Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization

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fPINNs: Fractional Physics-Informed Neural Networks (2018, neutral): “The first category exploits only the information of observed data in the spatio-temporal domain and employs surrogate models such as Gaussian process regression (GP regression) [30], stochastic collocation methods [49, 50], and feedforward neural networks (NNs) [9, 11] to approximate the mapping fro”
Neural-net-induced Gaussian process regression for function approximation and PDE solution (2018, methodology): “Specifically, so far GP regression has been successfully applied to solution of PDEs including linear and nonlinear forward problems [6] as well as inverse problems [9,10].”
Machine Learning of Space-Fractional Differential Equations (2018, methodology): “Our work differs from [21] in that we do not repeatedly solve the forward problem, and from [10] in that we do not place a prior on the fractional order or on other parameters; rather, the parameters are inferred by placing a prior and training on the solution and right-hand side of the equation.”