Future simulation science will call for predictive computational models based on joint physical and data-based modeling concepts. Current limitations on the predictive capabilities of models stem from the lack of combined approaches. We are convinced that physics-based models that do not include data, or data-based models that fail to respect physical principles are both inadequate in modern simulation contexts. That said, as of now it is not clear how to systematically integrate data into physics-based simulation models beyond the mere fitting of low-dimensional model parameters. Also lacking are data-driven methods that integrate physical properties such as conservation laws, positivity constraints, symmetry conditions, or causality into purely data-based models.
To take the next steps toward achieving progress for our long-term Visionary Examples, innovative approaches are required. These include
- exploiting experimental and sensor data to partly replace models or to adapt available models on the fly;
- integrating simulation data and simulation metadata to optimize the accuracy or efficiency of simulations;
- generating surrogates with few samples that cope with limited resources and high dimensionalities but can adjust to new incoming observations;
- equipping machine learning algorithms with knowledge about physical constraints,
for example restricting their hypothesis spaces; and
- opening and influencing the “black box” of data models obtained by machine learning.
In summary, the challenge is to merge physics-based and data-based models in a seamless way, for their mutual benefit in future adaptive and interactive simulations of complex systems.