Lifting the Winding Number: Precise Discontinuities in Neural Fields for Physics Simulation

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.