A unified utility function-based framework for prior-informed surrogate modeling

Edvy, András and Kummer, Alex and Abonyi, János (2026) A unified utility function-based framework for prior-informed surrogate modeling. JOURNAL OF PROCESS CONTROL, 165. p. 103785. ISSN 09591524

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Abstract

Modern energy infrastructures operate under nonlinear, time-varying conditions and therefore require reliable surrogate models for optimization, predictive control and health monitoring. Existing approaches are brittle: first-principles simulators degrade under parameter drift and imperfect multiscale physics, while purely datadriven methods require large datasets and extrapolate poorly. We propose the Utility-balanced Prior-informed Model (UPriMo), a general training objective that integrates prior knowledge — such as physical laws, topology constraints, operating envelopes and expert heuristics — directly into the loss of any differentiable learner. UPriMo maps each prior residual to a bounded utility and minimizes data misfit plus utility shortfall. This yields automatic trade-offs between data and priors without manual weighting and recovers physics-informed learning as special cases. We demonstrate UPriMo on two energy-relevant problems. First, for stationary laminar pipe flow, a neural surrogate trained on five noisy velocity measurements satisfies Navier–Stokes, boundary and monotonicity constraints, and reduces mean-squared error by an order of magnitude compared with datadriven baselines. Second, for electric water-heater dynamics, nonlinear autoregressive models with exogenous inputs (NARX) augmented with steady-state and monotonicity priors remain stable over 1400-step free runs, whereas unconstrained models diverge. Across both problems, UPriMo improves accuracy, noise robustness and physical plausibility while remaining compatible with standard ML frameworks. Because the utilities are problem-independent, the framework supports a single recipe from component-level surrogates to system-level AI-based forecasting and control in future energy systems.

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