A randomized Taylor-mode jet pushforward that estimates arbitrary differential operator contractions without forming the full derivative tensor.
Deep splitting method for parabolic PDEs
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abstract
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high-dimensional PDEs. We test the method on different examples from physics, stochastic control and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times.
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Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators
A randomized Taylor-mode jet pushforward that estimates arbitrary differential operator contractions without forming the full derivative tensor.