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

• URL: http://arxiv.org/abs/2306.10990v1
• Date: Mon, 19 Jun 2023 15:00:04 GMT
• Title: Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach
• Authors: Daniel Kelshaw, Luca Magri
• Abstract summary: We propose a physics-constrained convolutional neural network (CNN) to infer the high-resolution solution from sparse observations of nonlinear partial differential equations. We show that, by constraining prior physical knowledge in the dataset, we can infer the unresolved physical dynamics without using the high-resolution training.
• Score: 6.85316573653194
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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