Modeling and simulating is generally subject to uncertainties arising from various sources. They can stem from limited understanding of governing processes leading to competing mathematical models, limited knowledge of initial and boundary conditions, and numerical approximation errors. As outlined in our Engineered Geosystems and Digital Human Model visions, noisy and sparse data do not allow unique selection, parametrization, calibration, and validation of models. Inherent stochasticity of the modeled systems further complicates the analysis. In combination, this leads to total uncertainty. The multitude and magnitude of uncertainties can skew decision making and end up derailing further scientific progress.
The challenges in tackling these issues, in particular for complex multi-X simulations, consist of having to
- incorporate the quantification of all uncertainties and provide reliable/guaranteed predictions;
- address the completely unknown dependency structure of all involved uncertainties;
- understand, interpret, and communicate goal-oriented error measures and provide sensible interpretations;
- and to investigate appropriate risk measures compatible with the model’s requirements that allow evaluating the quality of predictions.
In summary, we need to develop efficient algorithms for computational statistics and stochastic analysis, inference and machine learning, combined with suitable error estimates and risk measures. The high dimensionality of the resulting problems requires to tightly integrate with adaptivity, optimization, and HPC.