Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach

2023/06/19 by Daniel Kelshaw, Kelshaw, Daniel, Luca Magri +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.2306.10990

openalex publication_date 2023/06/19 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

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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