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most citedAdaptive neural network basis methods for partial differential equations with low-regular solutions

1 citations · 1 across the 7 of their papers we have counts for

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math.NA2026

Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem

Yang Zhao, Junxiong Jia, Tao Zhou

This paper addresses infinite-dimensional Bayesian inference for inverse problem of partial differential equations with model parameters in infinite-dimensional Hilbert space. To e…

math.NA2026

Deep Policy Iteration for High-Dimensional Mean-Field Games with Regenerative Reformulation

Shuixin Fang, Shupeng Wang, Zhen Wu +2

This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games (MFG). We reformulate the game as a regenerative problem with deterministic…

math.NA2025

A derivative-free localized stochastic method for very high-dimensional semilinear parabolic PDEs

Shuixin Fang, Changtao Sheng, Bihao Su +1

We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed…

math.NA2025

Explicit Runge-Kutta schemes for Backward Stochastic Differential Equations

Shuixin Fang, Yue Qiu, Weidong Zhao

The Butcher theory provides a powerful tool for analyzing order conditions of Runge-Kutta schemes for ordinary differential equations (ODEs); however, such a theory has not yet bee…

math.NA2025

Deep random difference method for high-dimensional quasilinear parabolic partial differential equations

Wei Cai, Shuixin Fang, Tao Zhou

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for aut…

math.NA20241 cited

Adaptive neural network basis methods for partial differential equations with low-regular solutions

Jianguo Huang, Haohao Wu, Tao Zhou

This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions i…