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DGM: A deep learning algorithm for solving partial differentialequationsJustin Sirignano and Konstantinos Spiliopoulos September 7, 2018 AbstractHigh-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfythe differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which iskey since meshes become infeasible in higher dimensions. Instead of forming a mesh, the neural networkis trained on batches of randomly sampled time and space points.
DGM: A deep learning algorithm for solving partial di erential equations Justin Sirignano and Konstantinos Spiliopoulosyzx December 19, 2017 Abstract
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