arXiv Machine Learning
Fast Learning Rates for Physics-Informed Kernel Methods
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv Machine Learning
Jul 30
PIKS: Universal Physics-Informed Kernel Methods
arXiv:2607. 27062v1 Announce Type: cross Abstract: Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models.
arXiv Machine Learning
Aug 4
Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
arXiv:2605. 08170v2 Announce Type: replace Abstract: Neural operators have emerged as a powerful tool for learning mappings between infinite-dimensional function spaces.
arXiv Machine Learning
Jul 23
Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning
arXiv:2607. 15702v2 Announce Type: replace-cross Abstract: We develop a non-asymptotic approximation, sampling, and finite-iteration optimization theory for variational physics-informed approximation of uniformly monotone nonlinear multiscale elliptic equations.
arXiv Machine Learning
Jul 9
Statistical inverse learning and $\ell^1$-regularization
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
arXiv Machine Learning
Jul 8
Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
arXiv:2607. 06287v1 Announce Type: cross Abstract: We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations.
arXiv Machine Learning
Jun 25
A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.