Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations

We propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary both in space and time. In the first inverse problem, we are given data that is offset by spatially varying systematic error (i.e., the bias, also known as the epistemic uncertainty). The task is to uncover from the biased data the true state, which is the solution of the PDE. In the second inverse problem, …

cnn convolutional neural network convolutional neural networks cs.lg data differential error network networks neural network neural networks physics physics.flu-dyn solve space space and time types