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Statistical Inference in Deep Science-Aware Models

Kai-Hendrik Cohrs (Ph.D. Student)

Science-aware and science-guided machine learning attempts to combine knowledge of first principles and machine learning. One way of doing so is using explicit equations from theoretical knowledge and estimate parameters or latent states with machine learning approaches. This promises scientifically interpretable results to deepen our understanding of the latent states and parameters, and other advantages are promised; improved extrapolation capabilities and generally sparser models. The overarching goal of my project is the development of these so-called hybrid models. There are several questions that need to be answered on synthetic data before applying these approaches in the wild. Do parameters of interest in the equation also converge to the true value when using gradient-based optimization algorithms in the presence of over-parametrized deep neural networks for latent states? How do we overcome bias introduced through regularization techniques? What are the implications of equifinality, i.e., non-identifiability? I seek to answer these questions and apply the methods to pressing problems in Earth sciences, like the partitioning of carbon fluxes between ecosystem and atmosphere. In particular, I aim to study them through the Bayesian lens. In the spirit of hybrid modeling, the Bayesian approach provides another way to introduce prior domain knowledge and to quantify uncertainty for the models' predictions, representation and biophysical parameters. The explainability of the uncertainty and the effect of the introduction of physical knowledge on it are further topics I am investigating during my PhD. In a consecutive step, this opens the path to explore ways to reduce uncertainty.

Primary Host: Gustau Camps-Valls (Universitat de València)
Exchange Host: Markus Reichstein (Max Planck Institute for Biogeochemistry)
PhD Duration: 01 October 2021 - 30 September 2024
Exchange Duration: 01 August 2022 - 31 October 2022 01 August 2023 - 31 October 2023