Andrzej Dulny, M.Sc.

Chair of Data Science (Informatik X)
University of Würzburg
Campus Hubland Nord
Emil-Fischer-Straße 50
97074 Würzburg
Germany

Email: andrzej.dulny@uni-wuerzburg.de

Phone: (+49 931) 31 - 81316

Fax: (+49 931) 31 81316-0

Projects and Research Interests

I have been part of the DMIR Research Group since early 2021, after I received my master's degree in Mathematics at the University of Würzburg. Currently pursuing research at Prof. Hotho's research group, I am passionate about leveraging machine learning techniques to predict the evolution of physical systems, extract the physical equations governing the system, and enhance simulation methods with machine learning. My work lies at the intersection of machine learning and physics, with a particular emphasis on developing and applying novel deep learning methods to solve complex problems in the field of dynamical systems using:

Physics-Informed Neural Networks (PINNs)
NeuralODEs
Graph Neural Networks
Transformer-based models for spatial data

Furthermore, I am particularily interested in handling non-grid and low-resolution data.

The methods I develop in my research can be applied to improve simulation and prediction of a variety of physical systems including weather prediction, climate models, wave simulations, fluid dynamics etc. Additionally, I apply the results of my research within the MAGNET4cardiac7T research project, where I aim to train neural networks for simulating electromagnetic fields within a MRI scanner.

Education

2017–2020: M.Sc. Mathematics at the University of Würzburg
2013–2016: B.Sc. Mathematics at the Jagiellonian University in Cracow

Publications

2023[ to top ]

Wankerl, S., Dulny, A., Götz, G., and Hotho, A. (2023) “Can Neural Networks Distinguish High-school Level Mathematical Concepts?”, in Accepted at ICDM.
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@conference{wankerl2023neural, author = {Wankerl, Sebastian and Dulny, Andrzej and Götz, Gerhard and Hotho, Andreas}, booktitle = {Accepted at ICDM}, keywords = {from:sew03dg}, title = {Can Neural Networks Distinguish High-school Level Mathematical Concepts?}, year = 2023 }
Heinisch, P., Dulny, A., Krause, A., and Hotho, A. (2023) “TaylorPDENet: Learning PDEs from non-grid Data”, available: http://arxiv.org/abs/2306.14511.
- [ Abstract ]
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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 = {research_knowledge}, note = {cite arxiv:2306.14511}, title = {TaylorPDENet: Learning PDEs from non-grid Data}, year = 2023 }
Dulny, A., Hotho, A., and Krause, A. (2023) “DynaBench: A Benchmark Dataset for Learning Dynamical Systems from Low-Resolution Data”, in Koutra, D., Plant, C., Gomez Rodriguez, M., Baralis, E. and Bonchi, F., eds., Machine Learning and Knowledge Discovery in Databases: Research Track, Cham: Springer Nature Switzerland, 438–455, available: http://arxiv.org/abs/2306.05805.
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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 }
Schaller, M., Steininger, M., Dulny, A., Schlör, D., and Hotho, A. (2023) “Liquor-HGNN: A heterogeneous graph neural network for leakage detection in water distribution networks”, LWDA’23: Lernen, Wissen, Daten, Analysen. October 09--11, 2023, Marburg, Germany.
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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 = {research_representation_learning}, month = {Oktober}, title = {Liquor-HGNN: A heterogeneous graph neural network for leakage detection in water distribution networks}, year = 2023 }

Andrzej Dulny, M.Sc.