2 citations · 3 across the 11 of their papers we have counts for
12 papers
Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Jaemin Oh, Youngkyu Lee, Jerome Darbon +1
Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction…
NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
Francesc Levrero-Florencio, Youngkyu Lee, Jay Pathak +1
The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, th…
Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions
Shanqing Liu, Paula Chen, Youngkyu Lee +1
We develop a new Hamiton-Jacobi (HJ) and differential game approach for exploring the Pareto front of (constrained) multi-objective optimization (MOO) problems. Given a preference…
Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEs
Youngkyu Lee, Francesc Levrero Florencio, Jay Pathak +1
The convergence behavior of classical iterative solvers for parametric partial differential equations (PDEs) is often highly sensitive to the domain and specific discretization of…
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…
XRePIT: A deep learning-computational fluid dynamics hybrid framework implemented in OpenFOAM for fast, robust, and scalable unsteady simulations
Shilaj Baral, Youngkyu Lee, Sangam Khanal +1
Autoregressive neural surrogates offer computational acceleration for fluid dynamics but inherently suffer from error accumulation and non-physical drift during long-term rollouts.…
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…
Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after ap…
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…
Automatic discovery of optimal meta-solvers via multi-objective optimization
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi…
Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
Youngkyu Lee, Alena Kopaničáková, George Em Karniadakis
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed pre…
Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
Youngkyu Lee, Shanqing Liu, Zongren Zou +5
Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applicati…