YASPS: A Symbolic Framework for Extensible, High-Performance IPC Simulation

2026-05-21

AI Summary

Existing high-performance implicit contact (IPC) simulation systems struggle to flexibly accommodate novel geometries or parametric formulations due to their reliance on fixed energy models and specialized kernels. This work proposes YASPS, a novel framework that, for the first time, elevates JOIN and UNION to first-class relational operators within a symbolic intermediate representation, enabling unified modeling of dependency and alternative parametric relationships. The approach supports automatic differentiation and efficient second-order optimization, and leverages JIT compilation to automatically generate sparse structures and optimized CUDA kernels. Experiments demonstrate that YASPS enables rapid extension to diverse IPC scenarios with minimal backend modifications, achieving nearly a 10× speedup in conjugate gradient iterations and delivering overall performance comparable to hand-tuned, specialized implementations.

Abstract

Incremental Potential Contact (IPC) enables robust, contact-rich simulation by casting elasticity and contact as a single energy minimization problem, but high-performance IPC pipelines are typically built from specialized kernels and assembly logic tied to fixed energies, primitive types, and parameterizations, making extensions costly and combinatorial. We present YASPS, a GPU-oriented framework that removes this extensibility bottleneck by making structure explicit in a differentiable intermediate representation. YASPS introduces two first-class relational operators: JOIN, which composes dependent quantities across user-declared relations (e.g., element-to-vertex connectivity), and UNION, which represents alternative parameterizations within a relation (e.g., mixing free vertices with affine-body or other parameterizations without fragmenting the program). Because JOIN and UNION are part of the symbolic program, YASPS differentiates through them using dedicated rules and an efficient second-order procedure that reuses intermediate Jacobians and reduces Hessian-projection cost. From the same relational description, YASPS derives the global gradient/Hessian sparsity and block layout, enabling structure-aware block-sparse storage and compression, and JIT-compiles CUDA kernels for evaluation, derivatives, assembly, and solving. Across IPC-style examples, including layered cloth-on-bunny, mixed rigid/deformable bunnies, and a caged deformation model, YASPS supports rapid front-end extensions with minimal back-end changes while achieving competitive end-to-end performance; its Hessian compression yields near 10x faster CG iterations in our benchmarks.

Problem

• Incremental Potential Contact
• extensibility
• high-performance simulation
• symbolic framework
• GPU-oriented

Innovation

• symbolic simulation
• relational operators
• differentiable programming
• block-sparse Hessian
• GPU JIT compilation