solutions expressed in an analytical form. We illustrate the…

Neural and Evolutionary Computing · Computer Science 2014-02-25 Khalid jebari , Mohammed Madiafi , Abdelaziz Elmoujahid

We consider a class of one dimensional vector Non-linear Schr$\ddot{o}$dinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of the Schr$\ddot{o}$dinger field. The…

Mathematical Physics · Physics 2023-06-13 Supriyo Ghosh , Pijush K. Ghosh

Given their ability to effectively learn non-linear mappings and perform fast inference, deep neural networks (NNs) have been proposed as a viable alternative to traditional simulation-driven approaches for solving high-dimensional…

Machine Learning · Computer Science 2022-02-16 Sangeeta Srivastava , Samuel Olin , Viktor Podolskiy , Anuj Karpatne , Wei-Cheng Lee , Anish Arora

Finding accurate solutions to the Schr\"odinger equation is the key unsolved challenge of computational chemistry. Given its importance for the development of new chemical compounds, decades of research have been dedicated to this problem,…

Machine Learning · Computer Science 2022-10-12 Leon Gerard , Michael Scherbela , Philipp Marquetand , Philipp Grohs

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

Computational Physics · Physics 2020-07-29 Martin Magill , Andrew M. Nagel , Hendrick W. de Haan

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of…

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive…

Pattern Formation and Solitons · Physics 2025-09-09 Sandy H. S. Herho , Iwan P. Anwar , Faruq Khadami , Rusmawan Suwarman , Dasapta E. Irawan

A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and…

Chemical Physics · Physics 2025-01-22 Daniel Freedman , Eyal Rozenberg , Alex Bronstein

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Machine Learning · Computer Science 2021-01-29 Akshunna S. Dogra , William T Redman

This work presents a machine learning approach to optimize the energy efficiency (EE) in a multi-cell wireless network. This optimization problem is non-convex and its global optimum is difficult to find. In the literature, either simple…

Signal Processing · Electrical Eng. & Systems 2023-12-18 Bile Peng , Karl-Ludwig Besser , Ramprasad Raghunath , Eduard A. Jorswieck

Solving the time-dependent Schr\"odinger equation (TDSE) is pivotal for modeling non-adiabatic electron dynamics, a key process in ultrafast spectroscopy and laser-matter interactions. However, exact solutions to the TDSE remain…

Chemical Physics · Physics 2025-12-29 Bizi Huang , Weizhong Fu , Ji Chen

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…

Machine Learning · Computer Science 2025-05-08 Shuhao Cao , Francesco Brarda , Ruipeng Li , Yuanzhe Xi