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

Workflow:

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

Information:

Magnetic Image mapping:

• Black ... +1
• White ... -1

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 from Torch module -> X
• Revisited read.py for data-reading (exp. recordings) -> X
• preprocessing.py script for right MCD calculation -> X
• Integration of new MCD PreProcessing class -> X
  • Read PIL Image to Tensor
  • Compute MCD
  • Save as CSV for Post-Reading Simulations
• Preprocessing -> Reading -> Evaluation (params.json) -> Postprocessing -> X
• Lipschitz constant calculation -> X
• Finite Difference / Fourier method calculation -> X
• Initial File Reading methods (Raw, Standardized, Stand.+ Shift, Clipped) -> X
• Experimental Data Results -> X
• Fourier Modes -> X
• Master thesis Chapter Allignment -> X
• Check Energy convergence with exp. data -> X
• Comparison for non-dx / dx simulation -> X
• Make power law estimator plot -> X
• Implement asymptotic evolution (Condette page 75) -> X
• Check GD algorithm once for possible errors (such slow convergence) -> X
• Check Lipshitz constant -> implement in GD for rerun + autograd check once again -> X

Open:

High Priority:

• Integrate data-savings for all algorithms
• simulation evolution / concurrent savings for let'say max_it/10 times
• single domain evolution
• Check runtimes by multiple runs to get an appropriate estimator -> runtime.py script
• Standardize plotting schematic + LaTex Font integration (still open: axis + latex font)