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@@ -33,3 +33,5 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 *.zip filter=lfs diff=lfs merge=lfs -text
 *.zst filter=lfs diff=lfs merge=lfs -text
 *tfevents* filter=lfs diff=lfs merge=lfs -text
+results/training_curves.png filter=lfs diff=lfs merge=lfs -text
+results/validation_examples.png filter=lfs diff=lfs merge=lfs -text

README.md

@@ -0,0 +1,37 @@
+---
+license: apache-2.0
+language:
+- en
+tags:
+- OneScience
+- fluid-dynamics
+library_name: pytorch
+---
+
+# LiNO
+
+## Model
+
+This package reproduces the one-dimensional viscous Burgers final-state prediction experiment. The trained checkpoint is `weight/best_model.pth`; model code, configuration, training, inference, and visualization scripts are included. The package was trained once; reported numbers are not guarantees for another run.
+
+## Data
+
+Download only the needed file from [OneScience/fno](https://www.modelscope.cn/datasets/OneScience/fno) with `modelscope download OneScience/fno data/burgers_data_R10.mat --repo-type dataset --local_dir ./data`. The model reads `data/data/burgers_data_R10.mat`.
+
+Data provenance: [https://www.modelscope.cn/datasets/OneScience/fno](https://www.modelscope.cn/datasets/OneScience/fno).
+
+## Usage
+
+```bash
+hf download OneScience-Group/LiNO --local-dir ./LiNO
+cd LiNO
+pip install -r requirements.txt
+python scripts/inference.py
+python scripts/result.py
+```
+
+For training, run `python scripts/train.py` after installing the appropriate accelerator-enabled PyTorch environment and downloading the data above. See `config/config.yaml` for experiment parameters. Preserve the included checkpoint before retraining.
+
+## Result and citation
+
+validation relative L2: 0.00816638; paper Table 1: 0.0109. See `results/` for the recorded outputs and the [original paper or data page](https://arxiv.org/abs/2606.03262) for the research context. The dataset license, where not separately stated by its author, must not be inferred from the code license.

config.json

@@ -0,0 +1,10 @@
+{
+  "model_type": "lino_burgers",
+  "architectures": [
+    "LiNO"
+  ],
+  "framework": "pytorch",
+  "experiment": "one-dimensional viscous Burgers final-state prediction",
+  "checkpoint": "weight/best_model.pth",
+  "dataset": "OneScience/fno"
+}

config/config.yaml

@@ -0,0 +1,40 @@
+seed: 42
+data:
+  directory: data/data
+  filename: burgers_data_R10.mat
+  input_key: a
+  target_key: u
+  expected_shape: [2048, 8192]
+  resolution: 256
+  n_train: 1600
+  n_val: 448
+  interpolation: linear
+  normalization_eps: 1.0e-5
+model:
+  in_channels: 2
+  out_channels: 1
+  width: 128
+  depth: 8
+  scattering: efficient
+  rate_range: 0.25
+  eps: 1.0e-6
+training:
+  epochs: 500
+  batch_size: 4
+  learning_rate: 0.001
+  weight_decay: 1.0e-5
+  betas: [0.9, 0.999]
+  optimizer_eps: 1.0e-8
+  scheduler_step: 5
+  scheduler_gamma: 0.96
+  grad_clip: 1.0
+  num_workers: 0
+  log_interval: 50
+  device: cuda
+  checkpoint: weight/best_model.pth
+  last_checkpoint: weight/last_model.pth
+inference:
+  batch_size: 4
+  device: cuda
+results:
+  directory: results

model/__init__.py

@@ -0,0 +1,3 @@
+from .lino import LiNO
+
+__all__ = ["LiNO"]

model/lino.py

@@ -0,0 +1,110 @@
+"""Independent implementation of LiNO, arXiv:2606.03262, Eqs. (5)-(44).
+
+Only the efficient scattering variant for one-dimensional fields is implemented.
+Unspecified numerical choices are documented in results/reproduction_spec.md.
+"""
+
+import torch
+from torch import nn
+from torch.nn import functional as F
+
+
+class AdaptiveMirror(nn.Module):
+    def __init__(self, width, eps):
+        super().__init__()
+        self.direction = nn.Linear(width, width)
+        self.eps = eps
+
+    def forward(self, field):
+        normal = F.normalize(self.direction(field), dim=-1, eps=self.eps)
+        component = (field * normal).sum(-1, keepdim=True)
+        return field - 2 * component * normal
+
+
+class AdaptiveRefraction(nn.Module):
+    def __init__(self, width, rate_range, eps):
+        super().__init__()
+        self.direction = nn.Linear(width, width)
+        self.contrast = nn.Parameter(torch.zeros(()))
+        self.rate_range, self.eps = rate_range, eps
+
+    def forward(self, field):
+        normal = F.normalize(self.direction(field), dim=-1, eps=self.eps)
+        normal_component = (field * normal).sum(-1, keepdim=True) * normal
+        return field + self.rate_range * self.contrast.tanh() * normal_component
+
+
+class EfficientScattering(nn.Module):
+    def __init__(self, width, eps):
+        super().__init__()
+        self.query = nn.Linear(width, width, bias=False)
+        self.key = nn.Linear(width, width, bias=False)
+        self.value = nn.Linear(width, width, bias=False)
+        self.coordinates = nn.Sequential(nn.Linear(1, width), nn.GELU(), nn.Linear(width, width))
+        self.diffusion = nn.Conv1d(width, width, 3, padding=1, groups=width, bias=False)
+        self.local_projection = nn.Linear(width, width, bias=False)
+        self.local_logit = nn.Parameter(torch.tensor(-1.0))
+        self.log_strength = nn.Parameter(torch.tensor(-2.0))
+        self.scale, self.eps = width ** -0.5, eps
+
+    def forward(self, field, grid):
+        position = self.coordinates(grid)
+        query = F.elu(self.query(field) * self.scale + position) + 1
+        key = F.elu(self.key(field) * self.scale + position) + 1
+        value = self.value(field)
+        # Eq. (33): aggregate over space before contracting each query.
+        summary = key.transpose(1, 2) @ value
+        numerator = query @ summary
+        denominator = (query * key.sum(1, keepdim=True)).sum(-1, keepdim=True)
+        global_average = numerator / (denominator + self.eps)
+        local_field = self.diffusion(field.transpose(1, 2)).transpose(1, 2)
+        local_average = self.local_projection(local_field)
+        beta = self.local_logit.sigmoid()
+        average = (1 - beta) * global_average + beta * local_average
+        return self.log_strength.exp() * (average - field)
+
+
+class LightBlock(nn.Module):
+    def __init__(self, width, rate_range, eps):
+        super().__init__()
+        self.before_light = nn.LayerNorm(width)
+        self.before_ffn = nn.LayerNorm(width)
+        self.mirror = AdaptiveMirror(width, eps)
+        self.refraction = AdaptiveRefraction(width, rate_range, eps)
+        self.scattering = EfficientScattering(width, eps)
+        self.gate = nn.Sequential(nn.Linear(width, 2 * width), nn.GELU(), nn.Linear(2 * width, 3))
+        self.mix_projection = nn.Linear(width, width)
+        self.ffn = nn.Sequential(nn.Linear(width, 2 * width), nn.GELU(), nn.Linear(2 * width, width))
+
+    def forward(self, field, grid):
+        normalized = self.before_light(field)
+        weights = self.gate(normalized.mean(1)).softmax(-1)
+        branches = (self.mirror(normalized), self.refraction(normalized), self.scattering(normalized, grid))
+        mixture = sum(weights[:, i, None, None] * branch for i, branch in enumerate(branches))
+        field = field + self.mix_projection(mixture)
+        return field + self.ffn(self.before_ffn(field))
+
+
+class LiNO(nn.Module):
+    """[batch, space, 2] -> [batch, space, 1], normalized field and x input."""
+
+    def __init__(self, in_channels=2, out_channels=1, width=128, depth=8,
+                 scattering="efficient", rate_range=0.25, eps=1e-6):
+        super().__init__()
+        if scattering != "efficient":
+            raise ValueError("This experiment requires efficient scattering")
+        self.architecture = dict(in_channels=in_channels, out_channels=out_channels,
+                                 width=width, depth=depth, scattering=scattering,
+                                 rate_range=rate_range, eps=eps)
+        self.lift = nn.Linear(in_channels, width)
+        self.blocks = nn.ModuleList([LightBlock(width, rate_range, eps) for _ in range(depth)])
+        self.project = nn.Linear(width, out_channels)
+
+    def forward(self, inputs):
+        if inputs.ndim != 3 or inputs.shape[-1] != self.architecture["in_channels"]:
+            raise ValueError(f"Expected [B,N,{self.architecture['in_channels']}], got {inputs.shape}")
+        grid = torch.linspace(0, 1, inputs.shape[1], device=inputs.device, dtype=inputs.dtype).view(1, -1, 1)
+        field = self.lift(inputs)
+        for block in self.blocks:
+            field = block(field, grid)
+        return self.project(field)

requirements.txt

@@ -0,0 +1,5 @@
+torch>=2.0
+numpy>=1.24
+scipy>=1.10
+PyYAML>=6.0
+matplotlib>=3.7

results/metrics.json

@@ -0,0 +1,16 @@
+{
+  "n_validation": 448,
+  "checkpoint_epoch": 495,
+  "best_epoch": 495,
+  "validation_relative_l2": 0.00816638395190239,
+  "validation_relative_l2_std": 0.0073033287189900875,
+  "validation_mse_physical": 5.692711056326516e-05,
+  "validation_rmse_physical": 0.00754500599578023,
+  "checkpoint_recorded_relative_l2": 0.008166384883224964,
+  "reload_metric_absolute_difference": 9.313225746154785e-10,
+  "paper_table1_relative_l2": 0.0109,
+  "ratio_to_paper": 0.7492095368717788,
+  "inference_seconds": 7.967788686975837,
+  "checkpoint_sha256": "82ca744dfb18510e680edf20b02213a585c6d859d269a2775c7192be8f67f821",
+  "device": "BW"
+}

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+}

results/training_status.json

@@ -0,0 +1,14 @@
+{
+  "status": "completed",
+  "completed_epochs": 500,
+  "best_epoch": 495,
+  "best_val_relative_l2": 0.008166384883224964,
+  "paper_relative_l2": 0.0109,
+  "ratio_to_paper": 0.749209622314217,
+  "training_seconds": 12257.58068851661,
+  "n_train": 1600,
+  "n_val": 448,
+  "seed": 42,
+  "checkpoint": "weight/best_model.pth",
+  "slurm_job_id": "1059315"
+}

results/training_summary.json

@@ -0,0 +1,14 @@
+{
+  "status": "completed",
+  "completed_epochs": 500,
+  "best_epoch": 495,
+  "best_val_relative_l2": 0.008166384883224964,
+  "paper_relative_l2": 0.0109,
+  "ratio_to_paper": 0.749209622314217,
+  "training_seconds": 12257.58068851661,
+  "n_train": 1600,
+  "n_val": 448,
+  "seed": 42,
+  "checkpoint": "weight/best_model.pth",
+  "slurm_job_id": "1059315"
+}

results/verification.json

@@ -0,0 +1,34 @@
+{
+  "status": "passed",
+  "completed_epochs": 500,
+  "n_train": 1600,
+  "n_validation": 448,
+  "resolution": 256,
+  "seed": 42,
+  "history_continuous": true,
+  "scheduler_verified": true,
+  "split_disjoint_and_complete": true,
+  "best_checkpoint_selection_verified": true,
+  "checkpoint_reload_metric_difference": 9.313225746154785e-10,
+  "independent_float64_relative_l2": 0.008166383878061999,
+  "physical_outputs_finite": true,
+  "figures_nonempty": true,
+  "portability": "passed: physically relocated code and checkpoint, changed data/results directories; CPU load only",
+  "accelerator_execution": "Slurm job 1059315, a01r3n12",
+  "metrics": {
+    "n_validation": 448,
+    "checkpoint_epoch": 495,
+    "best_epoch": 495,
+    "validation_relative_l2": 0.00816638395190239,
+    "validation_relative_l2_std": 0.0073033287189900875,
+    "validation_mse_physical": 5.692711056326516e-05,
+    "validation_rmse_physical": 0.00754500599578023,
+    "checkpoint_recorded_relative_l2": 0.008166384883224964,
+    "reload_metric_absolute_difference": 9.313225746154785e-10,
+    "paper_table1_relative_l2": 0.0109,
+    "ratio_to_paper": 0.7492095368717788,
+    "inference_seconds": 7.967788686975837,
+    "checkpoint_sha256": "82ca744dfb18510e680edf20b02213a585c6d859d269a2775c7192be8f67f821",
+    "device": "BW"
+  }
+}

results/visualization_manifest.json

@@ -0,0 +1,32 @@
+{
+  "figures": [
+    "training_curves.png",
+    "training_curves.pdf",
+    "validation_examples.png",
+    "validation_examples.pdf",
+    "error_distribution.png"
+  ],
+  "selected_validation_indices": [
+    0,
+    111,
+    136
+  ],
+  "sample_count": 448,
+  "completed_epochs": 500,
+  "metrics": {
+    "n_validation": 448,
+    "checkpoint_epoch": 495,
+    "best_epoch": 495,
+    "validation_relative_l2": 0.00816638395190239,
+    "validation_relative_l2_std": 0.0073033287189900875,
+    "validation_mse_physical": 5.692711056326516e-05,
+    "validation_rmse_physical": 0.00754500599578023,
+    "checkpoint_recorded_relative_l2": 0.008166384883224964,
+    "reload_metric_absolute_difference": 9.313225746154785e-10,
+    "paper_table1_relative_l2": 0.0109,
+    "ratio_to_paper": 0.7492095368717788,
+    "inference_seconds": 7.967788686975837,
+    "checkpoint_sha256": "82ca744dfb18510e680edf20b02213a585c6d859d269a2775c7192be8f67f821",
+    "device": "BW"
+  }
+}

scripts/common.py

@@ -0,0 +1,131 @@
+"""Configuration, supplied MAT data, and portable checkpoint utilities."""
+
+import hashlib
+import json
+import os
+import random
+from pathlib import Path
+
+import numpy as np
+import scipy.io
+import torch
+import yaml
+from torch.nn import functional as F
+
+ROOT = Path(__file__).resolve().parents[1]
+
+
+def package_path(value):
+    path = Path(value).expanduser()
+    return path if path.is_absolute() else ROOT / path
+
+
+def load_config(path):
+    with open(package_path(path)) as stream:
+        return yaml.safe_load(stream)
+
+
+def save_json(path, value):
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temp = path.with_name(path.name + ".tmp")
+    temp.write_text(json.dumps(value, ensure_ascii=False, indent=2, allow_nan=False))
+    temp.replace(path)
+
+
+def seed_everything(seed):
+    random.seed(seed)
+    np.random.seed(seed)
+    torch.manual_seed(seed)
+    torch.cuda.manual_seed_all(seed)
+
+
+def compute_device(name):
+    device = torch.device(name)
+    if device.type == "cuda":
+        if not os.environ.get("SLURM_JOB_ID"):
+            raise RuntimeError("Accelerator execution requires a Slurm allocation")
+        if not torch.cuda.is_available():
+            raise RuntimeError("No accelerator visible inside the Slurm job")
+    return device
+
+
+def read_fields(config):
+    data = config["data"]
+    path = package_path(data["directory"]) / data["filename"]
+    arrays = scipy.io.loadmat(path, variable_names=[data["input_key"], data["target_key"]])
+    fields = []
+    for key in [data["input_key"], data["target_key"]]:
+        array = arrays[key]
+        if list(array.shape) != data["expected_shape"] or array.dtype != np.float64:
+            raise ValueError(f"Unexpected supplied data {key}: {array.shape}, {array.dtype}")
+        if not np.isfinite(array).all():
+            raise ValueError(f"Nonfinite values in {key}")
+        tensor = torch.from_numpy(array.astype(np.float32))
+        # Paper leaves resizing unspecified: author's linear interpolation,
+        # align_corners=False, evaluates at source centers 15.5,47.5,... .
+        tensor = F.interpolate(tensor[:, None], size=data["resolution"],
+                               mode=data["interpolation"], align_corners=False)
+        fields.append(tensor.transpose(1, 2).contiguous())
+    return fields
+
+
+def split_indices(config):
+    data = config["data"]
+    permutation = torch.randperm(data["expected_shape"][0], generator=torch.Generator().manual_seed(config["seed"]))
+    n, m = data["n_train"], data["n_val"]
+    if n + m != len(permutation):
+        raise ValueError("The formal experiment must use all 2048 supplied samples")
+    return permutation[:n], permutation[n:n + m]
+
+
+def fit_normalizers(initial, final, train_ids, eps):
+    result = {"eps": eps}
+    for prefix, field in [("a", initial), ("u", final)]:
+        training = field[train_ids]
+        result[prefix + "_mean"] = training.mean()
+        result[prefix + "_std"] = training.std(correction=1)
+    return result
+
+
+def encode(field, stats, prefix):
+    return (field - stats[prefix + "_mean"].to(field)) / (stats[prefix + "_std"].to(field) + stats["eps"])
+
+
+def decode(field, stats, prefix="u"):
+    return field * (stats[prefix + "_std"].to(field) + stats["eps"]) + stats[prefix + "_mean"].to(field)
+
+
+def make_inputs(initial, stats):
+    physical = encode(initial, stats, "a")
+    grid = torch.linspace(0, 1, initial.shape[1], dtype=initial.dtype).view(1, -1, 1)
+    return torch.cat([physical, grid.expand(initial.shape[0], -1, -1)], dim=-1)
+
+
+def relative_l2(prediction, target):
+    difference = (prediction - target).flatten(1)
+    return torch.linalg.vector_norm(difference, dim=1) / (torch.linalg.vector_norm(target.flatten(1), dim=1) + 1e-12)
+
+
+def atomic_checkpoint(path, state):
+    path = package_path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temp = path.with_name(path.name + ".tmp")
+    torch.save(state, temp)
+    temp.replace(path)
+
+
+def load_checkpoint(path):
+    # Tensor/primitive-only checkpoint; no pickled custom class or path equality.
+    state = torch.load(package_path(path), map_location="cpu", weights_only=True)
+    if state.get("format") != "lino-burgers-v1":
+        raise ValueError("Unsupported LiNO checkpoint")
+    return state
+
+
+def file_digest(path):
+    digest = hashlib.sha256()
+    with open(path, "rb") as stream:
+        for block in iter(lambda: stream.read(8 * 1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()

scripts/inference.py

@@ -0,0 +1,79 @@
+"""Reload the best checkpoint and evaluate every held-out validation sample."""
+
+import argparse
+import csv
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[1]))
+import numpy as np
+import torch
+from model.lino import LiNO
+from common import (compute_device, decode, file_digest, load_checkpoint, load_config,
+                    make_inputs, package_path, read_fields, relative_l2, save_json)
+
+
+@torch.no_grad()
+def inference(config, checkpoint=None):
+    device = compute_device(config["inference"]["device"])
+    checkpoint = package_path(checkpoint or config["training"]["checkpoint"])
+    state = load_checkpoint(checkpoint)
+    contract = state["data_contract"]
+    for key in ["resolution", "interpolation", "input_key", "target_key"]:
+        if config["data"][key] != contract[key]:
+            raise ValueError(f"Data contract mismatch for {key}")
+    data_path = package_path(config["data"]["directory"]) / config["data"]["filename"]
+    if file_digest(data_path) != contract["dataset_sha256"]:
+        raise ValueError("Dataset content differs from the training data (paths may change)")
+    initial, final = read_fields(config)
+    ids, stats = state["val_indices"], state["normalizers"]
+    model = LiNO(**state["architecture"]).to(device)
+    model.load_state_dict(state["model_state"], strict=True)
+    model.eval()
+    inputs = make_inputs(initial[ids], stats)
+    targets = final[ids]
+    predictions = []
+    started = time.monotonic()
+    batch_size = config["inference"]["batch_size"]
+    for start in range(0, len(ids), batch_size):
+        normalized = model(inputs[start:start+batch_size].to(device))
+        predictions.append(decode(normalized, stats).cpu())
+        if start % (batch_size * 25) == 0:
+            print(f"INFERENCE samples={min(start+batch_size,len(ids))}/{len(ids)} checkpoint_epoch={state['epoch']}", flush=True)
+    prediction = torch.cat(predictions)
+    errors = relative_l2(prediction, targets)
+    mse_by_sample = (prediction-targets).square().flatten(1).mean(1)
+    if not torch.isfinite(prediction).all():
+        raise FloatingPointError("Nonfinite inference output")
+    output = package_path(config["results"]["directory"])
+    output.mkdir(parents=True, exist_ok=True)
+    np.savez_compressed(output/"predictions.npz", initial=initial[ids].numpy(), target=targets.numpy(),
+                        prediction=prediction.numpy(), sample_indices=ids.numpy(), relative_l2=errors.numpy(),
+                        x=np.linspace(0,1,config["data"]["resolution"],dtype=np.float32))
+    with open(output/"per_sample_metrics.csv", "w", newline="") as stream:
+        writer = csv.writer(stream)
+        writer.writerow(["validation_index", "source_index", "relative_l2", "mse_physical"])
+        writer.writerows((i,int(source),float(rel),float(mse)) for i,(source,rel,mse) in enumerate(zip(ids,errors,mse_by_sample)))
+    metric = errors.mean().item()
+    metrics = dict(n_validation=len(ids), checkpoint_epoch=state["epoch"], best_epoch=state["best_epoch"],
+                   validation_relative_l2=metric, validation_relative_l2_std=errors.std(correction=0).item(),
+                   validation_mse_physical=mse_by_sample.mean().item(),
+                   validation_rmse_physical=mse_by_sample.mean().sqrt().item(),
+                   checkpoint_recorded_relative_l2=state["best_val_relative_l2"],
+                   reload_metric_absolute_difference=abs(metric-state["best_val_relative_l2"]),
+                   paper_table1_relative_l2=0.0109, ratio_to_paper=metric/0.0109,
+                   inference_seconds=time.monotonic()-started,
+                   checkpoint_sha256=file_digest(checkpoint), device=torch.cuda.get_device_name(device))
+    if metrics["reload_metric_absolute_difference"] > 1e-6:
+        raise AssertionError(f"Reloaded metric disagrees with checkpoint: {metrics}")
+    save_json(output/"metrics.json", metrics)
+    print("BEST CHECKPOINT INFERENCE COMPLETED", metrics, flush=True)
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--config", default="config/config.yaml")
+    parser.add_argument("--checkpoint", default=None)
+    args = parser.parse_args()
+    inference(load_config(args.config), args.checkpoint)

scripts/result.py

@@ -0,0 +1,66 @@
+"""Plot training curves and physical-space validation predictions."""
+
+import argparse
+import csv
+import json
+from pathlib import Path
+import matplotlib
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+from common import load_config, package_path, save_json
+
+
+def render(config):
+    output = package_path(config["results"]["directory"])
+    data = np.load(output/"predictions.npz")
+    metrics = json.loads((output/"metrics.json").read_text())
+    with open(output/"history.csv") as stream:
+        rows = list(csv.DictReader(stream))
+    epoch = np.array([int(r["epoch"]) for r in rows])
+    fig, axes = plt.subplots(1, 2, figsize=(11, 4), constrained_layout=True)
+    for name, label in [("train_loss","Training"),("val_loss","Validation")]:
+        axes[0].semilogy(epoch,[float(r[name]) for r in rows],label=label)
+    axes[0].set(xlabel="Epoch",ylabel="MSE + relative L2 (normalized)")
+    axes[0].legend()
+    axes[1].semilogy(epoch,[float(r["val_relative_l2"]) for r in rows],color="tab:blue",label="Validation")
+    axes[1].axhline(0.0109,color="tab:red",linestyle="--",label="Paper Table 1: 0.0109")
+    axes[1].set(xlabel="Epoch",ylabel="Relative L2 (physical space)")
+    axes[1].legend()
+    for ax in axes: ax.grid(alpha=0.2)
+    fig.savefig(output/"training_curves.png",dpi=200)
+    fig.savefig(output/"training_curves.pdf")
+    plt.close(fig)
+    errors=data["relative_l2"]
+    chosen=[0,int(np.argsort(errors)[len(errors)//2]),int(np.argmax(errors))]
+    fig, axes=plt.subplots(3,2,figsize=(12,10),constrained_layout=True)
+    x=data["x"]
+    for row,index in enumerate(chosen):
+        initial=data["initial"][index,:,0]; target=data["target"][index,:,0]; pred=data["prediction"][index,:,0]
+        axes[row,0].plot(x,initial,color="0.6",linewidth=1,label="Initial u0")
+        axes[row,0].plot(x,target,color="black",linewidth=1.5,label="Reference u(T)")
+        axes[row,0].plot(x,pred,color="tab:blue",linestyle="--",label="LiNO")
+        axes[row,0].set_title(f"Source sample {data['sample_indices'][index]}, relative L2={errors[index]:.4g}")
+        axes[row,0].set(xlabel="x",ylabel="u (dataset units)")
+        axes[row,0].legend()
+        axes[row,1].plot(x,pred-target,color="tab:red")
+        axes[row,1].axhline(0,color="0.5",linewidth=0.5)
+        axes[row,1].set(xlabel="x",ylabel="Prediction - reference")
+    fig.savefig(output/"validation_examples.png",dpi=200)
+    fig.savefig(output/"validation_examples.pdf")
+    plt.close(fig)
+    fig, ax=plt.subplots(figsize=(6,4),constrained_layout=True)
+    ax.hist(errors,bins=35,color="tab:blue",alpha=.85)
+    ax.set(xlabel="Validation relative L2",ylabel="Samples",title=f"All {len(errors)} held-out samples")
+    fig.savefig(output/"error_distribution.png",dpi=200)
+    plt.close(fig)
+    save_json(output/"visualization_manifest.json",dict(figures=["training_curves.png","training_curves.pdf","validation_examples.png","validation_examples.pdf","error_distribution.png"],
+              selected_validation_indices=chosen,sample_count=len(errors),completed_epochs=len(rows),metrics=metrics))
+    print(f"VISUALIZATION COMPLETED: {output} ({len(rows)} epochs, {len(errors)} validation samples)",flush=True)
+
+
+if __name__ == "__main__":
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--config",default="config/config.yaml")
+    args=parser.parse_args()
+    render(load_config(args.config))

scripts/train.py

@@ -0,0 +1,154 @@
+"""Full paper training: python scripts/train.py --config config/config.yaml."""
+
+import argparse
+import csv
+import os
+import platform
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[1]))
+import torch
+from torch.utils.data import DataLoader, TensorDataset
+from model.lino import LiNO
+from common import (atomic_checkpoint, compute_device, decode, encode, file_digest,
+                    fit_normalizers, load_checkpoint, load_config, make_inputs,
+                    package_path, read_fields, relative_l2, save_json,
+                    seed_everything, split_indices)
+
+
+@torch.no_grad()
+def evaluate(model, loader, stats, device):
+    model.eval()
+    total = torch.zeros(4, device=device)
+    count = 0
+    for inputs, targets in loader:
+        inputs, targets = inputs.to(device), targets.to(device)
+        prediction = model(inputs)
+        mse = (prediction - targets).square().mean()
+        rel = relative_l2(prediction, targets).mean()
+        physical_prediction, physical_target = decode(prediction, stats), decode(targets, stats)
+        physical_rel = relative_l2(physical_prediction, physical_target).mean()
+        physical_mse = (physical_prediction - physical_target).square().mean()
+        total += torch.stack([mse + rel, mse, physical_rel, physical_mse]) * len(inputs)
+        count += len(inputs)
+    values = (total / count).cpu().tolist()
+    if not all(torch.isfinite(torch.tensor(values))):
+        raise FloatingPointError("Nonfinite validation metrics")
+    return dict(zip(["val_loss", "val_mse_normalized", "val_relative_l2", "val_mse_physical"], values))
+
+
+def train(config, resume=None):
+    seed_everything(config["seed"])
+    settings = config["training"]
+    device = compute_device(settings["device"])
+    output = package_path(config["results"]["directory"])
+    output.mkdir(parents=True, exist_ok=True)
+    initial, final = read_fields(config)
+    train_ids, val_ids = split_indices(config)
+    stats = fit_normalizers(initial, final, train_ids, config["data"]["normalization_eps"])
+    restored = load_checkpoint(resume) if resume else None
+    if restored:
+        if restored["architecture"] != config["model"]:
+            raise ValueError("Resume architecture differs from config")
+        train_ids, val_ids, stats = restored["train_indices"], restored["val_indices"], restored["normalizers"]
+    inputs, targets = make_inputs(initial, stats), encode(final, stats, "u")
+    loader_args = dict(batch_size=settings["batch_size"], num_workers=settings["num_workers"], pin_memory=True, drop_last=False)
+    training = DataLoader(TensorDataset(inputs[train_ids], targets[train_ids]), shuffle=True, **loader_args)
+    validation = DataLoader(TensorDataset(inputs[val_ids], targets[val_ids]), shuffle=False, **loader_args)
+    model = LiNO(**config["model"]).to(device)
+    optimizer = torch.optim.AdamW(model.parameters(), lr=settings["learning_rate"],
+                                 weight_decay=settings["weight_decay"], betas=tuple(settings["betas"]), eps=settings["optimizer_eps"])
+    scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=settings["scheduler_step"], gamma=settings["scheduler_gamma"])
+    best, best_epoch, start_epoch = float("inf"), 0, 0
+    if restored:
+        model.load_state_dict(restored["model_state"], strict=True)
+        optimizer.load_state_dict(restored["optimizer_state"])
+        scheduler.load_state_dict(restored["scheduler_state"])
+        best, best_epoch, start_epoch = restored["best_val_relative_l2"], restored["best_epoch"], restored["epoch"]
+        torch.set_rng_state(restored["torch_rng_state"])
+        torch.cuda.set_rng_state_all(restored["accelerator_rng_states"])
+    data_path = package_path(config["data"]["directory"]) / config["data"]["filename"]
+    parameter_count = sum(p.numel() for p in model.parameters())
+    manifest = dict(config=config, architecture=model.architecture, parameter_count=parameter_count,
+                    dataset_path=str(data_path), dataset_sha256=file_digest(data_path),
+                    raw_shape=config["data"]["expected_shape"], resolution=config["data"]["resolution"],
+                    n_train=len(train_ids), n_val=len(val_ids), seed=config["seed"],
+                    dtype="float32", optimizer="AdamW", precision="float32", early_stopping=False,
+                    torch_version=str(torch.__version__), hip_version=torch.version.hip,
+                    python_version=platform.python_version(), hostname=platform.node(),
+                    slurm_job_id=os.environ.get("SLURM_JOB_ID"), device=torch.cuda.get_device_name(device),
+                    source_files={str(p.relative_to(Path(__file__).resolve().parents[1])):file_digest(p)
+                                  for folder in ["model", "scripts"] for p in (Path(__file__).resolve().parents[1]/folder).glob("*.py")})
+    save_json(output / "run_manifest.json", manifest)
+    save_json(output / "split_indices.json", {"seed":config["seed"], "train":train_ids.tolist(), "validation":val_ids.tolist()})
+    history_path = output / "history.csv"
+    columns = ["epoch", "train_loss", "train_mse_normalized", "train_relative_l2_normalized", "val_loss", "val_mse_normalized", "val_relative_l2", "val_mse_physical", "lr_used", "lr_next", "epoch_seconds", "best_val_relative_l2"]
+    print(f"FORMAL RUN device={manifest['device']} job={manifest['slurm_job_id']} params={parameter_count} train={len(train_ids)} val={len(val_ids)} resolution={inputs.shape[1]} epochs={settings['epochs']} batch={settings['batch_size']}", flush=True)
+    started = time.monotonic()
+    with open(history_path, "a" if resume else "w", newline="", buffering=1) as stream:
+        writer = csv.DictWriter(stream, fieldnames=columns)
+        if not resume:
+            writer.writeheader()
+        for epoch in range(start_epoch + 1, settings["epochs"] + 1):
+            epoch_start = time.monotonic()
+            lr_used = optimizer.param_groups[0]["lr"]
+            model.train()
+            totals = torch.zeros(3, device=device)
+            count = 0
+            for step, (batch_x, batch_y) in enumerate(training, 1):
+                batch_x, batch_y = batch_x.to(device), batch_y.to(device)
+                optimizer.zero_grad(set_to_none=True)
+                prediction = model(batch_x)
+                mse = (prediction - batch_y).square().mean()
+                relative = relative_l2(prediction, batch_y).mean()
+                loss = mse + relative
+                loss.backward()
+                gradient_norm = torch.nn.utils.clip_grad_norm_(model.parameters(), settings["grad_clip"], error_if_nonfinite=True)
+                optimizer.step()
+                totals += torch.stack([loss.detach(), mse.detach(), relative.detach()]) * len(batch_x)
+                count += len(batch_x)
+                if step % settings["log_interval"] == 0 or step == len(training):
+                    print(f"epoch={epoch:03d}/{settings['epochs']} step={step:03d}/{len(training)} loss={loss.item():.7e} mse={mse.item():.7e} rel_l2_norm={relative.item():.7e} grad_norm={gradient_norm.item():.5e}", flush=True)
+            scheduler.step()
+            metrics = evaluate(model, validation, stats, device)
+            train_loss, train_mse, train_rel = (totals / count).cpu().tolist()
+            improved = metrics["val_relative_l2"] < best
+            if improved:
+                best, best_epoch = metrics["val_relative_l2"], epoch
+            row = dict(epoch=epoch, train_loss=train_loss, train_mse_normalized=train_mse,
+                       train_relative_l2_normalized=train_rel, **metrics, lr_used=lr_used,
+                       lr_next=optimizer.param_groups[0]["lr"], epoch_seconds=time.monotonic()-epoch_start,
+                       best_val_relative_l2=best)
+            state = dict(format="lino-burgers-v1", architecture=model.architecture,
+                         model_state=model.state_dict(), optimizer_state=optimizer.state_dict(),
+                         scheduler_state=scheduler.state_dict(), epoch=epoch, best_epoch=best_epoch,
+                         best_val_relative_l2=best, normalizers=stats, train_indices=train_ids,
+                         val_indices=val_ids, data_contract={"resolution":config["data"]["resolution"],
+                         "interpolation":config["data"]["interpolation"], "input_key":config["data"]["input_key"],
+                         "target_key":config["data"]["target_key"], "dataset_sha256":manifest["dataset_sha256"]},
+                         torch_rng_state=torch.get_rng_state(), accelerator_rng_states=torch.cuda.get_rng_state_all(),
+                         validation_metrics=metrics)
+            if improved:
+                atomic_checkpoint(settings["checkpoint"], state)
+            atomic_checkpoint(settings["last_checkpoint"], state)
+            writer.writerow(row)
+            save_json(output / "training_status.json", {**row, "best_epoch":best_epoch, "status":"running", "completed_epochs":epoch})
+            print(f"EPOCH {epoch:03d}/{settings['epochs']} train_loss={train_loss:.8e} val_loss={metrics['val_loss']:.8e} val_relative_l2={metrics['val_relative_l2']:.8e} best={best:.8e} best_epoch={best_epoch} lr={lr_used:.6e} seconds={row['epoch_seconds']:.2f}", flush=True)
+    summary = dict(status="completed", completed_epochs=settings["epochs"], best_epoch=best_epoch,
+                   best_val_relative_l2=best, paper_relative_l2=0.0109,
+                   ratio_to_paper=best/0.0109, training_seconds=time.monotonic()-started,
+                   n_train=len(train_ids), n_val=len(val_ids), seed=config["seed"],
+                   checkpoint=str(settings["checkpoint"]), slurm_job_id=manifest["slurm_job_id"])
+    save_json(output / "training_summary.json", summary)
+    save_json(output / "training_status.json", summary)
+    print("TRAINING COMPLETED", summary, flush=True)
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--config", default="config/config.yaml")
+    parser.add_argument("--resume", default=None, help="Restore a full last checkpoint if interrupted")
+    args = parser.parse_args()
+    train(load_config(args.config), args.resume)

weight/best_model.pth

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:82ca744dfb18510e680edf20b02213a585c6d859d269a2775c7192be8f67f821
+size 22643009