3 papers
math.NA2025
A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We propose a novel neural preconditioned Newton (NP-Newton) method for solving parametric nonlinear systems of equations. To overcome the stagnation or instability of Newton iterat…
math.NA2025
Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Method
Alena Kopaničáková, Youngkyu Lee, George Em Karniadakis
We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equation…
physics.flu-dyn2025
Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling
Sunwoong Yang, Youngkyu Lee, Namwoo Kang
This study presents an enhanced multi-fidelity Deep Operator Network (DeepONet) framework for efficient spatio-temporal flow field prediction when high-fidelity data is scarce. Key…