Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional contact remains the "elephant in the room." Current frameworks often avoid contact singularities via non-Markovian position approximations or heuristic gradients. This lack of mathematical consistency distorts gradients, causing optimization stagnation or failure in complex frictional contact and large-deformation scenarios. We introduce our unified fully GPU-accelerated differentiable simulator, which establishes a rigorous theoretical paradigm through: Long-Horizon Consistency: enforcing strict Markovian dynamics on a coupled position-velocity manifold to prevent gradient collapse; Unified Contact Stability: employing a mass-aligned preconditioner and soft Fischer--Burmeister operator for smooth frictional optimization; Robust Material Identification: resolving FEM singularities via a derived "Within-block Commutation" condition. Our experiments demonstrate our solver efficacy in bridging the Sim-to-Real gap, delivering precise, low-noise gradients in contact-rich tasks like dexterous manipulation and cloth folding. By mitigating the gradient instability issues common in conventional approaches, our framework significantly enhances the fidelity of physical system identification and control.

翻译：可微仿真为计算机图形学与机器人学中求解具有挑战性的逆问题（如物理系统辨识与逆动力学控制）奠定了数学基础。然而，摩擦接触的严谨性始终是"房间里的大象"。现有框架常通过非马尔可夫位置近似或启发式梯度来回避接触奇异性。这种数学一致性的缺失会导致梯度失真，进而在复杂摩擦接触与大变形场景中引发优化停滞或失效。我们提出统一的完全GPU加速可微仿真器，通过以下途径建立严谨的理论范式：长程一致性——在耦合位置-速度流形上强制执行严格马尔可夫动力学以防止梯度崩溃；统一接触稳定性——采用质量对齐预条件子与软Fischer-Burmeister算子实现平滑摩擦优化；鲁棒材料辨识——通过推导出的"块内交换"条件消除有限元奇异性。实验表明，我们的求解器能有效弥合仿真与现实差距，在灵巧操作与布料折叠等高接触依赖性任务中提供精确低噪梯度。通过缓解传统方法中常见的梯度不稳定性问题，本框架显著提升了物理系统辨识与控制的保真度。