Achieving Long-term Turbulence Tracing By Tackling Spectral Bias

This repo is the official PyTorch implementation of Turb-L1.

📑 Datas

Dataset	Geometry	Link	Original Data shape
Decaying Isotropic Turbulence	Regular Grid	[Hugging Face]	(1280, 100, 128, 128)
Forced Isotropic Turbulence	Regular Grid	[Google Cloud]	(1200, 64, 64, 20)

Here's a brief description of the datasets:

Dataset 1

• Original dimensions: 1,280 samples × 100 timesteps
• Spatial resolution: 128×128
• Training strategy: 1-step prediction (1→1)
• Inference strategy: Multi-step prediction (1→99)
• Variable: Vorticity (single variable)

Dataset 2

• Original dimensions: 1,200 samples × 20 timesteps
• Spatial resolution: 64×64
• Training strategy: 1-step prediction (1→1)
• Inference strategy: Multi-step prediction (1→19)
• Variable: Vorticity (single variable)

The expected output dimensions of the dataloader are as follows (Mode details can be found in dataloader_McWilliams.py):

# --- Testing DataLoader Output ---

# Train DataLoader
train_input_shape = (32, 1, 1, 64, 64)  # (B, T_input, C, H, W)
train_target_shape = (32, 1, 1, 64, 64)  # (B, T_target, C, H, W)
batch_size = 32                          # B
input_timesteps = 1                      # T_input
channels = 1                             # C
height = 64                              # H
width = 64                               # W

# Validation DataLoader
val_input_shape = (32, 1, 1, 64, 64)    # (B, T_input, C, H, W)

# Test DataLoader
test_input_shape = (32, 1, 1, 64, 64)   # (B, T_input, C, H, W)

🔥 Get Started

• Core code: see ./turb_l1.py

• Decaying Isotropic Turbulence Task:

  • Train file: see train_McWilliams.py
  • Inference file: see inference_McWilliams.py
  • Parameters setting: see config_McWilliams.yaml

• Forced Isotropic Turbulence Task:

  • Train file: see train_Forced_Li.py
  • Inference file: see inference_Forced_Li.py
  • Parameters setting: see config_Forced_Li.yaml

you can run train code using this command:

torchrun --nnodes=1 --nproc_per_node=8 train_McWilliams.py

you can run inference code using this command:

python inference_McWilliams.py

🏆 Results

Trub-L1 achieves consistent state-of-the-art perfermance.

Table 1. Performance comparison on isotropic turbulence datasets.

🏆 Showcase

Figure 1. Long-term prediction on 2D Decaying Isotropic Turbulence.

🏆 Training Dynamics

Figure 2. Evolution of spectral error and visual prediction improvement for Turb-L1 during training.

📂 Acknowledgement

We appreciate the following github repos a lot for their valuable code base or datasets:

https://github.com/scaomath/torch-cfd

https://github.com/raj-brown/fourier_neural_operator