Seminar: Generatives maschinelles Lernen - Anwendungen neuronaler Netze bei räumlicher stochastischer Modellierung
In diesem Seminar werden wir uns auf den Einsatz von Techniken des maschinellen Lernens in der stochastischen Modellierung fokussieren, wie z.B. Faltungsnetzwerke zur Segmentierung von Bilddaten, generative Netzwerke zum Erzeugen neuer Bilddaten, oder physikalisch informierte Netzwerke zur Vorhersage bestimmter Transporteigenschaften einer Mikrostruktur. Darüber hinaus werden verschiedene wissenschaftliche Studien diskutiert, die die vorgestellten Methoden nutzen. Das Seminar eignet sich als Vorbereitung für die Anfertigung einer Bachelor- oder Masterarbeit zu ähnlichen Themen. Die Leistung im Seminar setzt sich zusammen aus einem eigenen Vortrag sowie der regelmäßigen und aktiven Teilnahme an den weiteren Seminarsitzungen.
| Voraussetzungen: | Wahrscheinlichkeitsrechnung |
| Zielgruppe: | Bachelor und Master Studierende in "Wirtschaftsmathematik", "Mathematik", "Mathematische Biometrie", "CSE", “Mathematical Data Science” oder "Lehramt Mathematik" |
| Credits: | 4 |
| Zeit und Ort: | TBA Erstes Treffen zur Themenvergabe: In der ersten Semesterwoche |
| Anmeldung: | Per Mail mit einer Top 3 Prioritätenliste der Themen an Léon Schröder |
Die quantitative Analyse digitaler (Bild-)Daten ist ein wichtiges Instrument in verschiedenen wissenschaftlichen Disziplinen wie Medizin, Geographie, Meteorologie, Elektrochemie oder Materialwissenschaften. Mathematische Techniken zur Mustererkennung oder zur Beschreibung komplexer Bildstrukturen mit Hilfe von räumlichen stochastischen Modellen können wertvolle Beiträge leisten. Die stochastische Geometrie bietet eine breite Palette an räumlichen stochastischen Modellen für verschiedene Anwendungen, z. B. zufällige Punktprozesse zur Beschreibung von Punktmustern im Raum, Zufallsgraphen zur Modellierung komplexer Netzwerkstrukturen und Zufallsmosaike zur Beschreibung von Mosaiken (zellulare oder granulare Strukturen).
Oft erfordern solche Techniken aber explizite Informationen über die Daten, die nur schwer zugänglich sind. In jüngster Zeit haben sich daher Methoden des maschinellen Lernens als nützliches Werkzeug für die Bildverarbeitung und damit auch für die räumliche stochastische Modellierung erwiesen. So können z. B. neuronale Faltungsnetze zur Verbesserung der Bildverarbeitung eingesetzt werden, die oft ein notwendiger Schritt vor der Modellierung ist. Darüber hinaus werden Methoden des maschinellen Lernens zur Vorhersage physikalischer Eigenschaften wie z. B. der Leitfähigkeit der Materialien, die mittels stochastischer Modelle generiert wurden, verwendet, die ansonsten nur schwer zu berechnen sind. Andererseits können sogenannte generative Netzwerke eingesetzt werden, um direkt neue virtuelle Bilddaten zu erzeugen, welche einem bekannten Datensatz ähnlich sind.
Kontakt
Seminar Supervisor
Prof. Dr. Volker Schmidt
E-Mail: volker.schmidt(at)uni-ulm.de
Dr. Benedikt Prifling
E-Mail: benedikt.prifling(at)uni-ulm.de
Seminar Advisor
Léon Schröder
E-Mail: leon.schroeder(at)uni-ulm.de
Liste von Vorträgen:
Fundamental concepts of stochastic geometry – point processes
| Speaker: | TBA |
| Date: | 06.11.2025 |
In order to assess whether a given realization of a spatial stochastic model is similar to a given measured image data set of a microstructured functional material, and in which sense this similarity holds, we require some fundamental concepts from stochastic geometry and probability theory [1]. This includes notions of random variables, random fields, random closed sets, random point processes and random tessellations, as well as basic characteristics and geometric descriptors used to obtain a statistical characteristic.
Graph-based stochastic microstructure modeling: Generating digital twins of electrode materials
| Speaker: | TBA |
| Date: | 13.11.2025 |
Random point processes can be used to generate digital twins of complex materials. For example in [2], random point processes were used to model the mesoporous structure of silica monoliths based on 3D image data. The fitted model can then generate new, statistically similar structures, making random point processes valuable tools for stochastic microstructure modeling.
Fundamental concepts of stochastic geometry – random fields and excursion sets
| Speaker: | TBA |
| Date: | 20.11.2025 |
In order to assess whether a given realization of a spatial stochastic model is similar to a given measured image data set of a microstructured functional material, and in which sense this similarity holds, we require some fundamental concepts from stochastic geometry and probability theory [1]. This includes notions of random variables, random fields, random closed sets, random point processes and random tessellations, as well as basic characteristics and geometric descriptors used to obtain a statistical characteristic.
Stochastic 3D microstructure modeling using excursion sets of random fields
| Speaker: | TBA |
| Date: | 27.11.2025 |
Random closed sets can be used to describe spatial structures with complex geometries, for instance the microstructures of nanoporous glass [3], gas-diffusion electrodes [4] and anodes of Lithium-ion batteries [5]. By fitting such models to 3D image data, one can generate virtual microstructures—so-called digital twins—that replicate key morphological features, enabling realistic simulations of material behavior and properties.
What is machine learning? An overview of different tasks and approaches
| Speaker: | TBA |
| Date: | 04.12.2025 |
For a general understanding and a short overview in the field of machine learning, different machine learning approaches and typical problems are briefly summarized. For example, techniques of unsupervised learning such as priniciple component analysis and techniques of supervised learning, such as linear regression and feed-forward neural networks networks [6] are explained.
Fundamental concepts of machine learning – CNNs and GANs
| Speaker: | TBA |
| Date: | 11.12.2025 |
Convolutional neural networks (CNNs) [7] are designed to process image data and are especially effective for tasks like image classification, object detection, and segmentation. Generative adversarial networks (GANs) [8], on the other hand, are used to generate realistic synthetic data by training two competing networks—a generator and a discriminator—leading to applications in image synthesis, super-resolution, and data augmentation.
Generative adversarial networks for the generation of multiphase microstructural data
| Speaker: | TBA |
| Date: | 18.12.2025 |
After training GANs [8] with a given data set of images, these networks can generate new images which are statistically similar to those of the training data set. Therefore, GANs can be considered to be spatial stochastic models. For example, in [9] a GAN was trained with with 3D image data depicting the three-phased microstructure of lithium-ion battery cathodes and solid oxide fuell cell anodes. Then, similar to a stochastic geometry model, the trained network is able to generate virtual, but realistic 3D image data.
Fundamental concepts of stochastic geometry – random tessellations
| Speaker: | TBA |
| Date: | 08.01.2026 |
In order to assess whether a given realization of a spatial stochastic model is similar to a given measured image data set of a microstructured functional material, and in which sense this similarity holds, we require some fundamental concepts from stochastic geometry and probability theory [1]. This includes notions of random variables, random fields, random closed sets, random point processes and random tessellations, as well as basic characteristics and geometric descriptors used to obtain a statistical characteristic.
Generating multi-scale NMC particles with radial grain architectures using spatial stochastics and GANs
| Speaker: | TBD |
| Date: | 15.01.2026 |
A stereological generative adversarial network (GAN)-based model fitting approach is presented that can generate representative 3D information from 2D data, enabling characterization of materials in 3D using cost-effective 2D data. Once calibrated, this multi-scale model is able to rapidly generate virtual NMC (Lithium-Nickel-Mangan-Cobalt-Oxide) cathode particles that are statistically similar to experimental data, and thus is suitable for virtual characterization and materials testing through numerical simulations [10].
Using convolutional neural networks for stereological characterization of 3D hetero-aggregates based on synthetic STEM data
| Speaker: | TBD |
| Date: | 22.01.2026 |
Since 3D imaging is complex and expensive, there are many approaches that attempt to reconstruct the information of a tomographic 3D image from a series of less expensive 2D STEM (scanning transmission electron microscopy) measurements. In this work, the 3D microstructure of hetero-aggregates is predicted from 2D data. A stochastic model is used to generate synthetic training data on which a convolutional network can be trained [11]. Ultimately, the network can then be used to predict the associated 3D structure from a 2D image.
Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion
| Speaker: | TBD |
| Date: | 29.01.2026 |
Generative adversarial networks (GANs) can be trained to generate 3D image data based on 3D training data. However, the acquisition 3D image data for model calibration is a time consuming and expensive task. While 2D image data naturally contains much less information, it is possible in some cases that a cross-sectional 2D slice carries enough information to statistically reconstruct the 3D sample. Therefore, a particular GAN-architecture is introduced that is able to generate 3D data based on a single representative 2D image [12].
Calibration of stochastic geometry models by combining generative adversarial networks with excursion sets of random fields
| Speaker: | TBD |
| Date: | 05.02.2026 |
Generative adversarial networks (GANs) are a strong data-driven machine learning tool for generating new synthetic image data based on existing data. In order to create a sufficient data base for training these GANs, classical spatial stochastic modeling is deployed in order to generate a virtual data base used for network training. Subsequently, the trained GAN can be used to sample virtual images that can be further analyzed, for example in numerical simulations. This approach has been used to generate virtual data of all-solid-state battery cathodes [13].
Literature
[1] S.N. Chiu, D. Stoyan, W.S. Kendall, J. Mecke. Stochastic Geometry and its Applications, J. Wiley & Sons (2013).
[2] B. Prifling, M. Neumann, D. Hlushkou, C. Kübel, U. Tallarek and V. Schmidt. Generating digital twins of mesoporous silica by graph-based stochastic microstructure modeling, Computational Materials Science 187 (2021), 109934.
[3] M. Neumann, P. Gräfensteiner, C. Santos de Oliveira, J. Martins-Schalinski. S. Koppka, D. Enke, P. Huber and V. Schmidt. Morphology of nanoporous glass: Stochastic 3D modeling, stereology and the influence of pore width. Physical Review Materials 8 (2024), 045605.
[4] M. Neumann, M. Osenberg, A. Hilger, D. Franzen, T. Turek, I. Manke, V. Schmidt. On a pluri-Gaussian model for three-phase microstructures, with applications to 3D image data of gas-diffusion electrodes. Computational Materials Science 156 (2019), 325-331.
[5] B. Prifling, M. Ademmer, F. Single, O. Benevolenski, A. Hilger, M. Osenberg, I. Manke and V. Schmidt. Stochastic 3D microstructure modeling of anodes in Lithium-ion batteries with a particular focus on local heterogeneities. Computational Materials Science 192 (2021), 110354.
[6] M. Nielsen. Neural Networks and Deep Learning: A Textbook, Determination Press, 2015.
[7] Y. Lecun, L. Bottou, Y. Bengio, P. Haffner. Gradient-based learning applied to document recognition, Proceedings of the IEEE, vol. 86, no. 11, pp. 2278-2324 (1998).
[8] I.J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio. Generative adversarial networks (2014). arXiv preprint arXiv:1406.2661.
[9] A. Gayon-Lombardo, L. Mosser, N.P. Brandon, S.J. Cooper. Pores for thought: generative adversarial networks for stochastic reconstruction of 3D multi-phase electrode microstructures with periodic boundaries. npj Computational Materials (2020), 6(1), 1-11.
[10] L. Fuchs, O. Furat, D. P. Finegan, J. Allen, F. L.E. Usseglio-Viretta, B. Ozdogru, P. J. Weddle, K. Smith, V. Schmidt. Generating multi-scale NMC particles with radial grain architectures using spatial stochastics and GANs, Communications Materials 6 (2025), 4.
[11] L. Fuchs, T. Kirstein, C. Mahr, O. Furat, V. Baric, A. Rosenauer, L. Mädler and V. Schmidt, Using convolutional neural networks for stereological characterization of 3D hetero-aggregates based on synthetic STEM data. Machine Learning: Science and Technology 5 (2024), 025007.
[12] S. Kench, S.J. Cooper, Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion. Nature Machine Intelligence 3, 299–305 (2021).
[13] O. Furat, S. Weber, R. Rekers, J. Schubert, M. Luczak, E. Glatt, A. Wiegmann, J. Janek, A. Bielefeld and V. Schmidt. Generative adversarial framework to calibrate excursion set models for the 3D microstructure of all-solid-state battery cathodes (2025). arXiv preprint arXiv:2503.17171