Transcription of DGM: A deep learning algorithm for solving partial di ...
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DGM: A deep learning algorithm for solving partial di ...
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. The algorithm is tested on a class ofhigh-dimensional free boundary PDEs, which we are able to accurately solve in up to 200 algorithm is also tested on a high-dimensional Hamilton-Jacobi-Bellman PDE and Burgers deep learning algorithm approximates the general solution to the Burgers equation for a continuumof different boundary conditions and physical
The algorithm is also tested on a high-dimensional Hamilton-Jacobi-Bellman PDEand Burgers’ equation. The deep learning algorithm approximates the general solution to the Burgers’ equation for a continuum of di erent boundary conditions and physical conditions (which can be …
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