DiffXPBD：柔性约束动力学的可微基于位置的模拟
DiffXPBD : Differentiable Position-Based Simulation of Compliant Constraint Dynamics
AI总结：
提出DiffXPBD，一种用于柔性约束动力学可微基于位置模拟的高效解析方法，通过自动微分计算参数梯度，支持高分辨率几何和碰撞，在超过2600万自由度网格上实现高效优化。
摘要：
我们提出了DiffXPBD，一种用于柔性约束动力学（XPBD）可微基于位置模拟的新型高效解析公式。该方法利用高性能模拟模型，可同时计算众多参数相对于目标函数的梯度。该方法效率高，从而能够实现高分辨率几何和自由度（DoFs）的可微模拟。碰撞被自然地包含在框架中。我们的可微模型允许用户轻松添加额外的优化变量。每个控制变量梯度仅需计算少量偏导数，这些偏导数可使用自动微分代码计算。我们通过弹性材料参数估计、初始值优化、仅通过观察服装来优化底层身体形状和姿态，以及优化时变外力序列以匹配特定时间的稀疏关键帧形状等示例，证明了该方法的有效性。我们的方法展现出极高的效率，并在涉及超过2600万自由度的高分辨率网格上进行了优化演示。使现有求解器可微仅需少量修改，且该模型兼容现代CPU和GPU多核硬件。
英文摘要：
We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware.
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