Digital Teaching
[list]
[*]Course materials are provided in digital form via Moodle.
[*]Short learning videos on theoretical foundations may be provided
[/list]
Course Contents
In this tutorial, methods of machine learning are to be used to solve typical problems in solid mechanics. In particular, artificial neural networks are used here, which are to be formulated and trained in such a way that important physical and mathematical properties of the problems are taken into account. This shall ensure that neural networks yield reliable, robust, and physically meaningful predictions.
The tasks and the documentation of results will be done in teams of 2 students. Each of the problems will be first introduced and discussed in a common session, then the teams will have 2-3 weeks to solve the current problem and document their results.
[u]Theoretical foundations:[/u]
[list]
[*]Structure and functioning of “Feed-Forward Neural Networks” (FFNNs)
[*]Construction principles for “Physics-Informed Neural Networks” (PINNs) that fulfill essential physical and mathematical problem requirements and properties, e.g. by network structure or training algorithms
[*]Basics of solid mechanics and numerical mechanics
[/list]
[u]Practical tasks:[/u]
[list]
[*]Implementation, training and evaluation of FFNNs / PINNs in TensorFlow / Python
[*]Construction of PINNs with the help of convex neural networks, data augmentation, and analytical formulations
[*]Applications on problems such as constitutive modelling, multiscale simulation, dynamics, or model order reduction
[/list]
Literature
[list]
[*]G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang. “Physics-informed machine learning”. Nature Reviews Physics 3:422–440 (2021)
[*]C. Y. Peng et al. “Multiscale Modeling Meets Machine Learning: What Can We Learn?”. Archives of Computational Methods in Engineering 28:1017–1037 (2020)
[*]K. E. Willcox, O. Ghattas, P. Heimbach. “The imperative of physics-based modeling and inverse theory in computational science”. Nature Computational Science 1(3):166–168 (2021)
[*]S. Kollmannsberger, D. D’Angella, M. Jokeit, L. Herrmann. “Deep Learning in Computational Mechanics: An Introductory Course”. In: Studies in Computational Intelligence, Vol. 977. Springer International Publishing, Cham (2021)
[*]D. K. Klein, M. Fernández, R. J. Martin, P. Neff, O. Weeger. “Polyconvex anisotropic hyperelasticity with neural networks”. Journal of the Mechanics and Physics of Solids 159:104703 (2022)
[/list]
Preconditions
Basic knowledge in computational mechanics and machine learning are desirable (e.g., numerical methods, finite element method, machine learning applications)
Expected Number of Participants
16
Further Grading Information
[u]Assessment methods:[/u]
Result presentations and discussions in small groups during the semester
[u]Registration for the tutorial:[/u]
Please register for the tutorial as a group of 2 students by sending an email to Dominik Klein (klein@cps.tu-darmstadt.de) after September 1, 2022. In the email, include your names, matriculation numbers, and a short summary of your knowledge and courses on the subjects of solid mechanics and machine learning.
Online Offerings
moodle
[list]
[*]Course materials are provided in digital form via Moodle.
[*]Short learning videos on theoretical foundations may be provided
[/list]
Course Contents
In this tutorial, methods of machine learning are to be used to solve typical problems in solid mechanics. In particular, artificial neural networks are used here, which are to be formulated and trained in such a way that important physical and mathematical properties of the problems are taken into account. This shall ensure that neural networks yield reliable, robust, and physically meaningful predictions.
The tasks and the documentation of results will be done in teams of 2 students. Each of the problems will be first introduced and discussed in a common session, then the teams will have 2-3 weeks to solve the current problem and document their results.
[u]Theoretical foundations:[/u]
[list]
[*]Structure and functioning of “Feed-Forward Neural Networks” (FFNNs)
[*]Construction principles for “Physics-Informed Neural Networks” (PINNs) that fulfill essential physical and mathematical problem requirements and properties, e.g. by network structure or training algorithms
[*]Basics of solid mechanics and numerical mechanics
[/list]
[u]Practical tasks:[/u]
[list]
[*]Implementation, training and evaluation of FFNNs / PINNs in TensorFlow / Python
[*]Construction of PINNs with the help of convex neural networks, data augmentation, and analytical formulations
[*]Applications on problems such as constitutive modelling, multiscale simulation, dynamics, or model order reduction
[/list]
Literature
[list]
[*]G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang. “Physics-informed machine learning”. Nature Reviews Physics 3:422–440 (2021)
[*]C. Y. Peng et al. “Multiscale Modeling Meets Machine Learning: What Can We Learn?”. Archives of Computational Methods in Engineering 28:1017–1037 (2020)
[*]K. E. Willcox, O. Ghattas, P. Heimbach. “The imperative of physics-based modeling and inverse theory in computational science”. Nature Computational Science 1(3):166–168 (2021)
[*]S. Kollmannsberger, D. D’Angella, M. Jokeit, L. Herrmann. “Deep Learning in Computational Mechanics: An Introductory Course”. In: Studies in Computational Intelligence, Vol. 977. Springer International Publishing, Cham (2021)
[*]D. K. Klein, M. Fernández, R. J. Martin, P. Neff, O. Weeger. “Polyconvex anisotropic hyperelasticity with neural networks”. Journal of the Mechanics and Physics of Solids 159:104703 (2022)
[/list]
Preconditions
Basic knowledge in computational mechanics and machine learning are desirable (e.g., numerical methods, finite element method, machine learning applications)
Expected Number of Participants
16
Further Grading Information
[u]Assessment methods:[/u]
Result presentations and discussions in small groups during the semester
[u]Registration for the tutorial:[/u]
Please register for the tutorial as a group of 2 students by sending an email to Dominik Klein (klein@cps.tu-darmstadt.de) after September 1, 2022. In the email, include your names, matriculation numbers, and a short summary of your knowledge and courses on the subjects of solid mechanics and machine learning.
Online Offerings
moodle
- Lehrende: Yusuf Elbadry
- Lehrende: Maximilian Kannapinn
- Lehrende: Dominik Klein
- Lehrende: Oliver Weeger
Semester: WT 2023/24