Presentation
Precise Gradient Discontinuities in Neural Fields for Subspace Physics
DescriptionMany physical phenomena exhibit discontinuities in their spatial derivatives—such as folds in creased materials or interfaces in heterogeneous solids—making their accurate representation essential for high-fidelity simulation. Traditional approaches address such discontinuities by aligning mesh discretizations with the interface, but this tight coupling between geometry and simulation limits generalization: changes in discontinuity geometry require remeshing, which alters the system’s discrete operators and prevents consistent reuse of reduced-order basis. Since these basis are typically derived from mesh-dependent operators, applying reduced-order modeling across varying geometries remains a fundamental challenge.Neural representations offer an alternative by encoding basis functions as continuous neural fields, enabling generalization across shape variations. However, their inherent continuity makes it difficult to represent functions with discontinuous gradients. While recent work has explored discontinuities in function values, modeling continuous functions with discontinuous derivatives has remained largely unexplored.We introduce a neural field construction capable of capturing gradient discontinuities while maintaining continuity in the function itself. Our approach augments input coordinates with a non-trainable, smoothly clamped distance function within a lifting framework, allowing the gradient discontinuity to be encoded explicitly. We show that this construction yields higher-quality basis functions compared to traditional neural fields and supports reduced-order simulation across families of shapes with heterogeneous materials and creases—capabilities not demonstrated by prior work. Furthermore, our method can be combined with previous techniques that model function-value discontinuities via lifting, enabling the simulation of examples with simultaneous cuts and creases.
Event Type
Technical Papers
TimeMonday, 15 December 20252:50pm - 3:00pm HKT
LocationMeeting Room S221, Level 2