Surrogate-based active learning for parameter inference in geosciences via Bayesian sparse² multi-adaptivity enhanced by information theory

• Applicant: Professor Dr.-Ing. Sergey Oladyshkin, Ph.D.
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 432343452

The water-food-energy nexus is central to sustainable development. Society needs a better understanding of the environment in order to have an efficient and safe interaction for the sake of maximized welfare and sustainability in resources management. Simulations with well-calibrated models offer a unique way to predict the multifaceted behavior of subsurface systems, such as multiphase flow transport in fractured media, coupled hydrosystem model and multi-species reactive transport in porous media, etc. Due to the roughness or lack of available data and high computational costs of the numerical simulation, this class of problems is still challenging for modern methods of uncertainty quantification and Machine Learning (ML). The proposed project seeks to address this challenge on the example of modelling carbon dioxide (CO2) storage in geological formations. The CO2 storage problem is a representative case for the broad class of subsurface problems, because it involves multiphase flow where the CO2 displacement fronts are very non-linearity, which can be difficult capture. ML techniques are become increasing popular in the scientific community and seem to be very suitable candidates for such non-linear problems. Classical ML approaches require huge amounts of data coming from model parameters, as well as model response. Unfortunately, many problems addressed in geosciences can only provide very sparse data. Data sparsity is caused by lack of available measurements and high computational costs of numerical simulation of realistic models. In the current project, we propose to develop a ML approach that will be able to treat the non-linearity of the physical problem adaptively taking into account the sparse nature of the available data. The project intend to explore the link between the Bayesian inference and information theory in a goal-oriented fashion to localize non-linearity of the physical problem adaptively according to available observation data and computational resources. We will follow the recent trend in stochastic model reduction and will train a mathematically optimal response surface using limited (sparse) information from the original CO2 model in light of observed data. Here, we suggest to develop the multi-adaptivity for polynomial chaos employing sparse reconstruction based on Bayesian theory accompanied by the information-theoretic arguments. Combining Bayesian inference with information theory will help adaptively improvement of the response surface, while iteratively including relevant information into the adaptive response surface. With the novel Bayesian sparse2 multi-adaptivity, it will be possible to calibrate highly non-linear models at strongly reduced computational costs and with quantified post-calibration uncertainty. We also expect that the suggested Bayesian sparse2 multi-adaptivity concept will open a physics-based pathway for other ML approaches and will be very beneficial for various environmental problems.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr.-Ing. Wolfgang Nowak