Precise Gradient Discontinuities in Neural Fields for Subspace Physics

TL;DR

This paper introduces a neural field method capable of modeling gradient discontinuities in physical systems, enabling accurate simulation of creases and material interfaces without explicit remeshing or prior knowledge of discontinuity locations.

Contribution

We propose a novel neural field construction that captures gradient discontinuities through coordinate augmentation, allowing for flexible, discretization-agnostic simulation of complex shape families with evolving interfaces.

Findings

Supports shape morphing and crease editing

Enables simulation of soft-rigid hybrid structures

Jointly captures gradient and value discontinuities

Abstract

Discontinuities in spatial derivatives appear in a wide range of physical systems, from creased thin sheets to materials with sharp stiffness transitions. Accurately modeling these features is essential for simulation but remains challenging for traditional mesh-based methods, which require discontinuity-aligned remeshing -- entangling geometry with simulation and hindering generalization across shape families. Neural fields offer an appealing alternative by encoding basis functions as smooth, continuous functions over space, enabling simulation across varying shapes. However, their smoothness makes them poorly suited for representing gradient discontinuities. Prior work addresses discontinuities in function values, but capturing sharp changes in spatial derivatives while maintaining function continuity has received little attention. We introduce a neural field construction that captures gradient discontinuities without baking their location into the network weights. By augmenting input coordinates with a smoothly clamped distance function in a lifting framework, we enable encoding of gradient jumps at evolving interfaces. This design supports discretization-agnostic simulation of parametrized shape families with heterogeneous materials and evolving creases, enabling new reduced-order capabilities such as shape morphing, interactive crease editing, and simulation of soft-rigid hybrid structures. We further demonstrate that our method can be combined with previous lifting techniques to jointly capture both gradient and value discontinuities, supporting simultaneous cuts and creases within a unified model.