Submitted as: review and perspective paper
27 Mar 2023
Submitted as: review and perspective paper |  | 27 Mar 2023
Status: this preprint is currently under review for the journal GMD.

Perspectives of Physics-Based Machine Learning for Geoscientific Applications Governed by Partial Differential Equations

Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendriks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann

Abstract. An accurate assessment of the physical states of the Earth system is an essential component of many scientific, societal and economical considerations. These assessments are becoming an increasingly challenging computational task since we aim to resolve models with high resolutions in space and time, to consider complex coupled partial differential equations, and to estimate uncertainties, which often requires many realizations. Machine learning methods are becoming a very popular method for the construction of surrogate 5 models to address these computational issues. However, they also face major challenges in producing explainable, scalable, interpretable and robust models. In this manuscript, we evaluate the perspectives of geoscience applications of physics-based machine learning, which combines physics-based and data-driven methods to overcome the limitations of each approach taken alone. Through three designated examples (from the fields of geothermal energy, geodynamics, and hydrology), we show that the non-intrusive reduced basis method as a physics-based machine learning approach is able to 10 produce highly precise surrogate models that are explainable, scalable, interpretable, and robust.

Denise Degen et al.

Status: open (extended)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2022-309', Anonymous Referee #1, 20 Apr 2023 reply
    • AC1: 'Reply on RC1', Denise Degen, 26 Apr 2023 reply
  • CEC1: 'Comment on gmd-2022-309', Juan Antonio Añel, 05 May 2023 reply
    • AC2: 'Reply on CEC1', Denise Degen, 10 May 2023 reply
      • CEC2: 'Reply on AC2', Juan Antonio Añel, 10 May 2023 reply

Denise Degen et al.

Denise Degen et al.


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Short summary
In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.