More and more work and codes are developed to solve high-dimensional PDEs, especially with the tools from deep learning. Here we collect a few code repositories to present the advancement of the field and promote the exploration of new problems. Suggestions and contributions are welcome to this page, including the codes you would like to share relevant to high-dimensional PDEs.
BSDE/Feynman-Kac related:
- Solving high-dimensional partial differential equations using deep learning (Deep BSDE solver)
- Numerically solving parametric families of high-dimensional Kolmogorov partial differential equations via deep learning
- Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
- Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
- Actor-critic method for high dimensional static Hamilton–Jacobi–Bellman partial differential equations based on neural networks
- Deep xVA solver — A neural network based counterparty credit risk management framework
- Solving high-dimensional parabolic PDEs using the tensor train format
- Deep learning algorithms for hedging with frictions
- Robust SDE-based variational formulations for solving linear PDEs via deep learning
Control and HJB equation:
Game:
- A machine learning framework for solving high-dimensional mean field game and mean field control problems
- Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games
- Random features for high-dimensional nonlocal mean-field games
Many-electron Schrödinger equation:
Others: