Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach
This enables super-resolution for experimental data and low-resolution simulations in fluid dynamics, offering a novel approach to a domain-specific bottleneck.
The paper tackles the problem of inferring high-resolution solutions from sparse observations in chaotic and turbulent fluid dynamics using partial differential equations, achieving this without requiring high-resolution training data by incorporating physical constraints into a convolutional neural network.
We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations. Results are shown for a chaotic and turbulent fluid motion, whose solution is high-dimensional, and has fine spatiotemporal scales. We show that, by constraining prior physical knowledge in the CNN, we can infer the unresolved physical dynamics without using the high-resolution dataset in the training. This opens opportunities for super-resolution of experimental data and low-resolution simulations.