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A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han, Arnulf Jentzen, Weinan E
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of t…
Deep Picard Iteration for High-Dimensional Nonlinear PDEs
Jiequn Han, Wei Hu, Jihao Long +1
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies…
A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem
Mo Zhou, Jiequn Han, Manas Rachh +1
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the…
Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
Weinan E, Jiequn Han, Arnulf Jentzen
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonli…
Universal approximation of symmetric and anti-symmetric functions
Jiequn Han, Yingzhou Li, Lin Lin +3
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering…
Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, Weinan E
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult pr…
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Weinan E, Jiequn Han, Arnulf Jentzen
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analog…