Guaranteed Approximation Bounds for Mixed-Precision Neural Operators

arXiv:2307.15034v3 Announce Type: replace
Abstract: Neural operators, such as Fourier Neural Operators (FNO), form a principled approach for learning solution operators for PDEs and other mappings between function spaces. However, many real-world problems require high-resolution training data, and the training time and limited GPU memory pose big barriers. One solution is to train neural operators in mixed precision to reduce the memory requirement and increase training speed. However, existing mixed-precision training techniques are designed for standard neural networks, and we …

abstract approximation arxiv big cs.lg cs.na data form fourier function gpu however math.na memory mixed mixed-precision operators precision real-world problems resolution solution spaces train training training data type world