Articles | Volume 16, issue 24
https://doi.org/10.5194/gmd-16-7375-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-7375-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review and perspective paper
| 
19 Dec 2023
Review and perspective paper |
| 19 Dec 2023
| 19 Dec 2023
Perspectives of physics-based machine learning strategies for geoscientific applications governed by partial differential equations
Denise Degen
CORRESPONDING AUTHOR
Computational Geoscience, Geothermics and Reservoir Geophysics (CG3), RWTH Aachen University, Mathieustraße 30, 52074 Aachen, Germany
Daniel Caviedes Voullième
Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre (JSC), Simulation and Data Lab. Terrestrial Systems, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Forschungszentrum Jülich GmbH, Agrosphere, IBG-3, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Susanne Buiter
RWTH Aachen University, Tectonics and Geodyamics (TAG), Lochnerstraße 4-20, 52064 Aachen, Germany
Helmholtz Centre Potsdam – GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Harrie-Jan Hendricks Franssen
Forschungszentrum Jülich GmbH, Agrosphere, IBG-3, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Centre for High-Performance Computing Terrestrial Systems, Geoverbund ABC/J, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Harry Vereecken
Forschungszentrum Jülich GmbH, Agrosphere, IBG-3, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Centre for High-Performance Computing Terrestrial Systems, Geoverbund ABC/J, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Ana González-Nicolás
Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre (JSC), Simulation and Data Lab. Terrestrial Systems, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Florian Wellmann
Computational Geoscience, Geothermics and Reservoir Geophysics (CG3), RWTH Aachen University, Mathieustraße 30, 52074 Aachen, Germany
Fraunhofer Research Institution for Energy Infrastructures and Geothermal Systems (IEG), Am Hochschulcampus 1, 44801 Bochum, Germany
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12 citations as recorded by crossref.
- Sparse-to-Dense Prediction of Ocean Subsurface Temperature Using Multilevel Spatiotemporal Information Fusion L. Lei et al. 10.1109/TGRS.2025.3564468
- Incremental Stable/Dynamic Disentanglement Learning for Ocean Subsurface Temperature Prediction L. Lei & Y. Zhou 10.1109/TGRS.2024.3522998
- Sensitivity analysis using physics-based machine learning: an example from surrogate modelling for magnetotellurics N. Lindner et al. 10.1093/gji/ggaf166
- A dynamic informed deep-learning method for future estimation of laboratory stick–slip E. Yue et al. 10.5194/gmd-18-6275-2025
- Current status and construction scheme of smart geothermal field technology G. LI et al. 10.1016/S1876-3804(24)60523-9
- Nonintrusive reduced basis approximation to the solution of the Helmholtz equation: The magnetotellurics case A. Quiaro et al. 10.1190/geo2024-0594.1
- Groundwater LNAPL Contamination Source Identification Based on Stacking Ensemble Surrogate Model Y. Bai et al. 10.3390/w16162274
- Surrogate-model-based calibration of effective transport parameters from push-pull tests in the Horonobe aquifer (Japan) E. Petrova et al. 10.1016/j.geothermics.2025.103449
- About the trustworthiness of physics-based machine learning – considerations for geomechanical applications D. Degen et al. 10.5194/se-16-477-2025
- Quantum-Inspired Neural Radiative Transfer (QINRT): A Multi-Scale Computational Framework for Next-Generation Climate Intelligence M. Akhtar 10.3390/appliedmath5040145
- Novel physics informed-neural networks for estimation of hydraulic conductivity of green infrastructure as a performance metric by solving Richards–Richardson PDE M. Elkhadrawi et al. 10.1007/s00521-023-09378-z
- Toward Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields A. Xu & L. Heagy 10.1109/TGRS.2025.3583970
12 citations as recorded by crossref.
- Sparse-to-Dense Prediction of Ocean Subsurface Temperature Using Multilevel Spatiotemporal Information Fusion L. Lei et al. 10.1109/TGRS.2025.3564468
- Incremental Stable/Dynamic Disentanglement Learning for Ocean Subsurface Temperature Prediction L. Lei & Y. Zhou 10.1109/TGRS.2024.3522998
- Sensitivity analysis using physics-based machine learning: an example from surrogate modelling for magnetotellurics N. Lindner et al. 10.1093/gji/ggaf166
- A dynamic informed deep-learning method for future estimation of laboratory stick–slip E. Yue et al. 10.5194/gmd-18-6275-2025
- Current status and construction scheme of smart geothermal field technology G. LI et al. 10.1016/S1876-3804(24)60523-9
- Nonintrusive reduced basis approximation to the solution of the Helmholtz equation: The magnetotellurics case A. Quiaro et al. 10.1190/geo2024-0594.1
- Groundwater LNAPL Contamination Source Identification Based on Stacking Ensemble Surrogate Model Y. Bai et al. 10.3390/w16162274
- Surrogate-model-based calibration of effective transport parameters from push-pull tests in the Horonobe aquifer (Japan) E. Petrova et al. 10.1016/j.geothermics.2025.103449
- About the trustworthiness of physics-based machine learning – considerations for geomechanical applications D. Degen et al. 10.5194/se-16-477-2025
- Quantum-Inspired Neural Radiative Transfer (QINRT): A Multi-Scale Computational Framework for Next-Generation Climate Intelligence M. Akhtar 10.3390/appliedmath5040145
- Novel physics informed-neural networks for estimation of hydraulic conductivity of green infrastructure as a performance metric by solving Richards–Richardson PDE M. Elkhadrawi et al. 10.1007/s00521-023-09378-z
- Toward Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields A. Xu & L. Heagy 10.1109/TGRS.2025.3583970
Latest update: 06 Nov 2025
Executive editor
This manuscript provides a review of physics-based machine learning methods, and provides a perspective on their use.
This manuscript provides a review of physics-based machine learning methods, and provides a...
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.
In geosciences, we often use simulations based on physical laws. These simulations can be...
