PIKS: Universal Physics-Informed Kernel Methods
Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models. While physics-informed neural networks (PINNs) dominate empirical applications, the complexity of neural network architectures and optimization landscapes hinders the development of a corresponding learning theory. In turn, kernel methods offer an appealing alternative with closed-form solutions and analytical tractability, yet existing guarantees primarily cover the well-specified setting where the target belongs to the native Reproducing Kernel Hilbert Space (RKHS). This imposes unrealistic regularity assumptions that physical targets often fail to s...
| Authors | Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria et al. |
|---|---|
| Primary category | stat.ML |
| Published | 29 July 2026 |
| Last updated at source | 29 July 2026 |
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