Residual-Aware Output Representations for Scientific Surrogates

Scientific surrogates are commonly trained to predict a complete physical response, whereas designs care about performance metrics derived from that response. This creates a distinct failure mode when a design-relevant metric is controlled by a small physical residual recovered through cancellation. We propose the residual-aware output representation method, where the surrogate exposes the small residual as an explicit output coordinate, reconstructs the complete response through an invertible transformation, and retains the original response-space training objective. In radio-frequency passives, exposing dissipation through impedance-like coordinates reduces relative $Q$ error by $3.3\times$ on differential inductors and $6.7\times$ on six-port transformers with minimal change in scattering-response error; it also reduces circuit-level prediction violations. We further validate the proposed method on nanophotonic metasurfaces, reducing relative absorptance error. These results establish residual-aware output representation as a practical approach to cancellation-sensitive scientific problems.