# Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach

@article{Han2020SolvingHE, title={Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach}, author={Jiequn Han and Jianfeng Lu and Mo Zhou}, journal={J. Comput. Phys.}, year={2020}, volume={423}, pages={109792} }

## 29 Citations

A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2022

Reproducing Activation Function for Deep Learning

- Computer ScienceArXiv
- 2021

The proposed reproducing activation function can facilitate the convergence of deep learning optimization for a solution with higher accuracy than existing deep learning solvers for audio/image/video reconstruction, PDEs, and eigenvalue problems.

Interpolating between BSDEs and PINNs - deep learning for elliptic and parabolic boundary value problems

- Computer ScienceArXiv
- 2021

This paper reviews the literature and suggests a methodology based on the novel diffusion loss that interpolates between BSDEs and PINNs, which opens the door towards a unified understanding of numerical approaches for high-dimensional PDEs, as well as for implementations that combine the strengths of BS DEs andPINNs.

Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

- Computer Science
- 2021

A numerical algorithm based on training artiﬁcial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem.

Convergence of the deep BSDE method for coupled FBSDEs

- Computer ScienceProbability, Uncertainty and Quantitative Risk
- 2020

A posteriori error estimation of the solution is provided and it is proved that the error converges to zero given the universal approximation capability of neural networks.

A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems

- Mathematics, Computer ScienceCommunications of the American Mathematical Society
- 2022

It is proved that the convergence rate of the generalization error is independent of dimension and under the a priori assumption that the ground state lies in a spectral Barron space, which is achieved by a fixed point argument based on the Krein-Rutman theorem.

A new efficient approximation scheme for solving high-dimensional semilinear PDEs: Control variate method for Deep BSDE solver

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2022

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Randomized Subspace Iteration

- Mathematics
- 2022

from Randomized Subspace Iteration Samuel M. Greene,1 Robert J. Webber,2, a) James E. T. Smith,3 Jonathan Weare,2, b) and Timothy C. Berkelbach1, 3, c) 1)Department of Chemistry, Columbia University,…

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

- Chemistry, Physics
- 2022

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full…

Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing

- Computer ScienceArXiv
- 2022

A new numerical approximation strategy for parametric approximation problems including the parametric financial pricing problems described above is introduced and it is illustrated by means of several numerical experiments that the introduced approximation strategy achieves a very high accuracy for a variety of high-dimensional parametric approximate problems, even in the L∞-norm.

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