Discovery of PDEs driven by data with sharp gradient or discontinuity
COMPUTERS & MATHEMATICS WITH APPLICATIONS(2023)
Abstract
In the data-driven discovery of partial differential equations, previous researchers have successfully employed various methods to derive estimation of parameters from smooth data, but not from data with sharp gradient or discontinuity. To capture the sharp gradient/discontinuous part in data, we introduce a non-zero mean function in terms of the Sigmoid function in the Gaussian process prior. We test the method using noise-free and noisy data on the regression problem and the inverse problem of Burgers' equation, inviscid Burgers' equation, and the nonlinear wave system (NLWS), and verify its effectiveness and robustness.
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Key words
System identification,Partial differential equations,Gaussian process,Discontinuous data,Machine learning
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