课程信息

Digital Teaching
Digital course materials; Interactive tutorials and programming examples (with MATLAB, Python, TensorFlow, Jupyter, GitHub, ...)

Course Contents
[list]
[*]Physics-aware machine learning (ML) combines classical, physics-based modeling approaches with ML methods to improve the generalization capabilities, interpretability, robustness, reliability and efficiency of ML methods in engineering applications
[*]Introduction to ML methods and their essential theoretical properties, including in particular artificial neural networks (approximation capabilities, training, gradients, etc.)
[*]Foundations of physics-based modeling and simulation using differential equations and suitable temporal and spatial discretization methods (time integration and finite elements)
[*]Physics-based and data-driven model order reduction and surrogate modeling (e.g. modal analysis, orthogonal decompositions, kriging, kernel methods, etc.)
[*]Mathematical knowledge representations of conservation equations & quantities, symmetries, invariances, etc. for physics-aware ML
[*]Construction principles for informing or augmenting ML methods through appropriate design of training data, hypotheses for input and output variables of ML models, ML model architectures, or learning or training algorithms
[*]Methods include e.g. Sobolev training, convex & monotonic NNs, physics-informed NNs (PINNs), Langrangian NNs, neural operators, stochastic NNs, recurrent NNs, convolutional NNs, graph NNs, autoencoders, generative NNs, Gaussian processes & kernel methods, etc.
[*]Applications and examples for solid mechanics, structural dynamics, material modeling, dynamic systems, multiscale and multiphysics problems, (additive) manufacturing processes, digital twins, etc.
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Preconditions
Basic knowledge on machine learning, physical modelling, and numerical simulation (in particular differential equations, time integration, finite elements) is recommended.
Experience with machine learning and programming skills are advantageous, but not essential.

Official Course Description
On successful completion of this module, students should be able to:
1.    Know and identify possible applications for physics-aware machine learning in engineering modeling and simulation
2.    Mathematically formalize physical and mathematical properties such as energy conservation, symmetries, invariances, and solvability requirements
3.    Describe, explain and discuss basic approaches and algorithms of physics-aware ML
4.    Explain and evaluate suitable physics-informed and physics-augmented model architectures with neural networks for various fields of application
5.    Describe and explain the improved generalization capabilities, interpretability, robustness, reliability, and efficiency of physics-aware ML concepts

Online Offerings
Moodle