Data-driven Modeling#
Clustering of Time-Series Data#
Content:
This course enables students to apply clustering procedures to analyze time series data and teach them how and why this data requires special procedures.
Learning Objectives:
Students will learn about time series data in general, clustering methods, and distance measures.
Link to the repository:
Check out https://git.rz.tu-bs.de/scibiome/ki4all/clustering-of-time-series-data.git or
git clone https://git.rz.tu-bs.de/scibiome/ki4all/clustering-of-time-series-data.git
Previous Microcredits: Machine Learning Introduction
Extent: 1 ECTS
Responsible: Peter L. Reichertz Institute for Medical Informatics, TU Braunschweig
DeepONet#
Content:
In this microcredit, you will be introduced to the concept of designing a deep neural network (DNN) for accurate approximation of operators which map input functions into output functions. These operators can be explicit or implicit types. In its simplest form an explicit operator could be a derivative or integral operator of any desired functions. A good example of implicit type would be the solution operators of ordinary/partial differential equations (ODEs/PDEs).
Learning Objectives:
The students are familiar with deep neural networks (DNN).
Link to the repository:
Check out https://git.rz.tu-bs.de/irmb/teaching/microcredentials/deeponet.git or
git clone https://git.rz.tu-bs.de/irmb/teaching/microcredentials/deeponet.git
Previous Microcredits: Machine Learning Introduction
Extent: 1 ECTS
Responsible: iRMB, TU BS
Dimensionality Reduction and Feature Selection#
Content:
This course familiarizes students with the background and methods of dimension reduction and feature selection.
The course covers topics like the Curse of Dimensionality and forward/backward feature elimination. It also teaches essential methods like Principal Component Analysis (PCA), T-distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP).
Learning Objectives:
The students are familiar with the methods of dimension reduction and feature selection.
Link to the repository:
Check out https://git.rz.tu-bs.de/scibiome/ki4all/dimensionality-reduction-and-feature-selection.git or
git clone https://git.rz.tu-bs.de/scibiome/ki4all/dimensionality-reduction-and-feature-selection.git
Previous Microcredits: Machine Learning Introduction
Extent: 1 ECTS
Responsible: Peter L. Reichertz Institute for Medical Informatics, TU Braunschweig
Physics-Informed Neural Networks#
Content:
Neural networks are an exciting technique to solve a variety of scientific
problems. They are usually used in the data-driven regime. Less known is their
applicability to partial differential equations (PDE), where they can
be used to obtain solutions to boundary value problems directly without any
data. This approach is called physics informed neural networks (PINN).
Learning Objectives:
In this small project, you will familiarize yourself with this approach and
solve a simple steady-state heat equation.
Link to the repository:
Check out https://git.rz.tu-bs.de/irmb/teaching/microcredentials/physics-informed-neural-networks.git or
git clone https://git.rz.tu-bs.de/irmb/teaching/microcredentials/physics-informed-neural-networks.git
Previous Microcredits: Machine Learning Introduction
Extent: 1 ECTS
Responsible: iRMB, TU BS
Statistical Finite Element Method#
Content:
Nowadays, digital image correlation is used to measure strain and displacement, though it’s often limited to accessible areas. To gauge inaccessible regions, constitutive models calibrated via conventional Bayesian update to infer full-field displacements and stress from sparse data. However, calibration accuracy can vary, particularly with aging structures. The recently proposed statistical Finite Element Method (statFEM) uses displacement as the stochastic prior, quantifying model-reality mismatch. It improves computational efficiency, reducing the need to solve partial differential equations online by identifying just three hyperparameters. This method, a type of physics-based regression, is particularly beneficial for online applications.
Learning Objectives:
The stuents are familiar with the statistical Finite Element Method (statFEM).
Link to the repository:
Check out https://git.rz.tu-bs.de/irmb/teaching/microcredentials/statfem.git or
git clone https://git.rz.tu-bs.de/irmb/teaching/microcredentials/statfem.git
Previous Microcredits: Machine Learning Introduction
Extent: 1 ECTS
Responsible: iRMB, TU BS