PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations. (arXiv:2204.02583v1 [stat.ML])

In this work, a Gaussian process regression(GPR) model incorporated with
given physical information in partial differential equations(PDEs) is
developed: physics-assisted Gaussian processes(PAGP). The targets of this model
can be divided into two types of problem: finding solutions or discovering
unknown coefficients of given PDEs with initial and boundary conditions. We
introduce three different models: continuous time, discrete time and hybrid
models. The given physical information is integrated into Gaussian process
model through our designed GP loss functions. Three types of …

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