Hybrid modeling design patterns

• Published in: Journal of mathematics in industry Vol. 14; no. 1; pp. 3 - 36
• Main Authors: Rudolph, Maja, Kurz, Stefan, Rakitsch, Barbara
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024; Springer Nature B.V; SpringerOpen
• Subjects: Applications of Mathematics; Climate models; Datasets; Design patterns; First principles; Hybrid modeling; Hypotheses; Knowledge; Math. Appl. in Environmental Science; Mathematical and Computational Biology; Mathematical and Computational Engineering; Mathematical Methods in Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Physics; Physics-inspired AI; Principles; Scientists; Survey; Physics-inspired AI; Hybrid modeling; Design patterns
• ISSN: 2190-5983; 2190-5983
• DOI: 10.1186/s13362-024-00141-0

Design patterns provide a systematic way to convey solutions to recurring modeling challenges. This paper introduces design patterns for hybrid modeling, an approach that combines modeling based on first principles with data-driven modeling techniques. While both approaches have complementary advantages there are often multiple ways to combine them into a hybrid model, and the appropriate solution will depend on the problem at hand. In this paper, we provide four base patterns that can serve as blueprints for combining data-driven components with domain knowledge into a hybrid approach. In addition, we also present two composition patterns that govern the combination of the base patterns into more complex hybrid models. Each design pattern is illustrated by typical use cases from application areas such as climate modeling, engineering, and physics.