When Does Cheap Physics Help? Gated Multi-Fidelity Physics-Informed Networks with Provable Sample Savings and Conformal Guarantees
Read the original on arXiv Machine Learning →The paper investigates when inexpensive low‑fidelity (LF) physics models can reduce the number of costly high‑fidelity (HF) simulations needed for accurate solutions of parametric partial differential equations. It derives a sample‑complexity bound showing that learning the HF field via its discrepancy from the LF model can cut HF samples by a factor of κ^{2γ}, where κ is the complexity ratio and γ the effective‑dimension exponent, and confirms this scaling in a kernel setting. Guided by this theory, the authors introduce GaMF‑PINN, a gated multi‑fidelity physics‑informed neural network that selectively trusts the LF model and falls back to physics‑only learning when necessary, coupled with a conformal uncertainty procedure that guarantees coverage of the HF solution. The method is evaluated on the newly released MFPDE‑Bench, achieving HF‑PINN accuracy with up to eight times fewer HF solves, robustness to corrupted LF models, and reliable uncertainty estimates compared to Bayesian PINNs and deep ensembles.
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