Physics-Informed Machine Learning

Understanding the Role of Domain Knowledge in Bayesian Optimization under Small-Data Constraints

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Abstract

Bayesian optimization (BO) enables data-efficient optimization of expensive black-box functions, yet real-world applications often provide partial domain knowledge from physical models or expert intuition. It remains unclear how the placement of such knowledge within the BO pipeline affects performance in small-data regimes. We present a systematic empirical comparison of three knowledge-injection strategies: surrogate-level integration, probabilistic priors over the search space, and acquisition-level regularization. The approaches are evaluated across different synthetic and materials-inspired multi-objective tasks under limited evaluation budgets using cumulative normalized hypervolume regret. Results show that surrogate-level injection can accelerate early learning when knowledge is well aligned but is sensitive to misspecification, whereas acquisition-level regularization provides more robust guidance under imperfect knowledge. Prior-based strategies yield only modest improvements over standard BO.

How to Cite:

Schuscha, B., Rohrhofer, F., Geiger, B. & Scheiber, D., (2026) “Understanding the Role of Domain Knowledge in Bayesian Optimization under Small-Data Constraints”, Proceedings of the Austrian Symposium on AI, Robotics, and Vision 3(1), 152-155.