# Schrodinet
[](https://app.codacy.com/gh/NLESC-JCER/Schrodinet?utm_source=github.com&utm_medium=referral&utm_content=NLESC-JCER/Schrodinet&utm_campaign=Badge_Grade_Dashboard)
Quantum Monte-Carlo Simulations of one-dimensional problem using Radial Basis Functions Neural Networks.
<p align="center">
<img src="./pics/morse.gif" title="Optimization of the wave function">
</p>
## Installation
Clone the repo and `pip` insatll the code
```
git clone https://github.com/NLESC-JCER/Schrodinet/
cd Schrodinet
pip install .
```
## Harmonic Oscillator in 1D
The script below illustrates how to optimize the wave function of the one-dimensional harmonic oscillator.
```python
import torch
from torch import optim
from schrodinet.sampler.metropolis import Metropolis
from schrodinet.wavefunction.wf_potential import Potential
from schrodinet.solver.solver_potential import SolverPotential
from schrodinet.solver.plot_potential import plot_results_1d, plotter1d
def pot_func(pos):
'''Potential function desired.'''
return 0.5*pos**2
def ho1d_sol(pos):
'''Analytical solution of the 1D harmonic oscillator.'''
return torch.exp(-0.5*pos**2)
# Define the domain and the number of RBFs
# wavefunction
wf = Potential(pot_func, domain, ncenter, fcinit='random', nelec=1, sigma=0.5)
# sampler
sampler = Metropolis(nwalkers=1000, nstep=2000,
step_size=1., nelec=wf.nelec,
ndim=wf.ndim, init={'min': -5, 'max': 5})
# optimizer
opt = optim.Adam(wf.parameters(), lr=0.05)
scheduler = optim.lr_scheduler.StepLR(opt, step_size=100, gamma=0.75)
# Solver
solver = SolverPotential(wf=wf, sampler=sampler,
optimizer=opt, scheduler=scheduler)
# Train the wave function
plotter = plotter1d(wf, domain, 100, sol=ho1d_sol)
solver.run(300, loss='variance', plot=plotter, save='model.pth')
# Plot the final wave function
plot_results_1d(solver, domain, 100, ho1d_sol, e0=0.5, load='model.pth')
```
After otpimization the following trajectory can easily be generated :
<p align="center">
<img src="./pics/ho1d.gif" title="Optimization of the wave function">
</p>
The same procedure can be done on different potentials. The figure below shows the performace of the method on the harmonic oscillator and the morse potential.
<p align="center">
<img src="./pics/rbf1d_summary.png" title="Results of the optimization">
</p>
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"description": "# Schrodinet\n\n\n[](https://app.codacy.com/gh/NLESC-JCER/Schrodinet?utm_source=github.com&utm_medium=referral&utm_content=NLESC-JCER/Schrodinet&utm_campaign=Badge_Grade_Dashboard)\n\nQuantum Monte-Carlo Simulations of one-dimensional problem using Radial Basis Functions Neural Networks.\n<p align=\"center\">\n<img src=\"./pics/morse.gif\" title=\"Optimization of the wave function\">\n</p>\n\n\n## Installation\n\nClone the repo and `pip` insatll the code\n\n```\ngit clone https://github.com/NLESC-JCER/Schrodinet/\ncd Schrodinet\npip install .\n```\n\n## Harmonic Oscillator in 1D\n\nThe script below illustrates how to optimize the wave function of the one-dimensional harmonic oscillator.\n\n```python\nimport torch\nfrom torch import optim\n\nfrom schrodinet.sampler.metropolis import Metropolis\nfrom schrodinet.wavefunction.wf_potential import Potential\nfrom schrodinet.solver.solver_potential import SolverPotential\nfrom schrodinet.solver.plot_potential import plot_results_1d, plotter1d\n\ndef pot_func(pos):\n '''Potential function desired.'''\n return 0.5*pos**2\n\n\ndef ho1d_sol(pos):\n '''Analytical solution of the 1D harmonic oscillator.'''\n return torch.exp(-0.5*pos**2)\n\n# Define the domain and the number of RBFs\n\n# wavefunction\nwf = Potential(pot_func, domain, ncenter, fcinit='random', nelec=1, sigma=0.5)\n\n# sampler\nsampler = Metropolis(nwalkers=1000, nstep=2000,\n step_size=1., nelec=wf.nelec,\n ndim=wf.ndim, init={'min': -5, 'max': 5})\n\n# optimizer\nopt = optim.Adam(wf.parameters(), lr=0.05)\nscheduler = optim.lr_scheduler.StepLR(opt, step_size=100, gamma=0.75)\n\n# Solver\nsolver = SolverPotential(wf=wf, sampler=sampler,\n optimizer=opt, scheduler=scheduler)\n\n# Train the wave function\nplotter = plotter1d(wf, domain, 100, sol=ho1d_sol)\nsolver.run(300, loss='variance', plot=plotter, save='model.pth')\n\n# Plot the final wave function\nplot_results_1d(solver, domain, 100, ho1d_sol, e0=0.5, load='model.pth')\n```\n\nAfter otpimization the following trajectory can easily be generated :\n\n<p align=\"center\">\n<img src=\"./pics/ho1d.gif\" title=\"Optimization of the wave function\">\n</p>\n\nThe same procedure can be done on different potentials. The figure below shows the performace of the method on the harmonic oscillator and the morse potential.\n\n<p align=\"center\">\n<img src=\"./pics/rbf1d_summary.png\" title=\"Results of the optimization\">\n</p>\n\n\n",
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