AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-20
When Does Cheap Physics Help? Gated Multi-Fidelity Physics-Informed Networks with Provable Sample Savings and Conformal Guarantees
High-fidelity simulations of parametric PDEs are expensive, while cheap low-fidelity models are biased, and it has been unclear when they actually reduce the number of high-fidelity solves. Guided by a sample-complexity analysis, the authors propose GaMF-PINN, a gated multi-fidelity physics-informed network that learns where to trust the low-fidelity model and falls back to physics-only learning elsewhere, paired with a function-level conformal procedure that returns uncertainty bands containing the entire high-fidelity solution with probability at least 1-alpha. On the released MFPDE-Bench, it matches a standard high-fidelity PINN with up to 8x fewer high-fidelity solves, stays robust when the low-fidelity model is deliberately corrupted, and attains nominal coverage where Bayesian PINNs and deep ensembles under-cover.