A new arXiv paper offers a more principled way to pick machine learning kernels: borrow the math structure of physics, not just the vocabulary.
The paper proposes a physics-informed strategy for choosing kernels in support vector regression, using the spectral structure of Green's functions as a design cue without requiring an exact match between the kernel and a real physical propagator. Its main contribution is a Jackson-damped Chebyshev kernel, adapted from the kernel polynomial method used in condensed-matter physics, which produces a valid positive-semidefinite Gram matrix by construction and an inspectable spectral prior. The authors test standard and custom SVR models against five physical systems: copper-conductivity proxies, Dirac-like band dispersion, quartic-oscillator energy levels, photonic-crystal transmission, and Fibonacci-chain transmission. Results are checked with repeated nested validation, learning curves, comparisons to random-forest and multilayer-perceptron baselines, and low-rank Nystrom approximations.
Kernel selection for regression, as the paper itself notes, is usually heuristic trial and error rather than a principled choice. Tying kernel design to physics-derived spectral structure gives a defensible starting point instead of a guess, which matters most when training data for physical observables is scarce.
That's a lower bar than it sounds: the paper doesn't claim to reverse-engineer physics, just to replace the usual pick-a-standard-kernel guesswork with something inspectable and provably valid.