Deep Operator BSDE: a Numerical Scheme to Approximate Solution Operators
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Abstract (arXiv)
Motivated by dynamic risk measures and conditional g-expectations, in this work we propose a numerical method to approximate the solution operator given by a Backward Stochastic Differential Equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can check the accuracy of the method.
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References · 9
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
- 2017Solving high-dimensional partial differential equations using deep learningcited by 556
- 2018Convergence of the Deep BSDE Method for Coupled FBSDEscited by 43
- 2020Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learningcited by 22
- 2022LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Datacited by 10
- 2024An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learningcited by 6
- 2018Unbiased deep solvers for linear parametric PDEscited by 5
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