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:
. ├── 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
notesis 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
MMAis for my Mathematica code related to this problem.
ipynbcontains 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 convention
vacOsc4Fourier.ipynb: Using Fourier as the internal network structure, aka, Fourier analysis as approximators.
vacOsc4Piecewise.ipynb: Using piecewise functions as approximators
vacuumClean.ipynb: Vacuum oscillations cleaned up
vacuum4Component.ipynb: Vacuum oscillations with 4-component conventions
pyfolder is for the python code.