Physics-aware Nonlinear Modeling and Inference from Earth Data

Abstract:

Process understanding and modeling are at the core of scientific reasoning. Principled parametric and mechanistic modeling has dominated science and engineering until recently with the advent of machine learning. Despite great success in many areas, machine learning algorithms in the Earth and Climate sciences face the problem of credibility and consistency, as often they do not respect the most elementary laws of physics. Motivated from the field of algorithmic fairness, we here reconcile data-driven machine learning models with physics modeling by introducing a nonlinear and non-parametric physics-aware regression methodology. The proposed algorithm includes an additional dependence-regularizer to the objective function that enforces model predictions to be consistent with external forces which can refer to data from a physical model, simulations, or ancillary observations. Models come with an analytic closed-form solution and statistical guarantees. Through a consistency-vs-accuracy path diagram, the model allows us to study the relative relevance of covariates in the predictions and to assess consistency between external forces and data. We demonstrate that the modeling improves accuracy and faithfulness through several examples in geosciences, Earth observation, and climate science. We also show how the method can be used in (observational) detection and attribution studies to assess the impact of anthropogenic activities on climate warming. The proposed framework generalizes plain linear and nonlinear kernel regression models, is easy to implement, and inherits all properties of kernel methods treatment so that recent advances in kernel and GP modeling could be easily included.