Forward Models

Overview

The Strong Scattering Neural Operator (S2NO) is a neural operator specifically designed for solving highly oscillatory partial differential equations (PDEs) over large computational domains. Using neural operators as surrogate models in full waveform inversion (FWI) enables accurate and efficient quantitative volumetric imaging of in vivo human breast and musculoskeletal tissues. We provide implementations and pre-trained weights for S2NO and two baseline neural operators, FNO and UNet. Each model is trained for 8 frequencies, ranging from 250 kHz to 600 kHz in 50 kHz increments.

Structure

• limb_wavefield.py: Performs forward inference. This example loads a limb sound speed map and uses a neural operator to simulate the corresponding wavefield at 600 kHz. The script plots the resulting wavefield, with two small figures showing detailed regions.

• S2NO_pretrain.py: Implementation of the S2NO model.

• FNO_pretrain.py: Implementation of the FNO model.

• UNet_pretrain.py: Implementation of the UNet model.

• S2NO: Weights for S2NO across 8 frequencies.

• FNO: Weights for FNO across 8 frequencies.

• UNet: Weights for UNet across 8 frequencies.

• homo: Homogeneous wavefield data for all 8 frequencies.

• speed: A sample limb sound speed map.

• result: Output directory for results generated by limb_wavefield.py.

How to Run the code

1. Environment Setup: python=3.9, torch=2.2.1+cu118, torch-lightning=2.2.0
2. Run limb_wavefield.py: Execute python limb_wavefield.py --model_name='S2NO'. The --model_name argument accepts one of the following: 'S2NO', 'FNO', or 'UNet'.

Citation

Please cite the associated paper if you use this data in your research:

@misc{zeng2025vivo3dultrasoundcomputed,
      title={In vivo 3D ultrasound computed tomography of musculoskeletal tissues with generative neural physics}, 
      author={Zhijun Zeng and Youjia Zheng and Chang Su and Qianhang Wu and Hao Hu and Zeyuan Dong and Shan Gao and Yang Lv and Rui Tang and Ligang Cui and Zhiyong Hou and Weijun Lin and Zuoqiang Shi and Yubing Li and He Sun},
      year={2025},
      eprint={2508.12226},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2508.12226}, 
}