Physics Informed Deep Learning

In several projects, we develop deep learning methods specifically to model physical systems with physical background knowledge. For example, we develop models for electro magnetic fields to help with magnetic resonance imaging in MAGNET. We're also building models to monitor the structural integrity of bridges in the P-BIM project.

Projects

Publications

Liquor-HGNN: A heterogeneous graph neural network for leakage detection in water distribution networks. Schaller, Melanie; Steininger, Michael; Dulny, Andrzej; Schlör, Daniel; Hotho, Andreas. In LWDA’23: Lernen, Wissen, Daten, Analysen. October 09--11, 2023, Marburg, Germany, M. Leyer (ed.). 2023.
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@article{schaller2023liquorhgnn, author = {Schaller, Melanie and Steininger, Michael and Dulny, Andrzej and Schlör, Daniel and Hotho, Andreas}, editor = {Leyer, M.}, journal = {LWDA'23: Lernen, Wissen, Daten, Analysen. October 09–11, 2023, Marburg, Germany}, keywords = {author:manli}, month = {Oktober}, title = {Liquor-HGNN: A heterogeneous graph neural network for leakage detection in water distribution networks}, year = 2023 }
DynaBench: A Benchmark Dataset for Learning Dynamical Systems from Low-Resolution Data. Dulny, Andrzej; Hotho, Andreas; Krause, Anna. In Machine Learning and Knowledge Discovery in Databases: Research Track, D. Koutra, C. Plant, M. Gomez Rodriguez, E. Baralis, F. Bonchi (eds.), pp. 438–455. Springer Nature Switzerland, Cham, 2023.
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Previous work on learning physical systems from data has focused on high-resolution grid-structured measurements. However, real-world knowledge of such systems (e.g. weather data) relies on sparsely scattered measuring stations. In this paper, we introduce a novel simulated benchmark dataset, DynaBench, for learning dynamical systems directly from sparsely scattered data without prior knowledge of the equations. The dataset focuses on predicting the evolution of a dynamical system from low-resolution, unstructured measurements. We simulate six different partial differential equations covering a variety of physical systems commonly used in the literature and evaluate several machine learning models, including traditional graph neural networks and point cloud processing models, with the task of predicting the evolution of the system. The proposed benchmark dataset is expected to advance the state of art as an out-of-the-box easy-to-use tool for evaluating models in a setting where only unstructured low-resolution observations are available. The benchmark is available at https://professor-x.de/dynabench.

@inproceedings{10.1007/978-3-031-43412-9_26, abstract = {Previous work on learning physical systems from data has focused on high-resolution grid-structured measurements. However, real-world knowledge of such systems (e.g. weather data) relies on sparsely scattered measuring stations. In this paper, we introduce a novel simulated benchmark dataset, DynaBench, for learning dynamical systems directly from sparsely scattered data without prior knowledge of the equations. The dataset focuses on predicting the evolution of a dynamical system from low-resolution, unstructured measurements. We simulate six different partial differential equations covering a variety of physical systems commonly used in the literature and evaluate several machine learning models, including traditional graph neural networks and point cloud processing models, with the task of predicting the evolution of the system. The proposed benchmark dataset is expected to advance the state of art as an out-of-the-box easy-to-use tool for evaluating models in a setting where only unstructured low-resolution observations are available. The benchmark is available at https://professor-x.de/dynabench.}, address = {Cham}, author = {Dulny, Andrzej and Hotho, Andreas and Krause, Anna}, booktitle = {Machine Learning and Knowledge Discovery in Databases: Research Track}, editor = {Koutra, Danai and Plant, Claudia and Gomez Rodriguez, Manuel and Baralis, Elena and Bonchi, Francesco}, keywords = {selected}, pages = {438–455}, publisher = {Springer Nature Switzerland}, title = {DynaBench: A Benchmark Dataset for Learning Dynamical Systems from Low-Resolution Data}, year = 2023 }
TaylorPDENet: Learning PDEs from non-grid Data. Heinisch, Paul; Dulny, Andrzej; Krause, Anna; Hotho, Andreas. 2023.
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Modeling data obtained from dynamical systems has gained attention in recent years as a challenging task for machine learning models. Previous approaches assume the measurements to be distributed on a grid. However, for real-world applications like weather prediction, the observations are taken from arbitrary locations within the spatial domain. In this paper, we propose TaylorPDENet - a novel machine learning method that is designed to overcome this challenge. Our algorithm uses the multidimensional Taylor expansion of a dynamical system at each observation point to estimate the spatial derivatives to perform predictions. TaylorPDENet is able to accomplish two objectives simultaneously: accurately forecast the evolution of a complex dynamical system and explicitly reconstruct the underlying differential equation describing the system. We evaluate our model on a variety of advection-diffusion equations with different parameters and show that it performs similarly to equivalent approaches on grid-structured data while being able to process unstructured data as well.

@misc{heinisch2023taylorpdenet, abstract = {Modeling data obtained from dynamical systems has gained attention in recent years as a challenging task for machine learning models. Previous approaches assume the measurements to be distributed on a grid. However, for real-world applications like weather prediction, the observations are taken from arbitrary locations within the spatial domain. In this paper, we propose TaylorPDENet - a novel machine learning method that is designed to overcome this challenge. Our algorithm uses the multidimensional Taylor expansion of a dynamical system at each observation point to estimate the spatial derivatives to perform predictions. TaylorPDENet is able to accomplish two objectives simultaneously: accurately forecast the evolution of a complex dynamical system and explicitly reconstruct the underlying differential equation describing the system. We evaluate our model on a variety of advection-diffusion equations with different parameters and show that it performs similarly to equivalent approaches on grid-structured data while being able to process unstructured data as well.}, author = {Heinisch, Paul and Dulny, Andrzej and Krause, Anna and Hotho, Andreas}, keywords = {from:martinr}, note = {cite arxiv:2306.14511}, title = {TaylorPDENet: Learning PDEs from non-grid Data}, year = 2023 }

Projects

AI@Knauf

P-BIM

MAGNET

KI@FlowChief

Publications

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