Deep Splitting Method for Parabolic PDEs
Christian Beck, S. Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
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.
Topics & Concepts
MathematicsOperator splittingNonlinear systemApplied mathematicsSequence (biology)Parabolic partial differential equationOperator (biology)Partial differential equationNumerical analysisGraphMathematical optimizationAlgorithmMathematical analysisDiscrete mathematicsGeneticsQuantum mechanicsBiochemistryPhysicsChemistryGeneRepressorTranscription factorBiologyModel Reduction and Neural NetworksStochastic processes and financial applicationsAdvanced Numerical Methods in Computational Mathematics