THB-Diff: a GPU-accelerated differentiable programming framework for THB-splines
THB-Diff: a GPU-accelerated differentiable programming framework for THB-splines
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DOI：
10.1007/s00366-023-01929-1
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发表时间：
2023-12
影响因子：
8.7
通讯作者：
A. Moola;Aditya Balu;A. Krishnamurthy;Aishwarya Pawar
中科院分区：
文献类型：
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作者：
A. Moola;Aditya Balu;A. Krishnamurthy;Aishwarya Pawar
我们已经开发了一个截断层次B样条（THB样条）的可微编程框架，该框架可用于几何建模中的几个应用，例如表面拟合和可变形图像配准，并且可以轻松地与几何深度学习框架集成。可微分编程是一种新的范式，它使算法能够通过自动微分来微分，即，使用自动微分来计算其输出相对于其输入或参数的导数。可微编程已广泛用于机器学习中，以获得优化算法（如随机梯度下降（SGD））所需的梯度。虽然将可微编程与传统函数结合起来很简单，但当函数很复杂时，如样条函数，这是一个挑战。在这项工作中，我们将可微编程范式扩展到THB样条。THB样条通过利用B样条的分层张量结构，提供了一种有效的方法来进行复杂的表面拟合，从而实现局部自适应细化。然而，这种方法带来了挑战，如较大的计算开销和非平凡的实现自动微分和并行评估算法。我们在THB样条的可微编程所需的向前和向后评估中使用自定义内核函数进行GPU加速。我们的方法不仅提高了计算效率，但也显着提高了速度的表面评价相比，以前的方法。我们的可微THB样条框架有助于更快，更准确的表面建模与局部细化，在CAD和等几何分析的几个应用程序。
We have developed a differentiable programming framework for truncated hierarchical B-splines (THB-splines), which can be used for several applications in geometry modeling, such as surface fitting and deformable image registration, and can be easily integrated with geometric deep learning frameworks. Differentiable programming is a novel paradigm that enables an algorithm to be differentiated via automatic differentiation, i.e., using automatic differentiation to compute the derivatives of its outputs with respect to its inputs or parameters. Differentiable programming has been used extensively in machine learning for obtaining gradients required in optimization algorithms such as stochastic gradient descent (SGD). While incorporating differentiable programming with traditional functions is straightforward, it is challenging when the functions are complex, such as splines. In this work, we extend the differentiable programming paradigm to THB-splines. THB-splines offer an efficient approach for complex surface fitting by utilizing a hierarchical tensor structure of B-splines, enabling local adaptive refinement. However, this approach brings challenges, such as a larger computational overhead and the non-trivial implementation of automatic differentiation and parallel evaluation algorithms. We use custom kernel functions for GPU acceleration in forward and backward evaluation that are necessary for differentiable programming of THB-splines. Our approach not only improves computational efficiency but also significantly enhances the speed of surface evaluation compared to previous methods. Our differentiable THB-splines framework facilitates faster and more accurate surface modeling with local refinement, with several applications in CAD and isogeometric analysis.