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caa4bd5 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 | """Train compact PCA/ridge baselines for T4 sparse sensing and rollout."""
from __future__ import annotations
import json
from pathlib import Path
import h5py
import numpy as np
try:
from .t4_structural_dynamics_v1 import CASE_DIR, DATA_DIR, configuration_design, load_config
except ImportError:
from t4_structural_dynamics_v1 import CASE_DIR, DATA_DIR, configuration_design, load_config
ARTIFACT_DIR = DATA_DIR.parents[1] / "artifacts" / "t4_structural_dynamics_v1"
PARAMETERS = (
"length_m",
"height_m",
"young_pa",
"density_kg_m3",
"damping_ratio",
"traction_amplitude_pa",
)
def trajectory_arrays(row: dict):
with h5py.File(CASE_DIR / f"{row['case_id']}.h5", "r") as h5:
config = json.loads(h5.attrs["config_json"])
parameter = np.array(
[
config["geometry"]["length_m"],
config["geometry"]["height_m"],
config["material"]["young_pa"],
config["material"]["density_kg_m3"],
config["dynamics"]["target_damping_ratio"],
config["dynamics"]["traction_amplitude_pa"],
],
dtype=np.float64,
)
for name in sorted(h5["trajectories"]):
group = h5[f"trajectories/{name}"]
field_time = np.asarray(group["fields/time_s"], dtype=np.float64)
time = np.asarray(group["time_s"], dtype=np.float64)
indices = np.rint(field_time / float(group.attrs["dt_s"])).astype(int)
sensors = np.asarray(group["sensor_displacement_m"], dtype=np.float64)[indices]
sensor_velocity = np.gradient(sensors, field_time, axis=0, edge_order=2)
force = np.asarray(group["force_scale"], dtype=np.float64)[indices]
fields = np.asarray(group["fields/displacement_m"], dtype=np.float64)[:, :, :2]
output = fields.reshape(fields.shape[0], -1)
parameter_rows = np.broadcast_to(parameter, (len(field_time), len(parameter)))
features = np.column_stack(
(
sensors,
sensor_velocity,
force,
field_time / field_time[-1],
parameter_rows,
)
)
yield name, output, features, force, parameter
def randomized_pca(values: np.ndarray, rank: int, seed: int = 20260927):
mean = np.mean(values, axis=0)
centered = values - mean
rng = np.random.default_rng(seed)
omega = rng.normal(size=(centered.shape[1], rank + 8))
projected = centered @ omega
projected = centered @ (centered.T @ projected)
basis, _ = np.linalg.qr(projected, mode="reduced")
small = basis.T @ centered
_, singular, vectors = np.linalg.svd(small, full_matrices=False)
components = vectors[:rank]
total_variance = float(np.sum(centered * centered))
explained = float(np.sum(singular[:rank] ** 2) / max(total_variance, np.finfo(float).eps))
return mean, components, explained
def standardize(values: np.ndarray):
mean = np.mean(values, axis=0)
scale = np.std(values, axis=0)
scale[scale < 1.0e-12] = 1.0
return mean, scale, (values - mean) / scale
def ridge_fit(features: np.ndarray, targets: np.ndarray, penalty: float):
augmented = np.column_stack((features, np.ones(len(features))))
system = augmented.T @ augmented
regularizer = penalty * np.eye(system.shape[0])
regularizer[-1, -1] = 0.0
return np.linalg.solve(system + regularizer, augmented.T @ targets)
def ridge_predict(features: np.ndarray, weights: np.ndarray):
return np.column_stack((features, np.ones(len(features)))) @ weights
def main() -> None:
config = load_config()
rows = configuration_design(config)
train_rows = [row for row in rows if row["split"] == "train"]
train_outputs = []
train_features = []
for row in train_rows:
for name, output, features, force, parameter in trajectory_arrays(row):
train_outputs.append(output.astype(np.float32))
train_features.append(features.astype(np.float32))
output_matrix = np.vstack(train_outputs).astype(np.float64)
feature_matrix = np.vstack(train_features).astype(np.float64)
del train_outputs, train_features
field_mean, components, explained = randomized_pca(output_matrix, rank=16)
latent = (output_matrix - field_mean) @ components.T
feature_mean, feature_scale, standardized_features = standardize(feature_matrix)
reconstruction_weights = ridge_fit(standardized_features, latent, penalty=1.0)
dynamic_features = []
dynamic_targets = []
for row in train_rows:
for _, output, _, force, parameter in trajectory_arrays(row):
z = (output - field_mean) @ components.T
count = len(output)
parameter_rows = np.broadcast_to(parameter, (count - 2, len(parameter)))
dynamic_features.append(
np.column_stack((z[1:-1], z[:-2], force[1:-1], force[2:], parameter_rows))
)
dynamic_targets.append(z[2:])
dynamic_matrix = np.vstack(dynamic_features)
dynamic_target = np.vstack(dynamic_targets)
dynamic_mean, dynamic_scale, standardized_dynamic = standardize(dynamic_matrix)
dynamic_weights = ridge_fit(standardized_dynamic, dynamic_target, penalty=10.0)
def evaluate(selected_rows: list[dict]) -> dict:
direct_sse = pca_sse = rollout_sse = reference = 0.0
count = 0
finite_rollout = True
for row in selected_rows:
for _, output, features, force, parameter in trajectory_arrays(row):
true_z = (output - field_mean) @ components.T
pca_reconstruction = field_mean + true_z @ components
predicted_z = ridge_predict((features - feature_mean) / feature_scale, reconstruction_weights)
direct = field_mean + predicted_z @ components
rollout_z = np.empty_like(true_z)
rollout_z[:2] = true_z[:2]
for step in range(1, len(true_z) - 1):
vector = np.concatenate(
(
rollout_z[step],
rollout_z[step - 1],
[force[step], force[step + 1]],
parameter,
)
)
rollout_z[step + 1] = ridge_predict(
((vector - dynamic_mean) / dynamic_scale)[None, :], dynamic_weights
)[0]
finite_rollout = finite_rollout and bool(np.all(np.isfinite(rollout_z)))
rollout = field_mean + rollout_z @ components
direct_sse += float(np.sum((direct - output) ** 2))
pca_sse += float(np.sum((pca_reconstruction - output) ** 2))
rollout_sse += float(np.sum((rollout[2:] - output[2:]) ** 2))
reference += float(np.sum(output * output))
count += output.size
return {
"trajectory_count": 4 * len(selected_rows),
"pca_rank_16_relative_l2": float(np.sqrt(pca_sse / reference)),
"sparse_sensor_reconstruction_relative_l2": float(np.sqrt(direct_sse / reference)),
"sparse_sensor_reconstruction_rmse_m": float(np.sqrt(direct_sse / count)),
"latent_second_order_rollout_relative_l2": float(np.sqrt(rollout_sse / reference)),
"latent_second_order_rollout_rmse_m": float(np.sqrt(rollout_sse / count)),
"rollout_all_finite": finite_rollout,
}
cohorts = {
"train": [row for row in rows if row["split"] == "train"],
"validation": [row for row in rows if row["split"] == "validation"],
"test_all": [row for row in rows if row["split"] == "test"],
"test_id": [row for row in rows if row["split"] == "test" and row["protocol_role"] == "id"],
"test_excitation_ood": [
row for row in rows if row["protocol_role"] == "excitation_ood"
],
"test_parameter_ood": [row for row in rows if row["protocol_role"] == "parameter_ood"],
}
metrics = {
"model": "PCA-16 + sparse-sensor ridge; PCA-16 second-order latent ridge rollout",
"training_configuration_count": len(train_rows),
"training_trajectory_count": 4 * len(train_rows),
"pca_explained_energy": explained,
"cohorts": {name: evaluate(selected) for name, selected in cohorts.items()},
}
ARTIFACT_DIR.mkdir(parents=True, exist_ok=True)
(ARTIFACT_DIR / "baseline_metrics.json").write_text(
json.dumps(metrics, indent=2, sort_keys=True) + "\n", encoding="utf-8"
)
np.savez_compressed(
ARTIFACT_DIR / "pca_ridge_baselines.npz",
field_mean=field_mean,
components=components,
feature_mean=feature_mean,
feature_scale=feature_scale,
reconstruction_weights=reconstruction_weights,
dynamic_mean=dynamic_mean,
dynamic_scale=dynamic_scale,
dynamic_weights=dynamic_weights,
parameter_names=np.asarray(PARAMETERS),
)
print(json.dumps(metrics, indent=2, sort_keys=True))
if __name__ == "__main__":
main()
|