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ANN - Artificial Neural Network Method

Artificial neural network for differential equation solving.


I gave a talk about this idea a while ago. A Physicist's Crash Course on Artificial Neural Network

We did not use the simple back-prop method for the project because it's aweful. (I do not have the original code for it but I rewrote an example using PyTorch.) We really need much better cost minimization method. So we tested the best minimization algorithms here.

Structure of this repository:

├── MMA
│   ├── homogeneousGas.nb
│   └── vac.nb
├── ipynb
│   ├── Basics.ipynb
│   ├── Basics.ipynb.bak
│   ├── HomogeneousModel.ipynb
│   ├── NetworkConstructor.ipynb
│   ├── Untitled.ipynb
│   ├── Untitled1.ipynb
│   ├── ann_julia.ipynb
│   ├── assets
│   ├── test.ipynb
│   ├── vacOsc4Comp.ipynb
│   ├── vacOsc4CompSSConvention.ipynb
│   ├── vacOsc4Fourier.ipynb
│   ├── vacOsc4Piecewise.ipynb
│   ├── vacuum-Copy1.ipynb
│   ├── vacuum-Copy2.ipynb
│   ├── vacuum.ipynb
│   ├── vacuum4Component.ipynb
│   └── vacuumClean.ipynb
├── notes
│   └── note-2015S.pdf
└── py
    ├── functionvalue-moretol.txt
    ├── functionvalue.txt
    ├── ss
    ├── timespent-moretol.txt
    ├── timespent.txt
    ├── xresult-1.txt
    ├── xresult-moretol.txt
    └── xresult.txt
  1. notes is the notes for the project. I explained some of the conventions and the preliminary results. I pulled this file from my private repo of the project. I think it can made public now.
  2. The folder MMA is for my Mathematica code related to this problem.
  3. ipynb contains the Jupyter Notebooks.
    1. Basics.ipynb: the basics of the idea. quite similar to the talk mentioned above.
    2. HomogeneousModel.ipynb: solving Homogeneous gas model of neutrino oscillations.
    3. NetworkConstructor.ipynb: example of network constructor for differential equations.
    4. ann_julia.ipynb: Julia code example.
    5. test.ipynb: testing different methods, benchmarking functions.
    6. vacOsc4Comp.ipynb: Solving neutrino vacuum oscillations.
    7. vacOsc4CompSSConvention.ipynb: vacuum oscillations using Shanshak's convention
    8. vacOsc4Fourier.ipynb: Using Fourier as the internal network structure, aka, Fourier analysis as approximators.
    9. vacOsc4Piecewise.ipynb: Using piecewise functions as approximators
    10. vacuumClean.ipynb: Vacuum oscillations cleaned up
    11. vacuum4Component.ipynb: Vacuum oscillations with 4-component conventions
  4. py folder is for the python code.
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