Structure-Preserving Machine Learning and Data-Driven Structure Discovery

Explore the intersection of machine learning and structural preservation in scientific computing through this 40-minute conference talk from IPAM's workshop on scientific machine learning. Discover how incorporating intrinsic structures into machine learning models can significantly enhance performance across applications including computer vision and computational modeling of physical and engineering systems. Learn about efficient methods for embedding specific structures into machine learning frameworks and understand the rigorous quantification of resulting performance improvements. Examine cutting-edge techniques for discovering fundamental structures such as conservation laws, integrability, and Lax pairs directly from observational physical data. Gain insights into the bidirectional relationship between structure and data, understanding both how known structures can inform better models and how unknown structures can be uncovered from empirical observations. The presentation addresses the growing interest in data-driven structure discovery while providing theoretical foundations for structure-preserving approaches in scientific machine learning applications.