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.

翻译：软体可微仿真为系统辨识、轨迹优化及Real2Sim迁移奠定基础。然而，现有可微投影动力学（DiffPD）方法在处理真实世界中常见场景——如具有极端刚度对比的异质材料、大变形下的超弹性以及密集接触交互——时面临挑战。我们提出DiffPhD，一种面向异质材料的统一GPU加速可微投影动力学框架，可同步应对上述交织难题。核心洞察在于精心整合以下技术：(i) 刚度感知投影权重，将异质性嵌入全局系统；(ii) 置信域特征值滤波（提升至反向传播阶段）以实现稳定的超弹性梯度，以及采用双门控收敛的II型安德森加速方案，在刚度对比极大的条件下稳定正向迭代过程；(iii) 统一GPU流水线，在前向、反向及接触计算中复用单一稀疏矩阵因子，并将刚度放大瑞利阻尼融入同一因子，实现零额外代价的异质性感知耗散。DiffPhD在保持严格梯度精度的同时，在异质、超弹性、密集接触基准测试中相较先前可微求解器实现高达一个数量级的加速。尤为关键的是，此加速并未以牺牲稳定性为代价：DiffPhD在刚度对比高达100倍时仍保持收敛，而此前PD求解器在此区间性能显著退化。这解锁了此前受限于求解器脆弱性或单次迭代代价的端到端梯度优化——壳-关节复合生物、手持刚性武器的柔体角色、软体夹爪操作——均可在单次前向-反向传播中完成。