| Abstract: |
| While data-driven methods have advanced the discovery of governing equations, extracting robust partial differential equations from real-world data remains challenging. Here we present a Fourier-based approach to rediscover a shallow water-equation akin to the Korteweg-De Vries (KdV) equation using only video footage of solitons.
The Fourier-multiplier technique is also compared to another distinct method, weak-form sparse identification of nonlinear dynamics (WSINDy), which independently recover the same PDE, confirming its inherent structure in the data. We validate the discovered equation by solving it forward and comparing it to unseen experimental cases. |
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