Please note: This PhD seminar will take place online.
Xiaochun Tong, PhD candidate
David R. Cheriton School of Computer Science
Supervisor: Professor Toshiya Hachisuka
Automatic differentiation (AD) is essential to gradient based optimizations. Existing AD framework primarily targets large dense computation graphs while mesh-based computation is dominated with sparse gradients and Hessian.
In this work, the authors present a GPU-based system for automatic differentiation of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Their system evaluates derivatives using per-element forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs, intermediate buffers, and device-host synchronization, the approach minimizes memory traffic and enables efficient differentiation under both static and dynamically changing sparsity. The programming model lets users express energy terms over mesh neighborhoods, while the system automatically manages parallel execution, derivative propagation, sparse assembly, and matrix-free operations such as Hessian-vector products. The system supports both scalar- and vector-valued objectives, dynamic interaction-driven sparsity updates, and seamless integration with external GPU sparse linear solvers.
The authors evaluate the system on applications including elastic and cloth simulation, surface parameterization, mesh smoothing, frame field design, ARAP deformation, and spherical manifold optimization. Across these tasks, the authors claimed that the system consistently outperforms state-of-the-art differentiation frameworks, including PyTorch, JAX, Warp, Dr.JIT, EnzymeAD, and Thallo. The authors demonstrate speedups across a range of solver types, from Newton and Gauss-Newton for nonlinear least squares to L-BFGS and gradient descent, and across different derivative usage modes, including Hessian-vector products as well as full sparse Hessian and Jacobian construction.
The system is available as open source at https://github.com/owensgroup/RXMesh.