Physics-Informed Machine Learning
Authors: Paul Horvath (CD Laboratory for Physics-driven Machine Learning in lndustrial Applications) , Marian Staggl (CD Laboratory for Physics-driven Machine Learning in lndustrial Applications) , Stefan Posch (Institute of Thermodynamics and Sustainable Propulsion Systems, Graz University of Technology)
Accurate surrogate modeling in engineering is often constrained by the high computational cost of generating training data from large scale numerical simulations. In many industrial applications, only a limited number of simulations can be afforded, which severely restricts the achievable surrogate accuracy, particularly in high dimensional parametric spaces. A promising approach to mitigate this curse of dimensionality is the incorporation of derivative information into surrogate training, which can be obtained efficiently via graph based implementations or adjoint calculations. This additional information captures local function structure, offering the potential to significantly improve data efficiency. In this work, we quantify the potential gains of derivative-enhanced training both theoretically and numerically, using a representative linear elasticity problem and an analytical benchmark. The findings provide guidance on the efficiency improvements achievable and the order of derivatives that yields the greatest benefit.
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How to Cite: Horvath, P. , Staggl, M. & Posch, S. (2026) “Derivative-Enhanced Training for Data-efficient Surrogate Modeling”, Proceedings of the Austrian Symposium on AI, Robotics, and Vision. 3(1).