Course Contents
The digital twin, a virtual representation of a physical object that mimics its structure and behavior to inform decisions and optimize operational efficiency, promises to revolutionize decision-making across domains. While modelling, simulation, and optimization have been a standard practice in science and engineering for long, the complementary role of models and data as well as a holistic and life cycle spanning approach distinguishes the digital twin paradigm. This requires complementary computational tools, specifically merging first principle and data-based methods.
The course „Computational Methods for (Real-time) Digital Twins” reviews the major computational methods enabling to put digital twins in practice. The topics of the lecture are mostly concerning the following:
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[*]Efficient classical approximation methods of solutions of ordinary and partial differential equations (finite-element methods, spectral methods,multi-grid methods)
[*]Regression and learning technologies (parameter estimation, polynomial regression, neural networks, gaussian processes)
[*]Model-order reduction technologies (proper orthogonal decomposition, operator inference,
[*]Regression based approximation methods of solutions of ordinary and partial differential equations (physics-informed neural networks, deep neuraloperators, random feature methods)
[*]Inverse problems and control theory for dynamical systems (linear control theory, Kalman filter)
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The corresponding topics will be presented along real-world application cases specifically also addressing implementation aspects, including the understanding of relevant hardware (CPUs, GPUs).
Literature
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[*]Lecture notes
[*]Brunton, S. L., & Kutz, J. N. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (2nd ed.). Cambridge: Cambridge University Press, ISBN: 978-1-00909-848-9
[*]Asch, M. (2022). A Toolbox for Digital Twins: From Model-Based to Data-Driven. SIAM, ISBN:978-1-61197-696-0
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Preconditions
Recommended: Basic knowledge of numerical methods for solving ordinary (and partial) differential equations.
- Lecturer: HartmannDirk
- Lecturer: SchöpsSebastian