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@@ -33,3 +33,9 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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README.md

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+---
+license: apache-2.0
+language:
+- en
+tags:
+- OneScience
+- computational-fluid-dynamics
+- neural-operator
+- pipe-flow
+---
+# HO-FNO-Pipe-Flow
+
+This package reproduces the Pipe experiment of [Higher-Order Fourier Neural Operator](https://arxiv.org/abs/2606.28122). An eight-layer, second-order spectral operator maps two pipe-coordinate channels to horizontal velocity on a 129 x 129 grid.
+
+## Download
+
+```bash
+hf download OneScience-Group/HO-FNO-Pipe-Flow --local-dir ./HO-FNO-Pipe-Flow
+cd HO-FNO-Pipe-Flow
+```
+
+Install PyTorch, NumPy, PyYAML and Matplotlib in a compatible GPU/DCU environment. The original 2310-sample Pipe dataset is available from the [paper's official repository](https://github.com/AlexColagrande/HO-FNO) and as the [OneScience ModelScope dataset](https://www.modelscope.cn/datasets/OneScience/HO-FNO-Pipe). Download `Pipe_X.npy`, `Pipe_Y.npy`, and `Pipe_Q.npy` into `data/`; no dataset files are included in this Hugging Face model repository.
+
+## Run
+
+```bash
+python scripts/inference.py
+python scripts/result.py
+# To repeat the 500-epoch training run on an accelerator:
+python scripts/train.py
+```
+
+The included `weight/best_model.pth` is from epoch 494. Its 200-case test mean relative L2 is 0.004887735; the paper reports 0.0049 for the Pipe setting. The weight SHA256 is `9d71053c64b62a6fc6f867108c29d2cc0d277d667a3504dc073a6b56072981d4`. See `results/` for the recorded metrics and plots.
+
+## Source and license
+
+Model code in this reproduction is distributed under Apache 2.0. The underlying Pipe data has separate source terms; consult the [original project](https://github.com/AlexColagrande/HO-FNO) before reuse.

config.json

@@ -0,0 +1,7 @@
+{
+  "model_type": "ho-fno-pipe",
+  "architectures": ["HOFNOPipe"],
+  "framework": "pytorch",
+  "task": "pipe-flow-field-regression",
+  "paper": "https://arxiv.org/abs/2606.28122"
+}

config/config.yaml

@@ -0,0 +1,66 @@
+experiment:
+  name: HO-FNO-Pipe-Flow
+  seed: 2026
+  paper: "Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs"
+  task: "Pipe horizontal fluid velocity prediction"
+
+paths:
+  data_dir: data
+  output_dir: .
+  checkpoint: weight/best_model.pth
+  results_dir: results
+
+data:
+  x_file: Pipe_X.npy
+  y_file: Pipe_Y.npy
+  q_file: Pipe_Q.npy
+  train_size: 1000
+  test_size: 200
+  total_used: 1200
+  input_channels: 2
+  output_channel_index: 0
+  resolution: [129, 129]
+  downsample: [1, 1]
+  normalizer_axes: [0, 1]
+  pin_memory: true
+  num_workers: 2
+
+model:
+  class_name: HOFNOPipe
+  order: 2
+  layers: 8
+  width: 128
+  modes: [50, 24]
+  input_channels: 2
+  output_channels: 1
+  add_unit_grid: true
+  mlp_expansion: 4
+  mlp_dropout: 0.0
+  drop_path_rate: 0.0
+
+training:
+  epochs: 500
+  batch_size: 8
+  optimizer: AdamW
+  learning_rate: 1.0e-3
+  final_learning_rate: 5.0e-5
+  weight_decay: 1.0e-5
+  scheduler: CosineAnnealingLR
+  loss: relative_l2
+  save_best_metric: test_mean_relative_l2
+  print_every: 1
+
+runtime:
+  device: auto
+  require_accelerator: true
+  accelerator_kind: dcu
+  slurm:
+    partition: hx1hdnormal01
+    nodes: 1
+    gres: dcu:1
+    cpus_per_task: 8
+    memory: 30G
+    time_limit: "24:00:00"
+    module: compiler/dtk/25.04
+    conda_activate: /public/software/sghpc_sdk/Linux_x86_64/25.6/das/conda/bin/activate
+    conda_env: onescience

model/__init__.py

@@ -0,0 +1,3 @@
+from .ho_fno_pipe import HOFNOPipe, count_parameters
+
+__all__ = ["HOFNOPipe", "count_parameters"]

model/ho_fno_pipe.py

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+"""HO-FNO model for the Pipe horizontal velocity experiment.
+
+This module implements the order-2 higher-order spectral mixer described in
+the HO-FNO paper. The model uses channel-last tensors at the public interface:
+``[batch, height, width, channels]``.
+"""
+
+from __future__ import annotations
+
+from typing import Sequence
+
+import torch
+from torch import nn
+
+
+class RMSNorm2d(nn.Module):
+    """RMS normalization over the channel dimension for channel-last fields."""
+
+    def __init__(self, channels: int, eps: float = 1e-6) -> None:
+        super().__init__()
+        self.weight = nn.Parameter(torch.ones(channels))
+        self.eps = eps
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        scale = torch.rsqrt(x.pow(2).mean(dim=-1, keepdim=True) + self.eps)
+        return x * scale * self.weight.view(1, 1, 1, -1)
+
+
+class DropPath(nn.Module):
+    def __init__(self, probability: float = 0.0) -> None:
+        super().__init__()
+        self.probability = float(probability)
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        if not self.training or self.probability <= 0.0:
+            return x
+        keep = 1.0 - self.probability
+        mask_shape = (x.shape[0],) + (1,) * (x.ndim - 1)
+        mask = torch.empty(mask_shape, device=x.device, dtype=x.dtype).bernoulli_(keep)
+        return x * mask / keep
+
+
+class DepthwiseSpectralConv2d(nn.Module):
+    """Depthwise complex Fourier convolution on retained low modes."""
+
+    def __init__(self, channels: int, modes: Sequence[int]) -> None:
+        super().__init__()
+        if len(modes) != 2:
+            raise ValueError("modes must contain exactly two integers")
+        self.channels = int(channels)
+        self.modes1 = int(modes[0])
+        self.modes2 = int(modes[1])
+        scale = 1.0 / max(1, self.channels)
+        self.weights_pos = nn.Parameter(
+            scale * torch.randn(self.channels, self.modes1, self.modes2, dtype=torch.cfloat)
+        )
+        self.weights_neg = nn.Parameter(
+            scale * torch.randn(self.channels, self.modes1, self.modes2, dtype=torch.cfloat)
+        )
+
+    @staticmethod
+    def _mul_modes(x_ft: torch.Tensor, weights: torch.Tensor) -> torch.Tensor:
+        return torch.einsum("bchw,chw->bchw", x_ft, weights)
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        batch, channels, height, width = x.shape
+        if channels != self.channels:
+            raise ValueError(f"expected {self.channels} channels, got {channels}")
+        x_ft = torch.fft.rfft2(x.float())
+        out_ft = torch.zeros(
+            batch,
+            self.channels,
+            height,
+            width // 2 + 1,
+            device=x.device,
+            dtype=torch.cfloat,
+        )
+        m1 = min(self.modes1, height)
+        m2 = min(self.modes2, width // 2 + 1)
+        out_ft[:, :, :m1, :m2] = self._mul_modes(
+            x_ft[:, :, :m1, :m2], self.weights_pos[:, :m1, :m2]
+        )
+        out_ft[:, :, -m1:, :m2] = self._mul_modes(
+            x_ft[:, :, -m1:, :m2], self.weights_neg[:, :m1, :m2]
+        )
+        return torch.fft.irfft2(out_ft, s=(height, width))
+
+
+class HigherOrderSpectralMixer2d(nn.Module):
+    """Order-m HO spectral mixer.
+
+    The input is projected by ``m`` independent 1x1 maps, their outputs are
+    multiplied channelwise in physical space, then a retained-mode spectral
+    convolution is applied.
+    """
+
+    def __init__(self, channels: int, modes: Sequence[int], order: int = 2) -> None:
+        super().__init__()
+        if order < 1:
+            raise ValueError("order must be positive")
+        self.order = int(order)
+        self.factor_projection = nn.Conv2d(channels, channels * self.order, kernel_size=1)
+        self.spectral = DepthwiseSpectralConv2d(channels, modes)
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        x_cf = x.permute(0, 3, 1, 2).contiguous()
+        factors = self.factor_projection(x_cf).chunk(self.order, dim=1)
+        product = factors[0]
+        for factor in factors[1:]:
+            product = product * factor
+        mixed = self.spectral(product)
+        return mixed.permute(0, 2, 3, 1).contiguous()
+
+
+class HOFNOBlock(nn.Module):
+    def __init__(
+        self,
+        width: int,
+        modes: Sequence[int],
+        order: int,
+        mlp_expansion: int = 4,
+        mlp_dropout: float = 0.0,
+        drop_path: float = 0.0,
+    ) -> None:
+        super().__init__()
+        self.norm_mixer = RMSNorm2d(width)
+        self.mixer = HigherOrderSpectralMixer2d(width, modes, order)
+        self.norm_ffn = RMSNorm2d(width)
+        hidden = int(width * mlp_expansion)
+        self.ffn = nn.Sequential(
+            nn.Linear(width, hidden),
+            nn.GELU(),
+            nn.Dropout(mlp_dropout),
+            nn.Linear(hidden, width),
+            nn.Dropout(mlp_dropout),
+        )
+        self.drop_path = DropPath(drop_path)
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        x = x + self.drop_path(self.mixer(self.norm_mixer(x)))
+        x = x + self.drop_path(self.ffn(self.norm_ffn(x)))
+        return x
+
+
+class HOFNOPipe(nn.Module):
+    """HO-FNO Pipe model with paper Table 13 defaults."""
+
+    def __init__(
+        self,
+        input_channels: int = 2,
+        output_channels: int = 1,
+        order: int = 2,
+        layers: int = 8,
+        width: int = 128,
+        modes: Sequence[int] = (50, 24),
+        add_unit_grid: bool = True,
+        mlp_expansion: int = 4,
+        mlp_dropout: float = 0.0,
+        drop_path_rate: float = 0.0,
+    ) -> None:
+        super().__init__()
+        self.add_unit_grid = bool(add_unit_grid)
+        lift_channels = int(input_channels) + (2 if self.add_unit_grid else 0)
+        self.lift = nn.Linear(lift_channels, width)
+        if layers <= 1:
+            drop_rates = [0.0] * layers
+        else:
+            drop_rates = torch.linspace(0.0, float(drop_path_rate), layers).tolist()
+        self.blocks = nn.ModuleList(
+            [
+                HOFNOBlock(
+                    width=width,
+                    modes=modes,
+                    order=order,
+                    mlp_expansion=mlp_expansion,
+                    mlp_dropout=mlp_dropout,
+                    drop_path=drop_rates[idx],
+                )
+                for idx in range(layers)
+            ]
+        )
+        self.project = nn.Linear(width, output_channels)
+
+    @staticmethod
+    def unit_grid(batch: int, height: int, width: int, device: torch.device, dtype: torch.dtype) -> torch.Tensor:
+        gx = torch.linspace(0.0, 1.0, height, device=device, dtype=dtype).view(1, height, 1, 1)
+        gy = torch.linspace(0.0, 1.0, width, device=device, dtype=dtype).view(1, 1, width, 1)
+        gx = gx.expand(batch, height, width, 1)
+        gy = gy.expand(batch, height, width, 1)
+        return torch.cat((gx, gy), dim=-1)
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        if x.ndim != 4:
+            raise ValueError("HOFNOPipe expects [batch, height, width, channels]")
+        if self.add_unit_grid:
+            grid = self.unit_grid(x.shape[0], x.shape[1], x.shape[2], x.device, x.dtype)
+            x = torch.cat((x, grid), dim=-1)
+        x = self.lift(x)
+        for block in self.blocks:
+            x = block(x)
+        return self.project(x)
+
+
+def count_parameters(model: nn.Module) -> int:
+    return sum(param.numel() for param in model.parameters() if param.requires_grad)

results/best_metrics.json

@@ -0,0 +1,5 @@
+{
+  "best_epoch": 494,
+  "test_mean_relative_l2": 0.004887734765652567,
+  "checkpoint": "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/weight/best_model.pth"
+}

results/inference_metrics.json

@@ -0,0 +1,8 @@
+{
+  "checkpoint": "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/weight/best_model.pth",
+  "test_samples": 200,
+  "mean_relative_l2": 0.00488773500546813,
+  "median_relative_l2": 0.0007863331120461226,
+  "max_relative_l2": 0.07080713659524918,
+  "min_relative_l2": 0.0002587482158560306
+}

results/inputs.npy

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results/predictions.npy

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results/relative_l2_per_sample.npy

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results/result_summary.json

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+  "figure_count": 8,
+  "figures": [
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+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_050.png",
+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_193.png",
+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_000.png",
+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_001.png",
+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_002.png",
+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_003.png",
+    "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/results/figures/pipe_case_004.png"
+  ],
+  "mean_relative_l2": 0.00488773500546813,
+  "best_case": 76,
+  "median_case": 50,
+  "worst_case": 193
+}

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results/training_summary.json

@@ -0,0 +1,7 @@
+{
+  "epochs": 500,
+  "best_epoch": 494,
+  "best_test_mean_relative_l2": 0.004887734765652567,
+  "total_seconds": 21283.793029546738,
+  "checkpoint": "/public/home/liuyushuang/zhaomingsi/onescience-cfd-repro-packages/HO-FNO-Pipe-Flow/weight/best_model.pth"
+}

scripts/common.py

@@ -0,0 +1,176 @@
+from __future__ import annotations
+
+import json
+import os
+import random
+import sys
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+import torch
+import yaml
+
+
+ROOT = Path(__file__).resolve().parents[1]
+if str(ROOT) not in sys.path:
+    sys.path.insert(0, str(ROOT))
+
+from model.ho_fno_pipe import HOFNOPipe, count_parameters  # noqa: E402
+
+
+class UnitTransformer:
+    def __init__(self, tensor: torch.Tensor, axes: tuple[int, ...] = (0, 1), eps: float = 1e-8) -> None:
+        self.axes = axes
+        self.eps = eps
+        self.mean = tensor.mean(dim=axes, keepdim=True)
+        self.std = tensor.std(dim=axes, keepdim=True) + eps
+
+    def encode(self, tensor: torch.Tensor) -> torch.Tensor:
+        return (tensor - self.mean) / self.std
+
+    def decode(self, tensor: torch.Tensor) -> torch.Tensor:
+        return tensor * self.std + self.mean
+
+    def to(self, device: torch.device) -> "UnitTransformer":
+        self.mean = self.mean.to(device)
+        self.std = self.std.to(device)
+        return self
+
+    def state_dict(self) -> dict[str, Any]:
+        return {"mean": self.mean.cpu(), "std": self.std.cpu(), "axes": self.axes, "eps": self.eps}
+
+    @classmethod
+    def from_state_dict(cls, state: dict[str, Any]) -> "UnitTransformer":
+        obj = cls.__new__(cls)
+        obj.mean = state["mean"]
+        obj.std = state["std"]
+        obj.axes = tuple(state.get("axes", (0, 1)))
+        obj.eps = float(state.get("eps", 1e-8))
+        return obj
+
+
+def load_config(path: str | os.PathLike[str] | None = None) -> dict[str, Any]:
+    cfg_path = Path(path) if path else ROOT / "config" / "config.yaml"
+    with cfg_path.open("r", encoding="utf-8") as handle:
+        cfg = yaml.safe_load(handle)
+    cfg["_config_path"] = str(cfg_path)
+    return cfg
+
+
+def set_seed(seed: int) -> None:
+    random.seed(seed)
+    np.random.seed(seed)
+    torch.manual_seed(seed)
+    if torch.cuda.is_available():
+        torch.cuda.manual_seed_all(seed)
+
+
+def resolve(path: str | os.PathLike[str], base: Path | None = None) -> Path:
+    p = Path(path)
+    if p.is_absolute():
+        return p
+    return (base or ROOT) / p
+
+
+def select_device(require_accelerator: bool = False) -> torch.device:
+    if torch.cuda.is_available():
+        return torch.device("cuda")
+    if require_accelerator:
+        raise RuntimeError("accelerator is required, but torch.cuda.is_available() is False")
+    return torch.device("cpu")
+
+
+def load_pipe_tensors(cfg: dict[str, Any]) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+    data_cfg = cfg["data"]
+    data_dir = Path(cfg["paths"]["data_dir"])
+    train_size = int(data_cfg["train_size"])
+    test_size = int(data_cfg["test_size"])
+    total_used = int(data_cfg["total_used"])
+    r1, r2 = (int(v) for v in data_cfg.get("downsample", [1, 1]))
+    s1 = int(((int(data_cfg["resolution"][0]) - 1) / r1) + 1)
+    s2 = int(((int(data_cfg["resolution"][1]) - 1) / r2) + 1)
+
+    x_raw = np.load(data_dir / data_cfg["x_file"], mmap_mode="r")[:total_used, ::r1, ::r2][:, :s1, :s2]
+    y_raw = np.load(data_dir / data_cfg["y_file"], mmap_mode="r")[:total_used, ::r1, ::r2][:, :s1, :s2]
+    q_raw = np.load(data_dir / data_cfg["q_file"], mmap_mode="r")[
+        :total_used, int(data_cfg["output_channel_index"]), ::r1, ::r2
+    ][:, :s1, :s2]
+
+    coords = np.stack((np.asarray(x_raw, dtype=np.float32), np.asarray(y_raw, dtype=np.float32)), axis=-1)
+    target = np.asarray(q_raw, dtype=np.float32)[..., None]
+    x_all = torch.from_numpy(coords.copy())
+    y_all = torch.from_numpy(target.copy())
+    return x_all[:train_size], y_all[:train_size], x_all[-test_size:], y_all[-test_size:]
+
+
+def make_normalized_loaders(cfg: dict[str, Any]):
+    x_train, y_train, x_test, y_test = load_pipe_tensors(cfg)
+    axes = tuple(int(v) for v in cfg["data"].get("normalizer_axes", [0, 1]))
+    x_normalizer = UnitTransformer(x_train, axes=axes)
+    y_normalizer = UnitTransformer(y_train, axes=axes)
+    x_train_n = x_normalizer.encode(x_train)
+    x_test_n = x_normalizer.encode(x_test)
+    y_train_n = y_normalizer.encode(y_train)
+    y_test_n = y_normalizer.encode(y_test)
+
+    batch_size = int(cfg["training"]["batch_size"])
+    loader_kwargs = {
+        "batch_size": batch_size,
+        "num_workers": int(cfg["data"].get("num_workers", 0)),
+        "pin_memory": bool(cfg["data"].get("pin_memory", False)),
+    }
+    train_ds = torch.utils.data.TensorDataset(x_train_n, y_train_n)
+    test_ds = torch.utils.data.TensorDataset(x_test_n, y_test_n)
+    train_loader = torch.utils.data.DataLoader(train_ds, shuffle=True, **loader_kwargs)
+    test_loader = torch.utils.data.DataLoader(test_ds, shuffle=False, **loader_kwargs)
+    return train_loader, test_loader, x_normalizer, y_normalizer
+
+
+def build_model(cfg: dict[str, Any]) -> HOFNOPipe:
+    m = cfg["model"]
+    return HOFNOPipe(
+        input_channels=int(m["input_channels"]),
+        output_channels=int(m["output_channels"]),
+        order=int(m["order"]),
+        layers=int(m["layers"]),
+        width=int(m["width"]),
+        modes=tuple(int(v) for v in m["modes"]),
+        add_unit_grid=bool(m.get("add_unit_grid", True)),
+        mlp_expansion=int(m.get("mlp_expansion", 4)),
+        mlp_dropout=float(m.get("mlp_dropout", 0.0)),
+        drop_path_rate=float(m.get("drop_path_rate", 0.0)),
+    )
+
+
+def relative_l2_per_sample(pred: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
+    pred_f = pred.reshape(pred.shape[0], -1)
+    target_f = target.reshape(target.shape[0], -1)
+    denom = torch.linalg.vector_norm(target_f, dim=1).clamp_min(1e-12)
+    return torch.linalg.vector_norm(pred_f - target_f, dim=1) / denom
+
+
+def relative_l2_sum(pred: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
+    return relative_l2_per_sample(pred, target).sum()
+
+
+def save_json(path: Path, payload: dict[str, Any]) -> None:
+    path.parent.mkdir(parents=True, exist_ok=True)
+    with path.open("w", encoding="utf-8") as handle:
+        json.dump(payload, handle, indent=2)
+
+
+__all__ = [
+    "ROOT",
+    "UnitTransformer",
+    "build_model",
+    "count_parameters",
+    "load_config",
+    "make_normalized_loaders",
+    "relative_l2_per_sample",
+    "relative_l2_sum",
+    "resolve",
+    "save_json",
+    "select_device",
+    "set_seed",
+]

scripts/inference.py

@@ -0,0 +1,86 @@
+from __future__ import annotations
+
+import argparse
+from pathlib import Path
+
+import numpy as np
+import torch
+
+from common import (
+    ROOT,
+    UnitTransformer,
+    build_model,
+    load_config,
+    load_pipe_tensors,
+    relative_l2_per_sample,
+    resolve,
+    save_json,
+    select_device,
+)
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description="Run HO-FNO Pipe inference with the best checkpoint.")
+    parser.add_argument("--config", default=str(ROOT / "config" / "config.yaml"))
+    parser.add_argument("--checkpoint", default=None)
+    args = parser.parse_args()
+
+    cfg = load_config(args.config)
+    output_dir = resolve(cfg["paths"]["output_dir"])
+    results_dir = resolve(cfg["paths"]["results_dir"], output_dir)
+    results_dir.mkdir(parents=True, exist_ok=True)
+    checkpoint = resolve(args.checkpoint or cfg["paths"]["checkpoint"], output_dir)
+    device = select_device(require_accelerator=False)
+
+    payload = torch.load(checkpoint, map_location=device)
+    ckpt_cfg = payload.get("config", cfg)
+    model = build_model(ckpt_cfg).to(device)
+    model.load_state_dict(payload["model_state"])
+    model.eval()
+    x_norm = UnitTransformer.from_state_dict(payload["x_normalizer"]).to(device)
+    y_norm = UnitTransformer.from_state_dict(payload["y_normalizer"]).to(device)
+
+    _, _, x_test, y_test = load_pipe_tensors(ckpt_cfg)
+    batch_size = int(ckpt_cfg["training"]["batch_size"])
+    predictions = []
+    targets = []
+    inputs = []
+    rel_values = []
+    with torch.no_grad():
+        for start in range(0, x_test.shape[0], batch_size):
+            x = x_test[start : start + batch_size].to(device)
+            y = y_test[start : start + batch_size].to(device)
+            pred = y_norm.decode(model(x_norm.encode(x)))
+            rel = relative_l2_per_sample(pred, y)
+            predictions.append(pred.cpu().numpy())
+            targets.append(y.cpu().numpy())
+            inputs.append(x.cpu().numpy())
+            rel_values.append(rel.cpu().numpy())
+
+    pred_arr = np.concatenate(predictions, axis=0)
+    target_arr = np.concatenate(targets, axis=0)
+    input_arr = np.concatenate(inputs, axis=0)
+    rel_arr = np.concatenate(rel_values, axis=0)
+    np.save(results_dir / "predictions.npy", pred_arr)
+    np.save(results_dir / "targets.npy", target_arr)
+    np.save(results_dir / "inputs.npy", input_arr)
+    np.save(results_dir / "relative_l2_per_sample.npy", rel_arr)
+    metrics = {
+        "checkpoint": str(checkpoint),
+        "test_samples": int(rel_arr.shape[0]),
+        "mean_relative_l2": float(rel_arr.mean()),
+        "median_relative_l2": float(np.median(rel_arr)),
+        "max_relative_l2": float(rel_arr.max()),
+        "min_relative_l2": float(rel_arr.min()),
+    }
+    save_json(results_dir / "inference_metrics.json", metrics)
+    print(
+        "inference_complete "
+        f"mean_relative_l2={metrics['mean_relative_l2']:.8f} "
+        f"predictions={results_dir / 'predictions.npy'}",
+        flush=True,
+    )
+
+
+if __name__ == "__main__":
+    main()

scripts/result.py

@@ -0,0 +1,90 @@
+from __future__ import annotations
+
+import argparse
+from pathlib import Path
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+from common import ROOT, load_config, resolve, save_json
+
+
+def plot_case(xy: np.ndarray, pred: np.ndarray, target: np.ndarray, out_path: Path, title: str) -> None:
+    x = xy[..., 0]
+    y = xy[..., 1]
+    p = pred[..., 0]
+    t = target[..., 0]
+    err = p - t
+    vmin = float(min(p.min(), t.min()))
+    vmax = float(max(p.max(), t.max()))
+    fig, axes = plt.subplots(1, 3, figsize=(13, 3.6), constrained_layout=True)
+    for ax, field, name, lo, hi, cmap in [
+        (axes[0], t, "target", vmin, vmax, "coolwarm"),
+        (axes[1], p, "prediction", vmin, vmax, "coolwarm"),
+        (axes[2], err, "error", float(-np.max(np.abs(err))), float(np.max(np.abs(err))), "coolwarm"),
+    ]:
+        mesh = ax.pcolormesh(x, y, field, shading="auto", cmap=cmap, vmin=lo, vmax=hi)
+        ax.set_aspect("equal", adjustable="box")
+        ax.set_title(name)
+        ax.set_xticks([])
+        ax.set_yticks([])
+        fig.colorbar(mesh, ax=ax, fraction=0.046, pad=0.02)
+    fig.suptitle(title)
+    fig.savefig(out_path, dpi=180)
+    plt.close(fig)
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description="Create HO-FNO Pipe visualizations from inference arrays.")
+    parser.add_argument("--config", default=str(ROOT / "config" / "config.yaml"))
+    parser.add_argument("--num-cases", type=int, default=8)
+    args = parser.parse_args()
+
+    cfg = load_config(args.config)
+    output_dir = resolve(cfg["paths"]["output_dir"])
+    results_dir = resolve(cfg["paths"]["results_dir"], output_dir)
+    pred_path = results_dir / "predictions.npy"
+    target_path = results_dir / "targets.npy"
+    input_path = results_dir / "inputs.npy"
+    rel_path = results_dir / "relative_l2_per_sample.npy"
+    for path in [pred_path, target_path, input_path, rel_path]:
+        if not path.exists():
+            raise FileNotFoundError(f"missing required inference artifact: {path}")
+
+    pred = np.load(pred_path)
+    target = np.load(target_path)
+    inputs = np.load(input_path)
+    rel = np.load(rel_path)
+    fig_dir = results_dir / "figures"
+    fig_dir.mkdir(parents=True, exist_ok=True)
+    order = np.argsort(rel)
+    chosen = []
+    if len(order) > 0:
+        chosen.extend([int(order[0]), int(order[len(order) // 2]), int(order[-1])])
+    for idx in range(min(args.num_cases, len(rel))):
+        if idx not in chosen:
+            chosen.append(idx)
+    chosen = chosen[: max(1, args.num_cases)]
+    figures = []
+    for idx in chosen:
+        out_path = fig_dir / f"pipe_case_{idx:03d}.png"
+        plot_case(inputs[idx], pred[idx], target[idx], out_path, f"Pipe case {idx} | rel L2={rel[idx]:.6f}")
+        figures.append(str(out_path))
+
+    summary = {
+        "figure_count": len(figures),
+        "figures": figures,
+        "mean_relative_l2": float(rel.mean()),
+        "best_case": int(order[0]) if len(order) else None,
+        "median_case": int(order[len(order) // 2]) if len(order) else None,
+        "worst_case": int(order[-1]) if len(order) else None,
+    }
+    save_json(results_dir / "result_summary.json", summary)
+    print(f"result_complete figures={len(figures)} summary={results_dir / 'result_summary.json'}", flush=True)
+
+
+if __name__ == "__main__":
+    main()

scripts/train.py

@@ -0,0 +1,168 @@
+from __future__ import annotations
+
+import argparse
+import csv
+import time
+from pathlib import Path
+
+import torch
+
+from common import (
+    ROOT,
+    build_model,
+    count_parameters,
+    load_config,
+    make_normalized_loaders,
+    relative_l2_per_sample,
+    relative_l2_sum,
+    resolve,
+    save_json,
+    select_device,
+    set_seed,
+)
+
+
+def evaluate(model, loader, y_normalizer, device):
+    model.eval()
+    total = 0.0
+    count = 0
+    with torch.no_grad():
+        for x, y_norm in loader:
+            x = x.to(device, non_blocking=True)
+            y_norm = y_norm.to(device, non_blocking=True)
+            pred = y_normalizer.decode(model(x))
+            target = y_normalizer.decode(y_norm)
+            rel = relative_l2_per_sample(pred, target)
+            total += float(rel.sum().item())
+            count += int(rel.numel())
+    return total / max(1, count)
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description="Train HO-FNO on Pipe horizontal velocity.")
+    parser.add_argument("--config", default=str(ROOT / "config" / "config.yaml"))
+    args = parser.parse_args()
+
+    cfg = load_config(args.config)
+    set_seed(int(cfg["experiment"].get("seed", 2026)))
+    output_dir = resolve(cfg["paths"]["output_dir"])
+    weight_path = resolve(cfg["paths"]["checkpoint"], output_dir)
+    results_dir = resolve(cfg["paths"]["results_dir"], output_dir)
+    weight_path.parent.mkdir(parents=True, exist_ok=True)
+    results_dir.mkdir(parents=True, exist_ok=True)
+
+    require_accelerator = bool(cfg["runtime"].get("require_accelerator", False))
+    device = select_device(require_accelerator=require_accelerator)
+    print(f"device={device}", flush=True)
+
+    train_loader, test_loader, x_normalizer, y_normalizer = make_normalized_loaders(cfg)
+    x_normalizer.to(device)
+    y_normalizer.to(device)
+
+    model = build_model(cfg).to(device)
+    print(f"parameters={count_parameters(model)}", flush=True)
+
+    train_cfg = cfg["training"]
+    optimizer = torch.optim.AdamW(
+        model.parameters(),
+        lr=float(train_cfg["learning_rate"]),
+        weight_decay=float(train_cfg.get("weight_decay", 0.0)),
+    )
+    scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(
+        optimizer,
+        T_max=int(train_cfg["epochs"]),
+        eta_min=float(train_cfg["final_learning_rate"]),
+    )
+
+    history_path = results_dir / "train_history.csv"
+    best_metric = float("inf")
+    best_epoch = -1
+    train_size = int(cfg["data"]["train_size"])
+    epochs = int(train_cfg["epochs"])
+    start_time = time.time()
+
+    with history_path.open("w", newline="", encoding="utf-8") as handle:
+        writer = csv.DictWriter(handle, fieldnames=["epoch", "train_loss", "test_mean_relative_l2", "lr", "seconds"])
+        writer.writeheader()
+        for epoch in range(1, epochs + 1):
+            model.train()
+            epoch_start = time.time()
+            train_loss_sum = 0.0
+            for x, y_norm in train_loader:
+                x = x.to(device, non_blocking=True)
+                y_norm = y_norm.to(device, non_blocking=True)
+                optimizer.zero_grad(set_to_none=True)
+                pred = y_normalizer.decode(model(x))
+                target = y_normalizer.decode(y_norm)
+                loss = relative_l2_sum(pred, target)
+                loss.backward()
+                optimizer.step()
+                train_loss_sum += float(loss.item())
+
+            scheduler.step()
+            train_loss = train_loss_sum / train_size
+            test_l2 = evaluate(model, test_loader, y_normalizer, device)
+            lr = float(optimizer.param_groups[0]["lr"])
+            seconds = time.time() - epoch_start
+            writer.writerow(
+                {
+                    "epoch": epoch,
+                    "train_loss": train_loss,
+                    "test_mean_relative_l2": test_l2,
+                    "lr": lr,
+                    "seconds": seconds,
+                }
+            )
+            handle.flush()
+            print(
+                f"epoch={epoch:04d} train_loss={train_loss:.8f} "
+                f"test_mean_relative_l2={test_l2:.8f} lr={lr:.8e}",
+                flush=True,
+            )
+
+            if test_l2 < best_metric:
+                best_metric = test_l2
+                best_epoch = epoch
+                torch.save(
+                    {
+                        "model_state": model.state_dict(),
+                        "config": cfg,
+                        "epoch": epoch,
+                        "best_metric": best_metric,
+                        "x_normalizer": x_normalizer.state_dict(),
+                        "y_normalizer": y_normalizer.state_dict(),
+                    },
+                    weight_path,
+                )
+                save_json(
+                    results_dir / "best_metrics.json",
+                    {"best_epoch": best_epoch, "test_mean_relative_l2": best_metric, "checkpoint": str(weight_path)},
+                )
+
+    torch.save(
+        {
+            "model_state": model.state_dict(),
+            "config": cfg,
+            "epoch": epochs,
+            "best_metric": best_metric,
+            "x_normalizer": x_normalizer.state_dict(),
+            "y_normalizer": y_normalizer.state_dict(),
+        },
+        weight_path.parent / "last_model.pth",
+    )
+    save_json(
+        results_dir / "training_summary.json",
+        {
+            "epochs": epochs,
+            "best_epoch": best_epoch,
+            "best_test_mean_relative_l2": best_metric,
+            "total_seconds": time.time() - start_time,
+            "checkpoint": str(weight_path),
+        },
+    )
+    print(f"best_checkpoint={weight_path}", flush=True)
+    print(f"best_epoch={best_epoch} best_test_mean_relative_l2={best_metric:.8f}", flush=True)
+
+
+if __name__ == "__main__":
+    main()

weight/best_model.pth

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9d71053c64b62a6fc6f867108c29d2cc0d277d667a3504dc073a6b56072981d4
+size 24981730