Add EddyFormer

examples/cfd/isotropic_eddyformer/README.md

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+# EddyFormer for 3D Isotropic Turbulence
+
+This example demonstrates how to use the EddyFormer model for simulating
+a three-dimensional isotropic turbulence. This example runs on a single GPU.
+
+## Problem Overview
+
+This example focuses on **three-dimensional homogeneous isotropic turbulence (HIT)** sustained by large-scale forcing. The flow is governed by the incompressible Navier–Stokes equations with an external forcing term:
+
+\[
+\frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u}
+= \nu \nabla^2 \mathbf{u} + \mathbf{f}(\mathbf{x})
+\]
+
+where:
+
+- **\(\mathbf{u}(\mathbf{x}, t)\)** — velocity field in a 3D periodic domain  
+- **\(\nu = 0.01\)** — kinematic viscosity  
+- **\(\mathbf{f}(\mathbf{x})\)** — isotropic forcing applied at the largest scales
+
+### Forcing Mechanism
+
+To maintain statistically steady turbulence, a **constant-power forcing** is applied to the lowest Fourier modes (\(|\mathbf{k}| \le 1\)). The forcing injects a prescribed amount of energy \(P_{\text{in}} = 1.0\) into the system:
+
+\[
+\mathbf{f}(\mathbf{x}) =
+\frac{P_{\text{in}}}{E_1}
+\sum_{\substack{|\mathbf{k}| \le 1 \\ \mathbf{k} \neq 0}}
+\hat{\mathbf{u}}_{\mathbf{k}} e^{i \mathbf{k} \cdot \mathbf{x}}
+\]
+
+where:
+
+\[
+E_1 = \frac{1}{2}
+\sum_{|\mathbf{k}| \le 1} 
+\hat{\mathbf{u}}_{\mathbf{k}} \cdot \hat{\mathbf{u}}_{\mathbf{k}}^{*}
+\]
+
+is the kinetic energy contained in the forced low-wavenumber modes.
+
+Under this forcing, the flow reaches a **statistically steady state** with a Taylor-scale Reynolds number of:
+
+**\(\mathrm{Re}_\lambda \approx 94\)**
+
+### Task Description
+
+The objective of this example is to **predict the future velocity field** of the turbulent flow. Given \(\mathbf{u}(\mathbf{x}, t)\), the task is:
+
+> **Predict the velocity field \(\mathbf{u}(\mathbf{x}, t + \Delta t)\) with \(\Delta t = 0.5\).**
+
+This requires modeling nonlinear, chaotic, multi-scale turbulent dynamics, including:
+
+- energy injection at large scales  
+- nonlinear transfer across the inertial range  
+- dissipation at the smallest scales  
+
+### Dataset Summary
+
+- **DNS resolution:** \(384^3\) (used to generate the dataset)  
+- **Stored dataset resolution:** \(96^3\)  
+- **Kolmogorov scale resolution:** ~0.5 η  
+- **Forcing:** applied to modes with \(|\mathbf{k}| \le 1\)  
+- **Viscosity:** \(\nu = 0.01\)  
+- **Input power:** \(P_{\text{in}} = 1.0\)  
+- **Flow regime:** statistically steady HIT at \(\mathrm{Re}_\lambda \approx 94\)
+
+## Prerequisites
+
+Install the required dependencies by running below:
+
+```bash
+pip install -r requirements.txt
+```
+
+## Download the Dataset
+
+The dataset is publicly available at [Huggingface](https://huggingface.co/datasets/ydu11/re94).
+To download the dataset, run (you might need to install the Huggingface CLI):
+
+```bash
+bash download_dataset.sh
+```
+
+## Getting Started
+
+To train the model, run
+
+```bash
+python train_ef_isotropic.py
+```
+
+## References
+
+- [EddyFormer: EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale](https://arxiv.org/abs/2510.24173)

examples/cfd/isotropic_eddyformer/config.yaml

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+model:
+  idim: 3
+  odim: 3
+  hdim: 32
+  num_layers: 4
+  layer_config:
+    basis: legendre
+    mesh: [8, 8, 8]
+    mode: [10, 10, 10]
+    mode_les: [5, 5, 5]
+    kernel_size: [2, 2, 2]
+    kernel_size_les: [2, 2, 2]
+    ffn_dim: 128
+    activation: GELU
+    num_heads: 4
+    heads_dim: 32
+
+training:
+  dataset: data/ns3d-re94
+  t: 0.5
+  batch_size: 4
+  num_epochs: 100
+  learning_rate: 1e-3

examples/cfd/isotropic_eddyformer/download_dataset.sh

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+hf download --repo-type dataset ydu11/re94 --local-dir ${1:-data/ns3d-re94}

examples/cfd/isotropic_eddyformer/requirements.txt

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+hydra-core>=1.2.0
+termcolor>=2.1.1

examples/cfd/isotropic_eddyformer/train_ef_isotropic.py

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+import hydra
+from typing import Tuple
+from torch import Tensor
+from omegaconf import DictConfig
+
+import os
+import numpy as np
+
+import torch
+from torch.nn import MSELoss
+from torch.optim import Adam
+from torch.utils.data import Dataset, DataLoader
+
+from physicsnemo.models.eddyformer import EddyFormer, EddyFormerConfig
+from physicsnemo.distributed import DistributedManager
+from physicsnemo.utils import StaticCaptureTraining
+from physicsnemo.launch.logging import PythonLogger, LaunchLogger
+
+
+class Re94(Dataset):
+
+    root: str
+    t: float
+
+    n: int = 50
+    dt: float = 0.1
+
+    def __init__(self, root: str, split: str, *, t: float = 0.5) -> None:
+        """
+        """
+        super().__init__()
+        self.root = root
+        self.t = t
+
+        self.file = []
+        for fname in sorted(os.listdir(root)):
+            if fname.startswith(split):
+                self.file.append(fname)
+
+    @property
+    def stride(self) -> int:
+        k = int(self.t / self.dt)
+        assert self.dt * k == self.t
+        return k
+
+    @property
+    def samples_per_file(self) -> int:
+        return self.n - self.stride + 1
+
+    def __len__(self) -> int:
+        return len(self.file) * self.samples_per_file
+
+    def __getitem__(self, idx: int) -> Tuple[Tensor, Tensor]:
+        file_idx, time_idx = divmod(idx, self.samples_per_file)
+
+        data = np.load(f"{self.root}/{self.file[file_idx]}", allow_pickle=True).item()
+        return torch.from_numpy(data["u"][time_idx]), torch.from_numpy(data["u"][time_idx + self.stride])
+
+@hydra.main(version_base="1.3", config_path=".", config_name="config.yaml")
+def isotropic_trainer(cfg: DictConfig) -> None:
+    """
+    """
+    DistributedManager.initialize()  # Only call this once in the entire script!
+    dist = DistributedManager()  # call if required elsewhere
+
+    # initialize monitoring
+    log = PythonLogger(name="re94_ef")
+    log.file_logging()
+    LaunchLogger.initialize()  # PhysicsNeMo launch logger
+
+    # define model, loss, optimiser, scheduler, data loader
+    model = EddyFormer(
+        idim=cfg.model.idim,
+        odim=cfg.model.odim,
+        hdim=cfg.model.hdim,
+        num_layers=cfg.model.num_layers,
+        cfg=EddyFormerConfig(**cfg.model.layer_config),
+    ).to(dist.device)
+    loss_fun = MSELoss(reduction="mean")
+    optimizer = Adam(model.parameters(), lr=cfg.training.learning_rate)
+    dataset = Re94(root=cfg.training.dataset, split="train", t=cfg.training.t)
+
+    # define forward passes for training and inference
+    @StaticCaptureTraining(
+        model=model, optim=optimizer, logger=log, use_amp=False, use_graphs=False
+    )
+    def training_step(input, target):
+        pred = torch.vmap(model)(input)
+        loss = loss_fun(pred, target)
+        return loss
+
+    for epoch in range(cfg.training.num_epochs):
+
+        dataloader = DataLoader(dataset, cfg.training.batch_size, shuffle=True)
+
+        for input, target in dataloader:
+
+            input = input.to(dist.device)
+            target = target.to(dist.device)
+            with torch.autograd.set_detect_anomaly(True):
+                loss = training_step(input, target)
+
+            with LaunchLogger("train", epoch=epoch) as logger:
+                logger.log_minibatch({"Training loss": loss.item()})
+
+    log.success("Training completed")
+
+
+if __name__ == "__main__":
+    isotropic_trainer()

physicsnemo/models/eddyformer/__init__.py

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+from ._basis import Legendre
+from ._datatype import SEM
+from .eddyformer import EddyFormer, EddyFormerLayer
+
+EddyFormerConfig = EddyFormerLayer.Config

physicsnemo/models/eddyformer/_basis.py

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+from typing import Protocol
+from torch import Tensor
+
+import torch
+import torch.nn as nn
+
+import numpy as np
+import functools
+
+class Basis(Protocol):
+
+    grid: Tensor
+    quad: Tensor
+
+    m: int
+    f: Tensor
+
+    def fn(self, xs: Tensor) -> Tensor:
+        """
+        Evaluate basis functions at given points.
+        """
+
+    def at(self, coef: Tensor, xs: Tensor) -> Tensor:
+        """
+        Evaluate basis expansion at given points.
+        """
+        return torch.tensordot(self.fn(xs), coef, dims=1)
+
+    def modal(self, vals: Tensor) -> Tensor:
+        """
+        Convert nodal values to modal coefficients.
+        """
+
+    def nodal(self, coef: Tensor) -> Tensor:
+        """
+        Convert modal coefficients to nodal values.
+        """
+
+class Element(Basis):
+
+    def __init__(self, base: Basis):
+        """
+        """
+
+# ---------------------------------------------------------------------------- #
+#                                   LEGENDRE                                   #
+# ---------------------------------------------------------------------------- #
+
+from numpy.polynomial import legendre
+
+@functools.cache
+class Legendre(nn.Module, Basis):
+
+    """
+    Shifted Legendre polynomials:
+    - `(1 - x^2) Pn''(x) - 2 x Pn(x) + n (n + 1) Pn(x) = 0`
+    - `Pn^~(x) = Pn(2 x - 1)`
+    """
+
+    def extra_repr(self) -> str:
+        return f"m={self.m}"
+
+    def __init__(self, m: int, endpoint: bool = False):
+        """
+        """
+        super().__init__()
+        self.m = m
+
+        if endpoint: m -= 1
+        c = (0, ) * m + (1, )
+        dc = legendre.legder(c)
+
+        x = legendre.legroots(dc if endpoint else c)
+        y = legendre.legval(x, c if endpoint else dc)
+
+        if endpoint:
+            x = np.concatenate([[-1], x, [1]])
+            y = np.concatenate([[1], y, [1]])
+
+        w = 1 / y ** 2
+        if endpoint: w /= m * (m + 1)
+        else: w /= 1 - x ** 2
+
+        self.register_buffer("grid", torch.tensor((1 + x) / 2, dtype=torch.float))
+        self.register_buffer("quad", torch.tensor(w, dtype=torch.float))
+
+        self.register_buffer("f", self.fn(self.grid))
+
+    def fn(self, xs: Tensor) -> Tensor:
+        """
+        """
+        P = torch.ones_like(xs), 2 * xs - 1
+
+        for i in range(2, self.m):
+            a, b = (i * 2 - 1) / i, (i - 1) / i
+            P += a * P[-1] * P[1] - b * P[-2],
+
+        return torch.stack(P, dim=-1)
+
+# --------------------------------- TRANSFORM -------------------------------- #
+
+    def modal(self, vals: Tensor) -> Tensor:
+        """
+        """
+        norm = 2 * torch.arange(self.m, device=vals.device) + 1
+        coef = self.f * norm * self.quad[:, None]
+        return torch.tensordot(coef.T, vals, dims=1)
+
+    def nodal(self, coef: Tensor) -> Tensor:
+        """
+        """
+        return self.at(coef, self.grid)