Physics-Informed Machine Learning

The term physics-informed machine learning comprises methods from the field of machine learning which integrate physical knowledge into the learning process. This increases the interpretability of the models while simultaneously reducing the amount of required data, which is often associated with great (computational) costs in engineering applications and thus scarce. Consequently, physics-informed machine learning is particularly attractive for computational engineers.

Schematic of a physics-informed neural network There are different ways of how the underlying physics of a problem can be integrated, e.g., including a physics-based regularizer into the loss function of a neural network gives rise to methods from the field of physics-informed neural networks (PINNs). We use PINNs, to create fast-to-evaluate surrogate models, e.g., for enabling (hybrid) digital twins or the application in multi-query scenarios, or to solve inverse parameter estimation problems.

Key Publications

Trávníková, V., Wolff, D., Dirkes, N., Elgeti, S., von Lieres, E., Behr, M. (2024): A model hierarchy for predicting the flow in stirred tanks with physics-informed neural networks, Advances in Computational Science and Engineering, 2:91-129, DOI (Open Access) , arXiv
Sahin, T., von Danwitz, M., Popp A. (2024): Solving forward and inverse problems of contact mechanics using physics-informed neural networks, Advanced Modeling and Simulation in Engineering Sciences, 11:11, DOI (Open Access) , arXiv

Current Projects

Surrogate Modeling

Surrogate modeling involves creating a simplified, computationally inexpensive approximation of a complex, high-fidelity model. These surrogate models are often built using statistical or machine learning techniques, such as polynomial regression, Gaussian processes, or neural networks, to replicate the behavior of the original model over a given input space. Surrogate models are crucial in multi-query applications, such as inverse problems, uncertainty quantification, and digital twins, because they allow for rapid evaluation of model outputs without repeatedly running costly and time-consuming high-fidelity simulations. By reducing computational overhead and providing quick model evaluations, surrogate models enable faster predictions of system behavior, facilitating monitoring, control, and decision-making. In this way, surrogate modeling is essential for making complex simulations more accessible and practical in various engineering and scientific applications.
Our research focuses on building surrogate models for complex nonlinear mechanics models, e.g. as they occur in contact mechanics. We also develop surrogate modeling techniques based on scientific machine learning to create digital twins of critical infrastructures. Lastly, we design advanced probabilistic surrogate models to conduct uncertainty quantification and global sensitivity analysis of large-scale computational models, as seen in fields like computational biomedical engineering, particularly in organ modeling.