Explore a 49-minute lecture where Ching-Yao Lai discusses the development of multi-stage neural networks that can achieve machine precision in scientific applications. Learn how these networks divide training into stages, with each new network optimized to fit residues from previous stages, allowing prediction errors to approach double-floating point precision within finite iterations. Discover how this breakthrough addresses longstanding accuracy limitations in neural network training and tackles spectral bias in multiscale problems, including applications in finding blow-up solutions in fluid dynamics. This presentation was part of the Simons Collaboration on Wave Turbulence Annual Meeting 2024.