Anjana Deva Prasad

Minsu Cho, Aditya Balu, Ameya Joshi et al.

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable "layer" in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis.

Anjana Deva Prasad, Aditya Balu, Harshil Shah et al.

Boundary representations (B-reps) using Non-Uniform Rational B-splines (NURBS) are the de facto standard used in CAD, but their utility in deep learning-based approaches is not well researched. We propose a differentiable NURBS module to integrate NURBS representations of CAD models with deep learning methods. We mathematically define the derivatives of the NURBS curves or surfaces with respect to the input parameters (control points, weights, and the knot vector). These derivatives are used to define an approximate Jacobian used for performing the "backward" evaluation to train the deep learning models. We have implemented our NURBS module using GPU-accelerated algorithms and integrated it with PyTorch, a popular deep learning framework. We demonstrate the efficacy of our NURBS module in performing CAD operations such as curve or surface fitting and surface offsetting. Further, we show its utility in deep learning for unsupervised point cloud reconstruction and enforce analysis constraints. These examples show that our module performs better for certain deep learning frameworks and can be directly integrated with any deep-learning framework requiring NURBS.