Charlot Lab · PINN × MPC · verify-first control
A learned surrogate of the plant's dynamics (a DD-PINN-style flow map — predict the next state in one pass, initial condition exact by construction) is the model inside model-predictive control. It plans by rolling the surrogate forward. The verify-first twist: every plan carries a certified trust band — a rigorous bound on how far the surrogate can drift from the true dynamics — so you know exactly how far ahead to believe it, and the certificate voids the moment the state leaves the region the surrogate was trained on.
P2 of the verify-first track · band B(t)=ε(Lᵗ−1)/(L−1), sound in-distribution · surrogate trained offline, MPC + certificate run live here
The plan is the gold dashed line; the gold tube around it is the certified trust band, which starts a hair wide (the next executed step is certified to ≤ ~0.02) and fans out with the horizon — so you trust the immediate action tightly and re-plan every step rather than believe a distant prediction. Press kick to shove the state past the dashed trust region: the surrogate is now extrapolating, the certificate voids (red), and the honest move is to distrust the plan until the state returns in-distribution. This is verify-first applied to the MODEL: a learned surrogate is only as good as its certificate, and the certificate names its own domain of validity. Honest scope: on this 2-D toy the surrogate is not faster than the true integrator — the large surrogate speedups (≈466× soft-robot MPC, ≈44,000× Cosserat-rod) are real only for stiff, soft, or high-DOF plants; here we demonstrate the certified-surrogate-in-the-loop mechanism, not the speedup. Nano, single-seed, simulation.