Complementing Models via Residual Learning

Physics-based models of dynamical systems deviate from observed behavior due to simplifying assumptions, abstraction, epistemic uncertainty, unmodeled variability, couplings with other systems, and environmental influences. We introduce a dynamical state reconstruction architecture that deploys an existing physics-based model as a predictive backbone, enhanced with data-driven residual corrections learned by a self-supervised transformer. The learning protocol relies on epistemic tokenization, representing each observation as a tuple of value, observation coordinate, and epistemic state. The epistemic state distinguishes available evidence from reconstruction queries, providing an explicit learning and inference signal. The learned correction is explicitly bounded, preventing arbitrarily large deviations from the physics-based model predictions. We instantiate the approach using transformer-based state reconstruction of a permanent magnet synchronous machine from multimodal signals, including quantities observed during training but unavailable at inference time. The resulting architecture integrates transparent, interpretable physics-based models with evidence-driven deep learning to close the gap between the reference model's predictions and observed system behavior.