Seminar: Generatives maschinelles Lernen: Anwendungen neuronaler Netze bei räumlicher stochastischer Modellierung

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In order to assess whether a given random realization of a model is similar to a given measured 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, fields, random closed sets, as well as basic characteristics and geometric descriptors used to obtain a statistical description, such as the covariance function of a random field or geometric descriptors such as volume fraction or geodesic tortuosity of a given random set.

[1] S.N. Chiu, D. Stoyan, W.S. Kendall, J. Mecke. Stochastic Geometry and its Applications, J. Wiley & Sons (2013).

In order to assess whether a given random realization of a model is similar to a given measured 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, fields, random closed sets, as well as basic characteristics and geometric descriptors used to obtain a statistical description, such as the covariance function of a random field or geometric descriptors such as volume fraction or geodesic tortuosity of a given random set.

[1] S.N. Chiu, D. Stoyan, W.S. Kendall, J. Mecke. Stochastic Geometry and its Applications, J. Wiley & Sons (2013).

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 un-supervised learning such as priniciple component analysis, Q-learning, reinforcement learning, and techniques of supervised learning, such as linear regression, random forest classifier and recurrent or convolutional neural networks networks [2]

[2] I. Goodfellow, Y. Bengio, A. Courville. Deep Learning, MIT Press (2016).

Real-valued non-volume preserving (NVP) transformations are a class of functions used to construct a general unsupervised learning algorithm for generative probabilistic modeling. Unsupervised learning has the great advantage of not requiring a ground-truth, which is often produced by time consuming hand labelling. The model is trained on four natural image data sets and produces sharp and realistic images, that are qualitatively competitive with other generative probabilistic modeling algorithms [5].

[5] L. Dinh, J. Sohl-Dickstein, and S. Bengio. "Density estimation using real nvp." arXiv preprint arXiv:1605.08803 (2016).

Although recent advances in deep generative networks have enabled the inverse design of material microstructures, most studies involve property-conditional generation and focus on a specific type of structure, resulting in limited generation diversity and poor human–computer interaction. In this study, a pioneering text-to-microstructure deep generative network (Txt2Microstruct-Net) is proposed that enables the generation of 3D material microstructures directly from text prompts without additional optimization procedures. The Txt2Microstruct-Net model is trained on a large microstructure-caption paired dataset that is extensible using the algorithms provided. Moreover, the model is sufficiently flexible to generate different geometric representations, such as voxels and point clouds. The model's performance is also demonstrated in the inverse design of material microstructures and metamaterials [6].

[6] X. Zheng, I. Watanabe, J. Paik, J. Li, X. Guo, M. Naito, Text-to-Microstructure Generation Using Generative Deep Learning. Small 2024, 20, 2402685.

A deep learning method that can synthesize realistic three-dimensional microstructures with controlled structural properties using the combination of generative adversarial networks (GAN) and actor-critic (AC) reinforcement learning is proposed. The scientific contribution of this paper resides in the novel design of the GAN-AC microstructure generator and the mathematical and algorithmic foundations therein [7].

[7] Nguyen, P.C.H., Vlassis, N.N., Bahmani, B. et al. Synthesizing controlled microstructures of porous media using generative adversarial networks and reinforcement learning. Sci Rep 12, 9034 (2022).

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 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 [8]. Ultimately, the network can then be used to predict the associated 3D structure from a 2D image.

[8] 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.

Three-dimensional (3D) images provide a comprehensive view of material microstructures, enabling numerical simulations unachievable with two-dimensional (2D) imaging alone. However, obtaining these 3D images can be costly and constrained by resolution limitations. A method capable of generating large-scale 3D images of material microstructures, such as metal or rock, from a single 2D image is introduced. The method combines a denoising diffusion probabilistic model with a generative adversarial network framework [9].

[9] Phan, J., Sarmad, M., Ruspini, L. et al. Generating 3D images of material microstructures from a single 2D image: a denoising diffusion approach. Sci Rep 14, 6498 (2024).

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 cathode particles that are statistically similar to experimental data, and thus is suitable for virtual characterization and materials testing through numerical simulations [10].

[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. arXiv preprint arXiv:2407.05333 (2024).

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 [11].

[11] S. Kench, S.J. Cooper, Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion. Nat Mach Intell 3, 299–305 (2021).