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import copy
import json
from pathlib import Path
import numpy as np
import pandas as pd
import torch
import trackio
from model import HamiltonianNetwork, VectorFieldNetwork, parameter_count
from physics import generate_states, true_derivative, true_energy
from safetensors.torch import save_file
from torch import nn
from torch.nn import functional as F
PROJECT_DIR = Path(__file__).resolve().parent
ARTIFACT_DIR = PROJECT_DIR / "artifacts" / "hamiltonian-pocket"
DATA_DIR = PROJECT_DIR / "data"
def model_derivative(model: nn.Module, states: torch.Tensor) -> torch.Tensor:
if isinstance(model, HamiltonianNetwork):
return model(states, create_graph=model.training)
return model(states)
def train_model(
name: str,
model: nn.Module,
states: torch.Tensor,
derivatives: torch.Tensor,
validation_states: torch.Tensor,
validation_derivatives: torch.Tensor,
) -> tuple[nn.Module, list[dict]]:
optimizer = torch.optim.AdamW(model.parameters(), lr=2e-3, weight_decay=1e-6)
rng = np.random.default_rng(2043)
best = copy.deepcopy(model.state_dict())
best_validation = float("inf")
history = []
for step in range(1, 3_001):
indices = rng.choice(len(states), 512, replace=False)
batch = states[indices].detach().clone()
prediction = model_derivative(model, batch)
loss = F.mse_loss(prediction, derivatives[indices])
optimizer.zero_grad()
loss.backward()
torch.nn.utils.clip_grad_norm_(model.parameters(), 2.0)
optimizer.step()
if step % 100 == 0:
model.eval()
validation_input = validation_states.detach().clone()
prediction = model_derivative(model, validation_input)
validation_loss = float(
F.mse_loss(prediction, validation_derivatives).detach()
)
record = {
"training_step": step,
f"{name}_training_mse": float(loss.detach()),
f"{name}_validation_mse": validation_loss,
}
history.append(record)
trackio.log(record)
if validation_loss < best_validation:
best_validation = validation_loss
best = copy.deepcopy(model.state_dict())
model.train()
model.load_state_dict(best)
model.eval()
return model, history
def derivative_numpy(model: nn.Module, states: np.ndarray) -> np.ndarray:
tensor = torch.from_numpy(states.astype(np.float32))
prediction = model_derivative(model, tensor)
return prediction.detach().numpy()
def rk4_step(model: nn.Module | None, states: np.ndarray, dt: float) -> np.ndarray:
derivative = (
true_derivative
if model is None
else lambda values: derivative_numpy(model, values)
)
k1 = derivative(states)
k2 = derivative(states + 0.5 * dt * k1)
k3 = derivative(states + 0.5 * dt * k2)
k4 = derivative(states + dt * k3)
return states + dt * (k1 + 2 * k2 + 2 * k3 + k4) / 6
def rollout(
model: nn.Module | None,
initial_states: np.ndarray,
steps: int,
dt: float,
) -> np.ndarray:
trajectory = [initial_states.copy()]
state = initial_states.copy()
for _ in range(steps):
state = rk4_step(model, state, dt)
trajectory.append(state.copy())
return np.stack(trajectory)
def rollout_metrics(
model: nn.Module,
initial_states: np.ndarray,
truth: np.ndarray,
dt: float,
) -> dict:
predicted = rollout(model, initial_states, len(truth) - 1, dt)
initial_energy = true_energy(predicted[0])
energy_drift = np.abs(true_energy(predicted) - initial_energy)
return {
"trajectory_mse": float(np.mean((predicted - truth) ** 2)),
"final_state_mse": float(np.mean((predicted[-1] - truth[-1]) ** 2)),
"mean_absolute_energy_drift": float(energy_drift.mean()),
"final_absolute_energy_drift": float(energy_drift[-1].mean()),
}
def main() -> None:
torch.manual_seed(2043)
torch.set_num_threads(1)
train_states, train_derivatives = generate_states(20_000, 2043)
validation_states, validation_derivatives = generate_states(3_000, 3043)
test_states, test_derivatives = generate_states(5_000, 4043)
hamiltonian = HamiltonianNetwork()
vector_field = VectorFieldNetwork()
trackio.init(
project="hamiltonian-pocket",
name="conservative-dynamics-v1",
config={
"training_samples": len(train_states),
"training_steps": 3_000,
"hamiltonian_parameters": parameter_count(hamiltonian),
"vector_field_parameters": parameter_count(vector_field),
},
)
hamiltonian, hamiltonian_history = train_model(
"hamiltonian",
hamiltonian,
torch.from_numpy(train_states),
torch.from_numpy(train_derivatives),
torch.from_numpy(validation_states),
torch.from_numpy(validation_derivatives),
)
vector_field, vector_history = train_model(
"vector_field",
vector_field,
torch.from_numpy(train_states),
torch.from_numpy(train_derivatives),
torch.from_numpy(validation_states),
torch.from_numpy(validation_derivatives),
)
initial_states, _ = generate_states(128, 5043)
dt = 0.05
steps = 400
truth = rollout(None, initial_states, steps, dt)
results = {}
for name, model in [
("hamiltonian", hamiltonian),
("vector_field", vector_field),
]:
derivative_mse = float(
np.mean((derivative_numpy(model, test_states) - test_derivatives) ** 2)
)
results[name] = {
"parameters": parameter_count(model),
"derivative_mse": derivative_mse,
"rollout": rollout_metrics(model, initial_states, truth, dt),
}
report = {
"benchmark": "Conservative pendulum dynamics",
"training_samples": len(train_states),
"rollout_initial_conditions": len(initial_states),
"rollout_steps": steps,
"dt": dt,
"results": results,
"training_history": {
"hamiltonian": hamiltonian_history,
"vector_field": vector_history,
},
}
ARTIFACT_DIR.mkdir(parents=True, exist_ok=True)
DATA_DIR.mkdir(parents=True, exist_ok=True)
save_file(
hamiltonian.state_dict(), ARTIFACT_DIR / "hamiltonian.safetensors"
)
save_file(
vector_field.state_dict(), ARTIFACT_DIR / "vector_field.safetensors"
)
(ARTIFACT_DIR / "evaluation.json").write_text(
json.dumps(report, indent=2), encoding="utf-8"
)
pd.DataFrame(
np.column_stack([train_states, train_derivatives]),
columns=["angle", "momentum", "d_angle", "d_momentum"],
).to_parquet(DATA_DIR / "pendulum_derivatives.parquet", index=False)
trackio.log(
{
"hamiltonian_derivative_mse": results["hamiltonian"][
"derivative_mse"
],
"vector_derivative_mse": results["vector_field"]["derivative_mse"],
"hamiltonian_energy_drift": results["hamiltonian"]["rollout"][
"final_absolute_energy_drift"
],
"vector_energy_drift": results["vector_field"]["rollout"][
"final_absolute_energy_drift"
],
}
)
trackio.finish()
print(json.dumps(report, indent=2))
if __name__ == "__main__":
main()
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