Abstract
The integration of machine learning (Keplerian paradigm) and more general artificial intelligence technologies with physical modeling based on first principles (Newtonian paradigm) will impact scientific computing in engineering in fundamental ways. Such hybrid models combine first principle-based models with data-based models into a joint architecture. This paper will give some background, explain trends and showcase recent achievements from an applied mathematics and industrial perspective. Examples include characterization of superconducting accelerator magnets by blending data with physics, data-driven magnetostatic field simulation without an explicit model of the constitutive law, and Bayesian free-shape optimization of a trace pair with bend on a printed circuit board.
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Notes
- 1.
We do not delve into regularity considerations or functional analytical frameworks here.
- 2.
This formulation was proposed on the Compumag Conference 1983 in Genoa. The related variational principle was called “Ligurian”, in honor of the Genoa region, and in similarity to “Lagrangian”. [21, p. 49].
- 3.
In this model problem, an array of slot machines is considered. The gambler must balance the goal to find the slot machine with the highest gain (exploitation) with the goal to achieve good results on every play (exploration).
- 4.
For simplicity evaluated at a fixed frequency of f = 500 MHz.
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Acknowledgements
Support in preparing the examples as well as inspiring discussions with the following colleagues are acknowledged: Armin Galetzka (TU Darmstadt); Andreas Klaedtke, **aobai Li, Manuel Schmidt (Bosch Corporate Research); Melih Kandemir, Zico Kolter (Bosch Center for Artificial Intelligence); Melvin Liebsch (CERN).
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Kurz, S. (2021). Hybrid Modeling: Towards the Next Level of Scientific Computing in Engineering. In: van Beurden, M., Budko, N., Schilders, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-84238-3_25
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