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Physics-Informed Neural Networks for Regional Geoid Modeling
This master thesis aims to explore the application of Physics-Informed Neural Networks (PINNs) to regional geoid modeling. PINNs integrate physical constraints into neural network architectures, offering a novel approach to accurate geoid modeling while maintaining interpretability.
Regional geoid modeling is crucial for various geospatial applications, such as maintaining height systems or enabling challenging tunnel construction projects. Traditional methods for geoid determination often face challenges such as limited accuracy or computational inefficiency. By integrating (well-known) physical constraints into neural network architectures, PINNs offer a promising solution to these limitations. The project will utilize a dataset comprising gravity anomalies, a digital elevation model, and other relevant geospatial data to train and validate the PINN model. The study will investigate the performance of PINNs for determining geoid models in a selected study area and how they compare to existing geoid solutions determined by traditional approaches. Concretely, we plan to conduct our study in Auvergne, France due to the publicly available gravity data and its interesting geographic features. Finally, the project will assess the interpretability of the PINN model, identifying anomalous geoid features that may have implications for its application.
**Figure Description**
Image reference: Foroughi, I., Vaníček, P., Kingdon, R.W. et al. Sub-centimetre geoid. J Geod 93, 849–868 (2019). https://doi.org/10.1007/s00190-018-1208-1
Regional geoid modeling is crucial for various geospatial applications, such as maintaining height systems or enabling challenging tunnel construction projects. Traditional methods for geoid determination often face challenges such as limited accuracy or computational inefficiency. By integrating (well-known) physical constraints into neural network architectures, PINNs offer a promising solution to these limitations. The project will utilize a dataset comprising gravity anomalies, a digital elevation model, and other relevant geospatial data to train and validate the PINN model. The study will investigate the performance of PINNs for determining geoid models in a selected study area and how they compare to existing geoid solutions determined by traditional approaches. Concretely, we plan to conduct our study in Auvergne, France due to the publicly available gravity data and its interesting geographic features. Finally, the project will assess the interpretability of the PINN model, identifying anomalous geoid features that may have implications for its application.
**Figure Description**
Image reference: Foroughi, I., Vaníček, P., Kingdon, R.W. et al. Sub-centimetre geoid. J Geod 93, 849–868 (2019). https://doi.org/10.1007/s00190-018-1208-1
The primary goal of this master thesis project is to investigate the feasibility and effectiveness of Physics-Informed Neural Networks (PINNs) for geoid modeling. The specific objectives include:
1. Implementing and training machine learning models using datasets from Auvergne that will be provided to the student
2. Incorporating the theoretical relationships between gravity anomalies and geoid height as physical constraints, resulting in a physical loss term in addition to the typical data-driven loss term
3. Performing an internal evaluation of the PINN-based geoid solution based on the agreement with the unseen gravity data of the test set
4. Performing external evaluations using different data sources, including other geoid models, all of which will be provided by the supervisors
The primary goal of this master thesis project is to investigate the feasibility and effectiveness of Physics-Informed Neural Networks (PINNs) for geoid modeling. The specific objectives include:
1. Implementing and training machine learning models using datasets from Auvergne that will be provided to the student 2. Incorporating the theoretical relationships between gravity anomalies and geoid height as physical constraints, resulting in a physical loss term in addition to the typical data-driven loss term 3. Performing an internal evaluation of the PINN-based geoid solution based on the agreement with the unseen gravity data of the test set 4. Performing external evaluations using different data sources, including other geoid models, all of which will be provided by the supervisors
Junyang Gou (jungou@ethz.ch)
Julia Koch (jukoch@ethz.ch)
Prof. Dr. Benedikt Soja (soja@ethz.ch)
Junyang Gou (jungou@ethz.ch) Julia Koch (jukoch@ethz.ch) Prof. Dr. Benedikt Soja (soja@ethz.ch)