arXiv:2607. 27062v1 Announce Type: cross Abstract: Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models.
By Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria, Lorenzo Rosasco
arXiv:2505. 07068v2 Announce Type: replace-cross Abstract: In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data.
By Jinchao Feng, Sui Tang
arXiv:2604. 20141v2 Announce Type: replace Abstract: We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection.
By Zhiheng Chen, Urban Fasel, Anastasia Bizyaeva
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.
By Nan-Hong Kuo, Renata Wong
The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.
By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen