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import json
from pathlib import Path
import pandas as pd
import torch
import trackio
from model import CalibratedDiscreteTransition, NeuralVectorField, parameter_count
from safetensors.torch import save_file
from torch.nn import functional as F
PROJECT_DIR = Path(__file__).resolve().parent
ARTIFACT_DIR = PROJECT_DIR / "artifacts" / "neural-ode-pocket"
DATA_DIR = PROJECT_DIR / "data"
SEED = 2213
def true_field(state: torch.Tensor) -> torch.Tensor:
x, velocity = state[:, :1], state[:, 1:]
return torch.cat(
[velocity, 1.5 * (1 - x.square()) * velocity - x],
dim=1,
)
def true_step(state: torch.Tensor, delta_time: torch.Tensor) -> torch.Tensor:
k1 = true_field(state)
k2 = true_field(state + 0.5 * delta_time * k1)
k3 = true_field(state + 0.5 * delta_time * k2)
k4 = true_field(state + delta_time * k3)
return state + delta_time * (k1 + 2 * k2 + 2 * k3 + k4) / 6
@torch.inference_mode()
def rollout(
model: torch.nn.Module,
initial: torch.Tensor,
delta_time: float,
steps: int,
*,
continuous: bool,
) -> torch.Tensor:
state = initial
output = []
dt = torch.full((len(initial), 1), delta_time)
for _ in range(steps):
state = model.step(state, dt) if continuous else model(state, dt)
output.append(state)
return torch.stack(output, dim=1)
@torch.inference_mode()
def true_rollout(
initial: torch.Tensor,
delta_time: float,
steps: int,
) -> torch.Tensor:
state = initial
output = []
dt = torch.full((len(initial), 1), delta_time)
for _ in range(steps):
state = true_step(state, dt)
output.append(state)
return torch.stack(output, dim=1)
def first_failure(error: torch.Tensor, threshold: float = 0.5) -> float:
horizons = []
for row in error:
failures = torch.nonzero(row > threshold)
horizons.append(int(failures[0]) if len(failures) else len(row))
return float(sum(horizons) / len(horizons))
@torch.inference_mode()
def evaluate(
model: torch.nn.Module,
delta_time: float,
steps: int,
*,
continuous: bool,
) -> dict:
generator = torch.Generator().manual_seed(SEED + int(delta_time * 1000))
initial = -2.5 + 5 * torch.rand(500, 2, generator=generator)
truth = true_rollout(initial, delta_time, steps)
prediction = rollout(
model, initial, delta_time, steps, continuous=continuous
)
error = (prediction - truth).square().sum(2).sqrt()
return {
"trajectory_rmse": float((prediction - truth).square().mean().sqrt()),
"final_state_rmse": float(
(prediction[:, -1] - truth[:, -1]).square().mean().sqrt()
),
"mean_horizon_before_error_0.5": first_failure(error),
"delta_time": delta_time,
"steps": steps,
"initial_conditions": len(initial),
}
def train_variant(
name: str,
model: torch.nn.Module,
*,
continuous: bool,
) -> torch.nn.Module:
optimizer = torch.optim.AdamW(model.parameters(), lr=1e-3, weight_decay=1e-6)
best = float("inf")
best_state = None
validation_generator = torch.Generator().manual_seed(SEED + 10_000)
validation_state = -3 + 6 * torch.rand(5_000, 2, generator=validation_generator)
validation_dt = torch.full((len(validation_state), 1), 0.05)
validation_target = true_step(validation_state, validation_dt)
for step in range(1, 5_001):
generator = torch.Generator().manual_seed(SEED + step)
state = -3 + 6 * torch.rand(512, 2, generator=generator)
dt = torch.full((len(state), 1), 0.05)
target = true_step(state, dt)
prediction = model.step(state, dt) if continuous else model(state, dt)
loss = F.mse_loss(prediction, target)
optimizer.zero_grad(set_to_none=True)
loss.backward()
optimizer.step()
if step % 250 == 0:
with torch.inference_mode():
validation_prediction = (
model.step(validation_state, validation_dt)
if continuous
else model(validation_state, validation_dt)
)
validation_rmse = float(
(validation_prediction - validation_target)
.square()
.mean()
.sqrt()
)
trackio.log(
{
"variant": name,
"training_step": step,
"training_mse": float(loss.detach()),
"validation_one_step_rmse": validation_rmse,
}
)
if validation_rmse < best:
best = validation_rmse
best_state = {
key: value.detach().cpu().clone()
for key, value in model.state_dict().items()
}
assert best_state is not None
model.load_state_dict(best_state)
return model
def main() -> None:
torch.manual_seed(SEED)
torch.set_num_threads(1)
models = {
"neural_ode_rk4": (NeuralVectorField(), True),
"discrete_transition": (CalibratedDiscreteTransition(), False),
}
assert {parameter_count(item[0]) for item in models.values()} == {1_218}
trackio.init(
project="neural-ode-pocket",
name="van-der-pol-rk4-v1",
config={
"parameters_per_model": 1_218,
"training_delta_time": 0.05,
"training_steps": 5_000,
},
)
results = {}
ARTIFACT_DIR.mkdir(parents=True, exist_ok=True)
DATA_DIR.mkdir(parents=True, exist_ok=True)
for name, (model, continuous) in models.items():
model = train_variant(name, model, continuous=continuous)
models[name] = (model, continuous)
results[name] = {
"parameters": parameter_count(model),
"trained_timestep": evaluate(
model, 0.05, 400, continuous=continuous
),
"unseen_four_x_timestep": evaluate(
model, 0.20, 100, continuous=continuous
),
}
save_file(model.state_dict(), ARTIFACT_DIR / f"{name}.safetensors")
initial = torch.tensor([[2.0, 0.0]])
truth = true_rollout(initial, 0.05, 400)[0]
frame = {
"step": list(range(400)),
"true_x": truth[:, 0].numpy(),
"true_velocity": truth[:, 1].numpy(),
}
for name, (model, continuous) in models.items():
prediction = rollout(model, initial, 0.05, 400, continuous=continuous)[0]
frame[f"{name}_x"] = prediction[:, 0].numpy()
frame[f"{name}_velocity"] = prediction[:, 1].numpy()
report = {
"experiment": "Neural ODE versus discrete transition model",
"system": "Van der Pol oscillator, mu=1.5",
"results": results,
}
(ARTIFACT_DIR / "evaluation.json").write_text(
json.dumps(report, indent=2), encoding="utf-8"
)
pd.DataFrame(frame).to_parquet(DATA_DIR / "phase_rollout.parquet", index=False)
trackio.log(
{
"ode_unseen_rmse": results["neural_ode_rk4"][
"unseen_four_x_timestep"
]["trajectory_rmse"],
"discrete_unseen_rmse": results["discrete_transition"][
"unseen_four_x_timestep"
]["trajectory_rmse"],
}
)
trackio.finish()
print(json.dumps(report, indent=2))
if __name__ == "__main__":
main()
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