GraphBC: Graph-Embedded Bias Correction for Differentiable Hybrid Simulators under Model-Plant Mismatch

Hybrid simulators combine mechanistic modules that are built on simplifying assumptions with data-driven modules learned from noisy or incomplete data. Local model–plant mismatches therefore compound through multi-stage computation, creating a dilemma: calibrating each module independently keeps intermediate states physically meaningful but leaves large terminal errors, whereas end-to-end training reduces terminal errors by letting modules compensate for one another's mismatch, at the cost of intermediate states and parameters losing their physical meaning. To address this dilemma, we propose Graph-embedded Bias Correction (GraphBC), which represents a hybrid simulator as a differentiable computation graph and embeds a learnable correction at an internal node, trained jointly with the simulator. We decompose simulation errors into propagated and local components and derive upper bounds along the error propagation. We then derive a gradient-alignment condition under which terminal supervision also improves intermediate states. Finally, we establish a turning-point criterion for correction placement in scaling-compatible chains. We evaluate GraphBC on two simulators driven by real-world data. On a freeway traffic simulator, it reduces terminal error by 29–43% relative to end-to-end training while shifting simulator parameters about 37% less, and gradient alignment identifies which intermediate states improve. On an industrial-scale ride-hailing simulator, it reduces terminal MAPE by 68% while preserving the physical meaning of intermediate states.