update

content/07_hub/3_datadrivenmodeling/3_datadrivenmodeling.md

+## DeepONet
+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).
+
+```console
+git clone https://git.rz.tu-bs.de/my-name-space/my-repo.git
+```
+**Extent: 1 ECTS**\
+**Responsible: iRMB, TU BS**
+## Physics-Informed Neural Networks
+
+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).
+In this small project, you will familiarize yourself with this approach and
+solve a simple steady-state heat equation.
+
+```console
+git clone https://git.rz.tu-bs.de/my-name-space/my-repo.git
+```
+**Extent: 1 ECTS**\
+**Responsible: iRMB, TU BS**
+## Statistical Finite Element Method
+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.
+```console
+git clone https://git.rz.tu-bs.de/my-name-space/my-repo.git
+```
+**Extent: 1 ECTS**\
+**Responsible: iRMB, TU BS**

content/07_hub/3_datadrivenmodeling/deeponet.md

+## DeepONet
+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).
+
+```console
+git clone https://git.rz.tu-bs.de/my-name-space/my-repo.git
+```
+**Extent: 1 ECTS**\
+**Responsible: iRMB, TU BS**

content/07_hub/3_datadrivenmodeling/pinn.md

+## Physics-Informed Neural Networks
+
+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).
+In this small project, you will familiarize yourself with this approach and
+solve a simple steady-state heat equation.
+
+```console
+git clone https://git.rz.tu-bs.de/my-name-space/my-repo.git
+```
+**Extent: 1 ECTS**\
+**Responsible: iRMB, TU BS**

content/07_hub/3_datadrivenmodeling/statFEM.md

+## Statistical Finite Element Method
+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.
+```console
+git clone https://git.rz.tu-bs.de/my-name-space/my-repo.git
+```
+**Extent: 1 ECTS**\
+**Responsible: iRMB, TU BS**