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Structured Extrema Errors in Classical Surrogates for Viscous Burgers: A Physics-Consistent Interpretation

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

We study the local errors of classical machine-learning surrogate models, which approximate the time evolution of the one-dimensional viscous Burgers equation. Four models are compared on the same prediction task, using the spatial grid values directly: radial basis function (RBF) kernel ridge regression (KRR), linear Ridge, ExtraTrees, and Random Forests. Across all four models, the one-step residual, defined here as the true value minus the predicted value at each grid point, forms clear curved branches near predicted maxima and minima. A more detailed analysis of KRR shows that these errors

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