# This example was adapated from https://github.com/muhrin/milad
# It is licensed under the GLPv3 license. You can find a copy of it
# here: https://www.gnu.org/licenses/gpl-3.0.en.html .

import torch
from torch import nn
from torch.nn.functional import mse_loss
from torch.func import jacrev, vmap

sigma = 0.5
epsilon = 4.


def lennard_jones(r):
    return epsilon * ((sigma / r)**12 - (sigma / r)**6)


def lennard_jones_force(r):
    """Get magnitude of LJ force"""
    return -epsilon * ((-12 * sigma**12 / r**13) + (6 * sigma**6 / r**7))


training_size = 1000
r = torch.linspace(0.5, 2 * sigma, steps=training_size, requires_grad=True)

# Create a bunch of vectors that point along positive-x
drs = torch.outer(r, torch.tensor([1.0, 0, 0]))
norms = torch.norm(drs, dim=1).reshape(-1, 1)
# Create training energies
training_energies = torch.stack(list(map(lennard_jones, norms))).reshape(-1, 1)
# Create forces with random direction vectors
training_forces = torch.stack([force * dr for force, dr in zip(map(lennard_jones_force, norms), drs)])

model = nn.Sequential(
    nn.Linear(1, 16),
    nn.Tanh(),
    nn.Linear(16, 16),
    nn.Tanh(),
    nn.Linear(16, 16),
    nn.Tanh(),
    nn.Linear(16, 16),
    nn.Tanh(),
    nn.Linear(16, 1)
)


def make_prediction(model, drs):
    norms = torch.norm(drs, dim=1).reshape(-1, 1)
    energies = model(norms)

    network_derivs = vmap(jacrev(model))(norms).squeeze(-1)
    forces = -network_derivs * drs / norms
    return energies, forces


def loss_fn(energies, forces, predicted_energies, predicted_forces):
    return mse_loss(energies, predicted_energies) + 0.01 * mse_loss(forces, predicted_forces) / 3


optimiser = torch.optim.Adam(model.parameters(), lr=1e-3)

for epoch in range(400):
    optimiser.zero_grad()
    energies, forces = make_prediction(model, drs)
    loss = loss_fn(training_energies, training_forces, energies, forces)
    loss.backward(retain_graph=True)
    optimiser.step()

    if epoch % 20 == 0:
        print(loss.cpu().item())
