EGU General Assembly 2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Differentiable modeling to unify machine learning and physical models and advance Geosciences

Chaopeng Shen1, Alison Appling2, Pierre Gentine3, Toshiyuki Bandai4, Hoshin Gupta5, Alexandre Tartakovsky6, Marco Baity-Jesi7, Fabrizio Fenicia7, Daniel Kifer8, Xiaofeng Liu1, Li Li1, Dapeng Feng1, Wei Ren9, Yi Zheng10, Ciaran Harman11, Martyn Clark12, Matthew Farthing13, and Praveen Kumar14
Chaopeng Shen et al.
  • 1Pennsylvania State University, Civil and Environmental Engineering, University Park, United States of America (
  • 2U.S. Geological Survey, Water Mission Area, Integrated Modeling and Prediction Division, Reston, VA, USA
  • 3National Science Foundation Science and Technology Center for Learning the Earth with Artificial Intelligence and Physics (LEAP), Columbia University, New York, NY USA
  • 4Life and Environmental Science Department, University of California, Merced, CA, USA
  • 5Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, AZ, USA
  • 6Civil and Environmental Engineering, University of Illinois, Urbana Champaign, IL, USA
  • 7Eawag: Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
  • 8Computer Science and Engineering, The Pennsylvania State University, University Park, PA, USA
  • 9Department of Natural Resources and the Environment, University of Connecticut, Storrs, CT, USA
  • 10Southern University of Science and Technology, Shenzhen, Guangdong Province, China
  • 11Department of Environmental Health and Engineering, Johns Hopkins University, Baltimore, MD, US
  • 12Global Institute for Water Security, University of Saskatchewan, Canmore, Alberta, Canada
  • 13US Army Engineer Research and Development Center, Vicksburg, MS, USA
  • 14Prairie Research Institute, University of Illinois, Urbana Champaign, IL, USA

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between them and ushering in a paradigm shift. For decades, PBM offered benefits in interpretability and physical consistency but struggled to efficiently leverage large datasets. ML methods, especially deep networks, presented strong predictive skills yet lacked the ability to answer specific scientific questions. While various methods have been proposed for ML-physics integration, an important underlying theme  — differentiable modeling — is not sufficiently recognized. Here we outline the concepts, applicability, and significance of differentiable geoscientific modeling (DG). “Differentiable” refers to accurately and efficiently calculating gradients with respect to model variables, critically enabling the learning of high-dimensional unknown relationships. DG refers to a range of methods connecting varying amounts of prior knowledge to neural networks and training them together, capturing a different scope than physics-guided machine learning and emphasizing first principles. In this talk we provide examples of DG in global hydrology, ecosystem modeling, water quality simulations, etc. Preliminary evidence suggests DG offers better interpretability and causality than ML, improved generalizability and extrapolation capability, and strong potential for knowledge discovery, while approaching the performance of purely data-driven ML. DG models require less training data while scaling favorably in performance and efficiency with increasing amounts of data. With DG, geoscientists may be better able to frame and investigate questions, test hypotheses, and discover unrecognized linkages. 

How to cite: Shen, C., Appling, A., Gentine, P., Bandai, T., Gupta, H., Tartakovsky, A., Baity-Jesi, M., Fenicia, F., Kifer, D., Liu, X., Li, L., Feng, D., Ren, W., Zheng, Y., Harman, C., Clark, M., Farthing, M., and Kumar, P.: Differentiable modeling to unify machine learning and physical models and advance Geosciences, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-15968,, 2023.