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Publications [#352641] of Jianfeng Lu

Papers Published

  1. Han, J; Lu, J; Zhou, M, Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach, Journal of Computational Physics, vol. 423 (December, 2020) [doi]
    (last updated on 2021/01/25)

    Abstract:
    © 2020 Elsevier Inc. We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks. The eigenvalue problem is reformulated as a fixed point problem of the semigroup flow induced by the operator, whose solution can be represented by Feynman-Kac formula in terms of forward-backward stochastic differential equations. The method shares a similar spirit with diffusion Monte Carlo but augments a direct approximation to the eigenfunction through neural-network ansatz. The criterion of fixed point provides a natural loss function to search for parameters via optimization. Our approach is able to provide accurate eigenvalue and eigenfunction approximations in several numerical examples, including Fokker-Planck operator and the linear and nonlinear Schrödinger operators in high dimensions.

 

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