7 papers · 1 filter
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…
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…
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…
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…