The paper proposes a physics‑informed kernel design for support vector regression, using Green’s function analogies and Jackson‑Chebyshev spectral methods to construct a positive‑semidefinite kernel without requiring exact correspondence to a physical propagator. The resulting Jackson‑damped Chebyshev kernel provides an explicit feature map and a spectral prior tailored to structured observables. The authors benchmark the kernel on several physical regression tasks—including copper conductivity, Dirac‑like band dispersion, quartic‑oscillator energy levels, photonic‑crystal transmission, and Fibonacci‑chain transmission—using nested validation, learning curves, and comparisons to random‑forest, multilayer‑perceptron, and Nyström baselines.
arXiv:2607. 27062v1 Announce Type: cross Abstract: Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models.
arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.
arXiv:2606. 21199v2 Announce Type: replace-cross Abstract: We introduce a semi-parametric framework for nonlinear system identification, which decouples discrepancy functions from physics-based components.
arXiv:2508. 19437v2 Announce Type: replace-cross Abstract: The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive.
arXiv:2602. 23006v2 Announce Type: replace-cross Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations.
arXiv:2510. 19399v2 Announce Type: replace Abstract: Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs).
arXiv:2606. 00401v1 Announce Type: cross Abstract: Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies.
arXiv:2506. 15199v4 Announce Type: replace Abstract: While there are many applications of ML to scientific problems that look promising, visuals can be deceiving.
arXiv:2608. 14619v1 Announce Type: new Abstract: This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture.
arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.
arXiv:2601. 17090v2 Announce Type: replace-cross Abstract: Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps.
The paper introduces a method for selecting the best neural‑operator model during deployment without needing high‑fidelity reference solutions. By using a squared Hilbert‑space loss, the authors show that ranking a finite library of models depends only on the low‑dimensional span of candidate differences, enabling simultaneous scoring of all models with a single anchor‑based linearized response of the governing equation. This shared physical diagnostic accurately recovered over 99.6% of pairwise preferences and 99.0% of optimal checkpoints across diverse Fourier and convolutional operator libraries for fluid, reaction‑diffusion, and wave dynamics, and often outperformed the best individual candidates.