Lecture "Physics-aware Machine Learning"

Lecturer: Prof. Oliver Weeger

Assistants: Dr.-Ing. Maximilian Kannapinn, Jasper O. Schommartz, Dominik K. Klein

Lecture website: link

Research group website: link

Description

This repository offers a collection of lecture materials and code examples accompanying the lecture "Physics-aware Machine Learning" at TU Darmstadt (module no. 16-73-4144).

Lecture material

Chapter 01: Introduction

• FFNN_introduction: Demo of regression of simple functions with FFNNs

Chapter 02: Physics-based modeling & simulation

• ode_examples: Numerical integration of ODEs in MATLAB
• nlebb: Finite element discretization and numerical integration of dynamic nonlinear Euler Bernoulli beam in MATLAB

Chapter 05: Physics-aware losses

• PINNs: Physics-informed neural networks for the geometrically linear and nonlinear Euler-Bernoulli beam using Python and Jax

Chapter 06: PAML for dynamic systems

• nlebb_dynamic_batch: Automated data generation with the non-linear Euler Bernoulli beam in MATLAB
• NeuralODE: Demo of augmented neural ODEs in JAX

Additional Information

Reproducing results for Task FFNN ROM

To reproduce the results for Task FFNN ROM in the FFNN_ROM directory, the following steps must be followed.

Step 1: Generation of SVD modes

Run the nlebb/nlebb_dynamic_svd.m MATLAB file for the following loads and make sure the svdUU1.mat and svdUS1.mat output files for the SVD modes are produced (They will be required in the next step.):

% -------------------------------------------------------------------------
% --- DEFINE LOADS 

load_f = 0;
load_q = 0;
load = @(x,t) [load_f, load_q];    

tPer = .1;
Nx = @(t) [0 0 0 0];
Qz = @(t) [0 0 0 multiphase_multisin(2,0.085,100,1,3,t)];
My = @(t) 0;

Step 2: Data generation

Next, run nlebb/nlebb_dynamic_proj.m several times for different exitations Qz. Save the produced q0all.txt, Qfall.txt, and QKQall.txt files to FFNN_ROM/data/${loadcase} accoding to their respective load case. The excitations are:

1. Multisine train 1: Qz = @(t) [0 0 0 multiphase_multisin(2,0.085,100,1,3,t)];
2. Multisine train 2: Qz = @(t) [0 0 0 multiphase_multisin(2,0.085,100,2,3,t)];
3. Multisine train 3: Qz = @(t) [0 0 0 multiphase_multisin(2,0.085,100,3,3,t)];
4. Multisine test: Qz = @(t) [0 0 0 multiphase_multisin(1,0.103,78,1,1,t)];
5. Sine test: Qz = @(t) [0 0 0 1.5*sin(2*pi*6*t)];
6. Step test: Qz = @(t) [0 0 0 -10*(t>.2)];
7. Dirac test: Qz = @(t) [0 0 0 -10*(t>.5)*(t<.51)];
8. Quasi-static test: Qz = @(t) [0 0 0 -2*t];

The remaining inputs are:

% -------------------------------------------------------------------------
% --- INPUTS

qmode = 2;
qm = 4;
qdeim = 0;

qnn = 0;

load_f = 0;
load_q = 0;
load = @(x,t) [load_f, load_q];    

tPer = .1;
Nx = @(t) [0 0 0 0];
Qz = @(t) % INSERT EXCITATION HERE
My = @(t) 0;

Step 3: Neural network model calibration

Execute the force.ipynb and potential.ipynb notebooks in FFNN_ROM/notebooks with default settings and save the obtained model weights in FFNN_ROM/data/force.weights.txt and FFNN_ROM/data/potential.weights.txt, respectively.

Step 4: Run simulation with NN models

To run the calibrated NN models in nlebb/nlebb_dynamic_proj.m, set qnn to the desired model and run for any of the excitations in (2).