A video-to-PDE pipeline extracts the model u_t + v(t)·∇u = 9.005|∇u|^2 + 0.666Δu from grayscale ink-plume footage, outperforming advection-diffusion baselines on held-out frames and reducing to linear form via Cole-Hopf transformation.
Pysindy: A comprehensive python package for robust sparse system identification
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Fourier Weak SINDy selects orthogonal sinusoidal test functions using multitaper spectral estimation to make weak-form SINDy robust and derivative-free for equation discovery in dynamical systems.
A mixed-integer quadratically constrained optimization learns interpretable stable dynamical models and their Lyapunov functions from data by enforcing stability constraints during training.
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From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamics
A video-to-PDE pipeline extracts the model u_t + v(t)·∇u = 9.005|∇u|^2 + 0.666Δu from grayscale ink-plume footage, outperforming advection-diffusion baselines on held-out frames and reducing to linear form via Cole-Hopf transformation.
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Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
Fourier Weak SINDy selects orthogonal sinusoidal test functions using multitaper spectral estimation to make weak-form SINDy robust and derivative-free for equation discovery in dynamical systems.
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Learning interpretable and stable dynamical models via mixed-integer Lyapunov-constrained optimization
A mixed-integer quadratically constrained optimization learns interpretable stable dynamical models and their Lyapunov functions from data by enforcing stability constraints during training.