Andrzej Dulny, M.Sc.

Chair of Data Science (Informatik X)
University of Würzburg
Am Hubland
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. I am working on applying Machine Learning and Neural Network models in the BigData@Geo project, where we work with time series and geospatial climate data. Our goal is to help the geography department to improve climate modeling using Machine Learning.

Education

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

Publications

2021[ to top ]

Wankerl, S., Dulny, A., Götz, G., Hotho, A. (2021) Learning Mathematical Relations Using Deep Tree Models, in 2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA), 1681–1687, available: https://doi.org/10.1109/ICMLA52953.2021.00268.
- [ Abstract ]
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To the present day, computer algebra systems used for calculating mathematical relations on a symbolic level are mainly rule-based systems. Only recently, deep learning has been applied to the task of symbolic mathematics. Researchers succeeded in developing neural networks which can do symbolic calculations of the equivalence of multiple pairing of equations. However, the generator used to create mathematical terms in previous research has several drawbacks and as with all deep learning tasks, the quality of the data used for training the models has a significant impact on the quality of the results. In this work, we propose a new generator for polynomials. We use it to train several recursive neural networks to recognize the equivalence, derivative, or variable substitution between pairs of polynomials for the first time. Our results indicate that these mathematical relations are identifiable with the help of deep learning.

@inproceedings{9680206, abstract = {To the present day, computer algebra systems used for calculating mathematical relations on a symbolic level are mainly rule-based systems. Only recently, deep learning has been applied to the task of symbolic mathematics. Researchers succeeded in developing neural networks which can do symbolic calculations of the equivalence of multiple pairing of equations. However, the generator used to create mathematical terms in previous research has several drawbacks and as with all deep learning tasks, the quality of the data used for training the models has a significant impact on the quality of the results. In this work, we propose a new generator for polynomials. We use it to train several recursive neural networks to recognize the equivalence, derivative, or variable substitution between pairs of polynomials for the first time. Our results indicate that these mathematical relations are identifiable with the help of deep learning.}, author = {Wankerl, Sebastian and Dulny, Andrzej and Götz, Gerhard and Hotho, Andreas}, booktitle = {2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA)}, keywords = {treemodels}, month = {dec}, pages = {1681-1687}, title = {Learning Mathematical Relations Using Deep Tree Models}, year = 2021 }
Kobs, K., Steininger, M., Dulny, A., Hotho, A. (2021) Do Different Deep Metric Learning Losses Lead to Similar Learned Features?, Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 10644–10654.
- [ BibTeX ]
@article{noauthororeditor, author = {Kobs, Konstantin and Steininger, Michael and Dulny, Andrzej and Hotho, Andreas}, journal = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)}, keywords = {myown}, month = {October}, pages = {10644-10654}, title = {Do Different Deep Metric Learning Losses Lead to Similar Learned Features?}, year = 2021 }
Dulny, A., Hotho, A., Krause, A. (2021) NeuralPDE: Modelling Dynamical Systems from Data, available: http://arxiv.org/abs/2111.07671.
- [ Abstract ]
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Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an emerging research field. However, current methods are restricted in various ways: they require prior knowledge about the governing equations, and are limited to linear or first-order equations. In this work we propose NeuralPDE, a model which combines convolutional neural networks (CNNs) with differentiable ODE solvers to model dynamical systems. We show that the Method of Lines used in standard PDE solvers can be represented using convolutions which makes CNNs the natural choice to parametrize arbitrary PDE dynamics. Our model can be applied to any data without requiring any prior knowledge about the governing PDE. We evaluate NeuralPDE on datasets generated by solving a wide variety of PDEs, covering higher orders, non-linear equations and multiple spatial dimensions.

@misc{dulny2021neuralpde, abstract = {Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an emerging research field. However, current methods are restricted in various ways: they require prior knowledge about the governing equations, and are limited to linear or first-order equations. In this work we propose NeuralPDE, a model which combines convolutional neural networks (CNNs) with differentiable ODE solvers to model dynamical systems. We show that the Method of Lines used in standard PDE solvers can be represented using convolutions which makes CNNs the natural choice to parametrize arbitrary PDE dynamics. Our model can be applied to any data without requiring any prior knowledge about the governing PDE. We evaluate NeuralPDE on datasets generated by solving a wide variety of PDEs, covering higher orders, non-linear equations and multiple spatial dimensions.}, author = {Dulny, Andrzej and Hotho, Andreas and Krause, Anna}, keywords = {neural-ode}, note = {cite arxiv:2111.07671}, title = {NeuralPDE: Modelling Dynamical Systems from Data}, year = 2021 }

2020[ to top ]

Dulny, A., Steininger, M., Lautenschlager, F., Krause, A., Hotho, A. (2020) Evaluating the multi-task learning approach for land use regression modelling of air pollution, in International Conference on Frontiers of Artificial Intelligence and Machine Learning, IASED.
- [ Abstract ]
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Air pollution has been linked to several health problems including heart disease, stroke and lung cancer. Modelling and analyzing this dependency requires reliable and accurate air pollutant measurements collected by stationary air monitoring stations. However, usually only a low number of such stations are present within a single city. To retrieve pollution concentrations for unmeasured locations, researchers rely on land use regression (LUR) models. Those models are typically developed for one pollutant only. However, as results in different areas have shown, modelling several related output variables through multi-task learning can improve the prediction results of the models significantly. In this work, we compared prediction results from single-task and multi-task learning multilayer perceptron models on measurements taken from the OpenSense dataset and the London Atmospheric Emissions Inventory dataset. LUR features were generated from OpenStreetMap using OpenLUR and used to train hard parameter sharing multilayer perceptron models. The results show multi-task learning with sufficient data significantly improves the performance of a LUR model.

@inproceedings{dulny2020evaluating, abstract = {Air pollution has been linked to several health problems including heart disease, stroke and lung cancer. Modelling and analyzing this dependency requires reliable and accurate air pollutant measurements collected by stationary air monitoring stations. However, usually only a low number of such stations are present within a single city. To retrieve pollution concentrations for unmeasured locations, researchers rely on land use regression (LUR) models. Those models are typically developed for one pollutant only. However, as results in different areas have shown, modelling several related output variables through multi-task learning can improve the prediction results of the models significantly. In this work, we compared prediction results from single-task and multi-task learning multilayer perceptron models on measurements taken from the OpenSense dataset and the London Atmospheric Emissions Inventory dataset. LUR features were generated from OpenStreetMap using OpenLUR and used to train hard parameter sharing multilayer perceptron models. The results show multi-task learning with sufficient data significantly improves the performance of a LUR model.}, author = {Dulny, Andrzej and Steininger, Michael and Lautenschlager, Florian and Krause, Anna and Hotho, Andreas}, booktitle = {International Conference on Frontiers of Artificial Intelligence and Machine Learning}, keywords = {myown}, organization = {IASED}, title = {Evaluating the multi-task learning approach for land use regression modelling of air pollution}, year = 2020 }

Andrzej Dulny, M.Sc.