Explore a data-driven approach to estimating persistence diagrams (PDs) of point clouds in this 54-minute conference talk. Delve into the practical limitations of persistent homology, including computational complexity and sensitivity to outliers. Discover RipsNet, a novel neural network architecture designed to efficiently estimate the vectorization of PDs for point clouds. Learn how RipsNet, once trained, can rapidly generate topological descriptors. Examine the proven robustness of RipsNet to input perturbations in terms of 1-Wasserstein distance, and understand how it outperforms exactly-computed PDs in noisy environments. Gain insights into overcoming challenges in topological data analysis and enhancing the practical application of persistent homology.