We present Wind Lifter, a novel neural representation designed to accurately model complex cuts in thin-walled deformable structures.
Our approach constructs neural fields that reproduce discontinuities precisely at specified locations, without ''baking in'' the position of the cut line.
To achieve this, we augment the input coordinates of the neural field with the generalized winding number of any given cut line, effectively lifting the input from two to three dimensions.
Lifting allows the network to focus on the easier problem of learning a 3D everywhere-continuous volumetric field, while a corresponding restriction operator enables the final output field to precisely resolve strict discontinuities. Crucially, our approach does not embed the discontinuity in the neural network's weights, opening avenues to generalization of cut placement.
Our method achieves real-time simulation speeds and supports dynamic updates to cut line geometry during the simulation. Moreover, the explicit representation of discontinuities makes our neural field intuitive to control and edit, offering a significant advantage over traditional neural fields, where discontinuities are embedded within the network’s weights, and enabling new applications that rely on general cut placement.
@inproceedings{Chang2025Winding,
title = {Lifting the Winding Number: Precise Discontinuities in Neural Fields for Physics Simulation},
author = {Yue Chang and Mengfei Liu and Zhecheng Wang and Peter Yichen Chen and Eitan Grinspun},
booktitle = {ACM SIGGRAPH 2025 Conference Papers},
year = {2025}
}
Acknowledgements
We would like to thank our lab system administrator, John Hancock, and our financial officer, Xuan Dam, for their invaluable administrative support in making this research possible. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) grant RGPIN-2021-03733.
