DiffPhD: A Unified Differentiable Solver for Projective Heterogeneous Materials in Elastodynamics with Contact-Rich GPU-Acceleration

2026-05-14

AI Summary

Existing differentiable simulation methods struggle to efficiently handle heterogeneous materials with vastly differing stiffnesses, large-deformation hyperelasticity, and complex contact interactions. This work proposes DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework that jointly solves forward dynamics, backpropagation, and contact constraints within a single sparse linear system. By incorporating stiffness-aware projection weights, trust-region eigenvalue filtering, and Type-II Anderson acceleration, DiffPhD seamlessly integrates stiffness-aware Rayleigh damping at zero additional computational cost. Notably, it is the first method to embed material heterogeneity directly into the global system matrix, significantly enhancing both numerical stability and computational efficiency. In multi-contact hyperelastic scenarios with stiffness ratios up to 100×, DiffPhD achieves nearly an order-of-magnitude speedup over current differentiable solvers, enabling end-to-end optimization of complex soft-body systems.

Abstract

Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with heterogeneous materials with extreme stiffness contrasts, hyperelasticity under large deformations, and contact-rich interactions, which are common scenarios in the real world. We present DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for heterogeneous materials that tackles these intertwined challenges simultaneously. Our key insight is a careful integration of: (i) stiffness-aware projective weights to embed heterogeneity into the global system; (ii) trust-region eigenvalue filtering lifted to the backward pass for stable hyperelastic gradients and a type-II Anderson Acceleration scheme with dual-gate convergence to stabilize forward iteration under large stiffness contrasts; and (iii) a unified GPU pipeline that reuses a single sparse factor across forward, backward, and contact computations, with stiffness-amplified Rayleigh damping folded into the same factor for heterogeneity-aware dissipation at zero recurring cost. DiffPhD achieves strict gradient accuracy while delivering up to an order-of-magnitude speedup over prior differentiable solvers on heterogeneous, hyperelastic, contact-rich benchmarks. Crucially, this speedup does not come at the cost of stability: DiffPhD remains convergent on stiffness contrasts up to 100x where prior PD solvers degrade. This unlocks end-to-end gradient-based optimization on regimes previously bottlenecked by either solver fragility or per-iteration cost -- shell--joint composite creatures, soft characters wielding stiff weapons, and soft-gripper robotic manipulation -- all handled within a single forward--backward pass.

Problem

• differentiable simulation
• heterogeneous materials
• contact-rich interactions
• hyperelasticity
• stiffness contrast

Innovation

• Differentiable Simulation
• Projective Dynamics
• Heterogeneous Materials
• GPU Acceleration
• Contact-Rich Interaction