
Deep learningbased numerical methods for highdimensional parabolic partial differential equations and backward stochastic differential equations
We propose a new algorithm for solving parabolic partial differential eq...
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On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
We propose novel connection between several neural network architectures...
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Deep Signature FBSDE Algorithm
We propose a deep signature/logsignature FBSDE algorithm to solve forwa...
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SelectNet: Selfpaced Learning for Highdimensional Partial Differential Equations
The residual method with deep neural networks as function parametrizatio...
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DerivativeInformed Projected Neural Networks for HighDimensional Parametric Maps Governed by PDEs
Manyquery problems, arising from uncertainty quantification, Bayesian i...
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Towards Robust and Stable Deep Learning Algorithms for Forward Backward Stochastic Differential Equations
Applications in quantitative finance such as optimal trade execution, ri...
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The Deep Minimizing Movement Scheme
Solutions of certain partial differential equations (PDEs) are often rep...
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FBSDE based neural network algorithms for highdimensional quasilinear parabolic PDEs
In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs). The algorithms relies on a learning process by minimizing the pathwise difference of two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively. The proposed algorithms demonstrate a convergence for a 100dimensional Black–Scholes–Barenblatt equation at a rate similar to that of the Euler–Maruyama discretization of the FBSDEs.
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