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
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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Cited
22 citations as recorded by crossref.
- Incremental Stable/Dynamic Disentanglement Learning for Ocean Subsurface Temperature Prediction L. Lei & Y. Zhou
- Emerging applications of physics-informed and physics-guided machine learning in geoenergy science: A review S. Davoodi et al.
- Dynamic heat extraction and development optimization of enhanced geothermal system based on forward simulation and data-driven methods-A review S. Mu et al.
- A dynamic informed deep-learning method for future estimation of laboratory stick–slip E. Yue et al.
- Groundwater LNAPL Contamination Source Identification Based on Stacking Ensemble Surrogate Model Y. Bai et al.
- Surrogate-model-based calibration of effective transport parameters from push-pull tests in the Horonobe aquifer (Japan) E. Petrova et al.
- About the trustworthiness of physics-based machine learning – considerations for geomechanical applications D. Degen et al.
- Quantum-Inspired Neural Radiative Transfer (QINRT): A Multi-Scale Computational Framework for Next-Generation Climate Intelligence M. Akhtar
- Enhancing the Resilience and Sustainability of Integrated Energy Systems Exposed to Extreme Natural Hazards by Means of Artificial Intelligence, Advanced Simulation, and Optimization Methods, Within an Integrative Systems Framework: A Critical Review of Literature A. Hallioui & N. Pedroni
- 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.
- Toward Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields A. Xu & L. Heagy
- Predictive models for dynamic properties of soils using machine learning approaches: A comprehensive review S. Ghorbanzadeh et al.
- Sparse-to-Dense Prediction of Ocean Subsurface Temperature Using Multilevel Spatiotemporal Information Fusion L. Lei et al.
- High-resolution regional SST AI downscaling based on multi-mode inputs from nested ROMS simulations X. Chen et al.
- Sensitivity analysis using physics-based machine learning: an example from surrogate modelling for magnetotellurics N. Lindner et al.
- Exploiting physics-based machine learning to quantify geodynamic effects – insights from the Alpine region D. Degen et al.
- Stable and efficient learning of degenerate stochastic differential equation in neural networks Z. Wang et al.
- Current status and construction scheme of smart geothermal field technology G. LI et al.
- Nonintrusive reduced basis approximation to the solution of the Helmholtz equation: The magnetotellurics case A. Quiaro et al.
- Uncertainty-Aware Deep Neural Network Training for Imbalanced Geochemical Data Distributions A. Dashti et al.
- Reduced-order modelling of Cascadia’s slow slip cycles Y. Magen et al.
- Separated-variable physics informed neural operators for solving dynamic PDEs Y. Wang et al.
22 citations as recorded by crossref.
- Incremental Stable/Dynamic Disentanglement Learning for Ocean Subsurface Temperature Prediction L. Lei & Y. Zhou
- Emerging applications of physics-informed and physics-guided machine learning in geoenergy science: A review S. Davoodi et al.
- Dynamic heat extraction and development optimization of enhanced geothermal system based on forward simulation and data-driven methods-A review S. Mu et al.
- A dynamic informed deep-learning method for future estimation of laboratory stick–slip E. Yue et al.
- Groundwater LNAPL Contamination Source Identification Based on Stacking Ensemble Surrogate Model Y. Bai et al.
- Surrogate-model-based calibration of effective transport parameters from push-pull tests in the Horonobe aquifer (Japan) E. Petrova et al.
- About the trustworthiness of physics-based machine learning – considerations for geomechanical applications D. Degen et al.
- Quantum-Inspired Neural Radiative Transfer (QINRT): A Multi-Scale Computational Framework for Next-Generation Climate Intelligence M. Akhtar
- Enhancing the Resilience and Sustainability of Integrated Energy Systems Exposed to Extreme Natural Hazards by Means of Artificial Intelligence, Advanced Simulation, and Optimization Methods, Within an Integrative Systems Framework: A Critical Review of Literature A. Hallioui & N. Pedroni
- 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.
- Toward Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields A. Xu & L. Heagy
- Predictive models for dynamic properties of soils using machine learning approaches: A comprehensive review S. Ghorbanzadeh et al.
- Sparse-to-Dense Prediction of Ocean Subsurface Temperature Using Multilevel Spatiotemporal Information Fusion L. Lei et al.
- High-resolution regional SST AI downscaling based on multi-mode inputs from nested ROMS simulations X. Chen et al.
- Sensitivity analysis using physics-based machine learning: an example from surrogate modelling for magnetotellurics N. Lindner et al.
- Exploiting physics-based machine learning to quantify geodynamic effects – insights from the Alpine region D. Degen et al.
- Stable and efficient learning of degenerate stochastic differential equation in neural networks Z. Wang et al.
- Current status and construction scheme of smart geothermal field technology G. LI et al.
- Nonintrusive reduced basis approximation to the solution of the Helmholtz equation: The magnetotellurics case A. Quiaro et al.
- Uncertainty-Aware Deep Neural Network Training for Imbalanced Geochemical Data Distributions A. Dashti et al.
- Reduced-order modelling of Cascadia’s slow slip cycles Y. Magen et al.
- Separated-variable physics informed neural operators for solving dynamic PDEs Y. Wang et al.
Saved (final revised paper)
Latest update: 30 Apr 2026
Editorial statement
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...