Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements

2019/10/21 by Chen, Xiaoli, Duan, Jinqiao, Karniadakis, George Em · 1 citation
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1910.09098

Abstract

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a nonlinear advection-diffusion-reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimize the hyper-parameters of sPINN by using the Bayesian optimization method (meta-learning), and compare the results with the empirically selected hyper-parameters of sPINN.

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