Warp-Geo: Differentiable Geometry Representation for Dynamic-Boundary Simulation and Shape Optimization

Abstract Modern inverse problems and adaptive simulations require efficient and differentiable representations of complex geometries that can be updated frequently for gradient-based optimization. Existing methods cannot simultaneously achieve both. We present Warp-Geo, a differentiable GPU-accelerated framework for reconstructing signed distance fields and evaluating surface normals from point clouds of complex 3D geometries. Warp-Geo combines uniform grids for GPU parallelism with implicit differentiation through the Poisson solve, enabling frequent geometry recomputation while maintaining full differentiability. We demonstrate Warp-Geo on forward SDF reconstruction, dynamic fluid--structure interaction with moving boundaries, and inverse shape optimization via automatic differentiation with gradient validation. GPU scalability analysis confirms practical feasibility for frequent geometry updates. The framework, implemented in Warp and JAX, enables seamless integration with differentiable physics solvers for end-to-end shape optimization.