Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential–Algebraic Systems
Neural surrogates for stiff differential-algebraic equations (DAEs) face two key challenges: soft-constraint methods leave algebraic residuals that stiffness amplifies into large errors, while hard-constraint methods require trajectory data from computationally expensive stiff integrators. We introduce an extended Newton implicit layer that enforces algebraic consistency and quasi-steady-state reduction within a single differentiable solve. Given slow-state predictions from a physics-informed DeepONet, the proposed layer recovers fast and algebraic states, eliminates the stiffness-amplification pathway within each time window, and reduces the […]