Neural actor-critic method for high-dimensional HJB PDEs converges in Sobolev space to an infinite-dimensional ODE whose fixed points solve the stochastic control problem under a convexity-like Hamiltonian assumption, with numerical success up to 200 dimensions.
Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations
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A high-level outline is given for a unified theory that reduces learning to a small set of ideas from dynamical systems, geometry, and physics via definitions of solvable problems and parametrized methods.
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Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies
Neural actor-critic method for high-dimensional HJB PDEs converges in Sobolev space to an infinite-dimensional ODE whose fixed points solve the stochastic control problem under a convexity-like Hamiltonian assumption, with numerical success up to 200 dimensions.
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Man, Machine, and Mathematics
A high-level outline is given for a unified theory that reduces learning to a small set of ideas from dynamical systems, geometry, and physics via definitions of solvable problems and parametrized methods.