Related papers: Schr\"{o}dingerNet: A Universal Neural Network Sol…
Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining…
We show a new family of neural networks based on the Schr\"{o}dinger equation (SE-NET). In this analogy, the trainable weights of the neural networks correspond to the physical quantities of the Schr\"{o}dinger equation. These physical…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
Due to the good performance of neural networks in high-dimensional and nonlinear problems, machine learning is replacing traditional methods and becoming a better approach for eigenvalue and wave function solutions of multi-dimensional…
Solving the Schr\"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron…
In this work we approach the Schr\"odinger equation in quantum wells with arbitrary potentials, using the machine learning technique. Two neural networks with different architectures are proposed and trained using a set of potentials,…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…
[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schr\"odinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the…
We introduce the Schrodinger Neural Network (SNN), a principled architecture for conditional density estimation and uncertainty quantification inspired by quantum mechanics. The SNN maps each input to a normalized wave function on the…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…
Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…
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…
The nonlinear Schr\"odinger equation (NLSE) is a fundamental model for wave dynamics in nonlinear media ranging from optical fibers to Bose-Einstein condensates. Accurately estimating its parameters, which are often strongly correlated,…
Nuclear quantum effects such as zero-point energy and hydrogen tunnelling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei…
Deep neural network (DNN) and auto differentiation have been widely used in computational physics to solve variational problems. When DNN is used to represent the wave function to solve quantum many-body problems using variational…
It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…
We demonstrate, for the first time, that neural scaling laws can deliver near-exact solutions to the many-electron Schr\"odinger equation across a broad range of realistic molecules. This progress is enabled by the Lookahead Variational…
In this work, we solve inverse problems of nonlinear Schr\"{o}dinger equations that can be formulated as a learning process of a special convolutional neural network. Instead of attempting to approximate functions in the inverse problems,…