Reproduce “Physics-informed kernel learning” on OpenResearch
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About this paper
Nathan Doumèche, Francis Bach, Gérard Biau, Claire Boyer
PIKL approximates physics-informed regression with deterministic low-frequency Fourier modes, turning a PDE-dependent kernel calculation into a finite-dimensional linear solve. In a one-dimensional wave-equation test, it reports relative L2 error 8.70×10−4, versus 4.52×10−1 for vanilla PINNs and 1.73×10−3 for NTK-optimized PINNs. The comparison uses fewer points and parameters; traditional solvers outperform PIKL on the clean wave problem.
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