Surrogate Modeling

Physics-informed and Data-based Surrogate Modeling

Project Description

The project "Reuse and Reanalysis of Simulation Data in Structural Dynamics" is part of the Cluster of Excellence "Data-Integrated Simulation Science (SimTech)". It is placed within the projekt network 7 "Adaptive Simulation and Interaction" and aims to generate accelerated and improved surrogate models for complex simulations using previous simulation data.  This includes data-based and physics-informed surrogate modeling as well as merging of physics- and data-based models.

Data-based Surrogate Modeling of High-dimensional Systems

Complex high-dimensional ("high-fidelity") simulation models require dedicated hardware and a considerable amount of computing time. They are therefore unsuitable for applications under time and resource constraints, as found in mobile devices (cell phones, virtual reality headsets).

Fig. 1 Surrogate modeling consisting of dimensionality reduction using MOR and prediction of reduced system behavior for unseen parameters using ML [Kneifl, Grunert & Fehr, 2021].

Hence, the goal of this project is to create efficient surrogate models based on previous simulation results instead of expensive high-fidelity simulation models.  We rely on a combination of model order reduction (MOR) and machine learning (ML) (see Fig. 1). Unlike classical linear MOR method, this approach can handle nonlinearities and, unlike classical nonlinear approaches, it does not require manipulations to the original simulation code.

In our method, previous simulation results generated by a high-fidelity model are used to find a low-dimensional representation of the simulation results. Regression algorithms from the field of machine learning are then used to approximate the system behavior in its reduced description.
As an example, the motion behavior of an occupant accelerating inside a vehicle [Kneifl, Hay & Fehr, 2021] is shown in Fig. 2 and the approximated behavior of a human arm in Fig. 3. 


Fig. 3 Approximation of static postures of a human arm and the resulting internal stresses. The greater the stress, the lighter the color of the corresponding area. (Cooperation with PN 7-1)


Fig. 2 Occupant simulation in a pre-crash simulation. Left: Reference model. Right: surrogate model colored with respect to individual nodal error [Kneifl, Hay & Fehr, 2021].


Fig. 4 Control of a manipulator based on a physics-informed model predictive controller.

Physics-informed Surrogate Modeling

In contrast to completely data-based approaches, it can be beneficial to consider domain knowledge, for example in the form of physical laws, in the surrogate modeling process.

Thus, a classical physically derived model can be enhanced with the help of a data-based one. For example, by learning the error between a simple physical ("low-fidelity") model and a high-fidelity model or experimental measurements.

Another methodology is to learn the physical laws directly. This allows, among other things, the real-time solution of complex optimal control problems for a robot manipulator [Nicodemus et al., 2021] or the identification of friction terms in equations of motion based on experimental measurements. 


The developed methods and algorithms are implemented in the in-house developed software solution MorMl.
Connections to LS-Dyna, Hyperworks and implementations in Matlab and Python already exist for the software.


  1. J. Nicodemus, J. Kneifl, J. Fehr, and B. Unger, “Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators,” ArXiv e-print 2109.10793, 2021, [Online]. Available:
  2. J. Kneifl, J. Hay, and J. Fehr, “Real-time Human Response Prediction Using a Non-intrusive Data-driven Model Reduction Scheme,” ArXiv e-print 2110.13583, 2021, [Online]. Available:
  3. J. Kneifl, D. Grunert, and J. Fehr, “A non-intrusive nonlinear model reduction method for structural dynamical problems based on machine learning,” International Journal for Numerical Methods in Engineering, Apr. 2021, doi: 10.1002/nme.6712.
  4. J. Kneifl and J. Fehr, “Machine Learning Algorithms for Learning Nonlinear Terms of Reduced Mechanical Models in Explicit Structural Dynamics,” PAMM, vol. 20, no. S1, Art. no. S1, Mar. 2021, doi: 10.1002/pamm.202000353.

Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2075 – 390740016. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech).

Principal investigators
Research Staff
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