CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations

arXiv:2402.14646v1 Announce Type: new
Abstract: This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new initial conditions. The adaptation can be either purely data-driven or via an equation-driven variational approach that provides Galerkin-optimal approximations. Because CoLoRA approximates solution fields locally in time, the rank of the …

abstract adapt arxiv continuous cs.lg cs.na differential differential equation equation evolution fields low low-rank adaptation math.na modeling networks neural networks physics solution stat.ml train type work