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:
.
├── LICENSE
├── MMA
│ ├── homogeneousGas.nb
│ └── vac.nb
├── README.md
├── 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
├── vacOsc4CompSSConvention-moretol.py
├── vacOsc4CompSSConvention-verify.py
├── xresult-1.txt
├── xresult-moretol.txt
└── xresult.txt
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.- The folder
MMA
is for my Mathematica code related to this problem. ipynb
contains the Jupyter Notebooks.Basics.ipynb
: the basics of the idea. quite similar to the talk mentioned above.HomogeneousModel.ipynb
: solving Homogeneous gas model of neutrino oscillations.NetworkConstructor.ipynb
: example of network constructor for differential equations.ann_julia.ipynb
: Julia code example.test.ipynb
: testing different methods, benchmarking functions.vacOsc4Comp.ipynb
: Solving neutrino vacuum oscillations.vacOsc4CompSSConvention.ipynb
: vacuum oscillations using Shanshak's conventionvacOsc4Fourier.ipynb
: Using Fourier as the internal network structure, aka, Fourier analysis as approximators.vacOsc4Piecewise.ipynb
: Using piecewise functions as approximatorsvacuumClean.ipynb
: Vacuum oscillations cleaned upvacuum4Component.ipynb
: Vacuum oscillations with 4-component conventions
py
folder is for the python code.