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

Understand

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.