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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PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
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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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A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data
PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.