# Physics-Informed Support Vector Kernels via Green-Function Analogies and Jackson-Chebyshev Spectral Design

arXiv: https://arxiv.org/abs/2502.11153 · HTML: https://mlsanity.com/paper/2502.11153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Builds on (most cited first, 4 of 4)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems](https://mlsanity.com/paper/2101.07206/) (2020)

## Abstract (arXiv)

Kernel selection for regression of physical observables is often heuristic. We investigate a physics-informed strategy in which functional forms and spectral structures associated with Green's functions motivate kernel selection without requiring an exact identification between a machine-learning kernel and a physical propagator. The principal construction is a Jackson-damped Chebyshev kernel inspired by the kernel polynomial method (KPM); its explicit feature map yields a positive-semidefinite Gram matrix by construction and provides an inspectable spectral prior for structured observables. We evaluate standard and custom SVR models on copper-conductivity proxies, local Dirac-like band dispersion, quartic-oscillator energy levels, photonic-crystal transmission, and Fibonacci-chain transmission using repeated nested validation, learning curves, random-forest and multilayer-perceptron baselines, and low-rank Nystr"om tests where relevant. The framework is intended for finite-data regression of precomputed observables while boundary conditions remain part of the physical model that generates those observables.