Magnetic Imaging

Master Thesis supervised by Prof. Martin Schultze and Prof. Thomas Pock.

Numerical optimization algorithms for simualating magnetic pattern formation

Various Gradient Descent methods + Adapted Crank Nicolson schematic re-implemented from Nicolas Condette: Pattern Formation in Magnetic Thin Films: Analysis and Numerics

Code Structure:

Parent scripts:

• env_utils.py ... helper functions and overall stuff which is multiple used
• params.py ... global parameter dataclasses
• pattern_formation.py ... pattern formation methods

Numerical methods:

• gradient_descent.py ... Gradient Descent method ()
• gd_proximal.py ... Proximal Gradient Descent method
• gd_nesterov.py ... Accelerated Gradient Descent method
• crank_nicolson.py ... Adapted Crank Nicolson method with reference to N.C.

Evaluation scripts:

• evaluation.py ... Evaluation script
• evaluation_add.py ... Evaluation script for multiple instances
• parameter_study.py ... Simulation parameters Gamma & Epsilon Parameter study

Auxilliary scripts:

• preprocessing.py ... Raw *.TIF data reader and MCD pre-processing -> to *.CSV
• read.py ... CSV-Reader Method

ToDo's:

Closed:

• Implement Gradient Descent for Pattern Formation -> X
• Check (2pi)² factor at linear operator at CN -> X
• Re-Implement Fourier Multiplier with safe operation for divergence + vectorized -> X
• Integrate GD Autograd for learning rate backtracking -> X
• Integrate Prox.GD + Nesterov -> X
• Check Sin() stripe-pattern evolution -> check / no parallel-diagonal stripes obtained -> X
• Implement CN STOP_BY_LIMIT -> X
• Check runtimes + convergence for correct implementation -> X
• Implement comparison.py script -> X
• Integrate function dataclasses asdict for main methods -> X
• comparison.py: plot all u's after e.g.: 1000 iterations -> X
• Check all scripts for loop efficiency & parallelization for Torch module -> X
• Revisited read.py for data-reading (exp. recordings) -> X
• preprocessing.py script for right MCD calculation -> X

Open:

High Priority:s

• Integrate data-savings for all algorithms (+ concurrent savings for let'say max_it/10 times)

Low Priority:

• Check runtimes by multiple runs to get an appropriate estimator -> runtime.py script
• Check GD algorithm once for possible errors (such slow convergence)
• Standardize plotting schematic + LaTex Font integration (still open: axis + latex font)

Workflow:

• preprocessing.py ... preprocess raw data
• read.py ... read preprocessed data
• pattern_formation.py ... run pattern formation algorithm
• evaluation_add.py ... evaluate results

Information:

• Black ... +1
• White ... -1

ToDo:

• Integrate seperate dataclasses for Spectral / Non-Spectral Simulation for GD Nesterov
• Comparison for non-dx / dx simulation
• Graphical representation