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Instructors: Prof. Dr. rer. nat. Oliver Weeger
Event type:
Tutorial
Org-unit: Dept. 16 - Mechanical Engineering
Displayed in timetable as:
Tut ML Solid Mech
Subject:
Crediting for:
Hours per week:
4
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Digital Teaching:
- Course materials are provided in digital form via Moodle.
- Short learning videos on theoretical foundations may be provided
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.
Theoretical foundations:
- 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
Practical tasks:
- 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
Literature:
- 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)
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:
Assessment methods:
Result presentations and discussions in small groups during the semester
Registration for the tutorial:
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
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