Diffeomorphic Interpolation for Persistence-Based Topological Optimization

Watch a research talk exploring innovative approaches to topological optimization through diffeomorphic interpolation techniques. Learn how to address the challenge of sparse gradients in topological optimization by transforming them into smooth vector fields with defined Lipschitz constants. Discover a novel method that combines diffeomorphic interpolation with subsampling techniques in Topological Data Analysis (TDA), enabling efficient optimization of large-scale point clouds. Understand how this approach extracts quantitative topological descriptors from structured objects and implements topological loss functions for gradient descent routines. Examine the practical applications and theoretical foundations of this work, which represents a collaboration between Mathieu Carrière, Theo Lacombe, and Marc Theveneau.