from __future__ import annotations 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()