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Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach
Published 19 Jun 2023 in physics.flu-dyn and cs.LG | (2306.10990v1)
Abstract: 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.
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