Cover Image

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Lee, Youngkyu, Liu, Shanqing, Darbon, Jerome, Karniadakis, George Em
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Automatic discovery of optimal meta-solvers via multi-objective optimization
by: Lee, Youngkyu, et al.
Published: (2024)

A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
by: Lee, Youngkyu, et al.
Published: (2025)

NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
by: Levrero-Florencio, Francesc, et al.
Published: (2026)

Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEs
by: Lee, Youngkyu, et al.
Published: (2025)

Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Method
by: Kopaničáková, Alena, et al.
Published: (2025)

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
by: Toscano, Juan Diego, et al.
Published: (2025)

Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
by: Lee, Youngkyu, et al.
Published: (2024)

DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations
by: Kopaničáková, Alena, et al.
Published: (2024)

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks
by: Gao, Zhiwei, et al.
Published: (2025)

Spectral Audit of In-Context Operator Networks
by: Gao, Zhiwei, et al.
Published: (2026)

Analysis of biologically plausible neuron models for regression with spiking neural networks
by: De Florio, Mario, et al.
Published: (2023)

UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning
by: Qiao, Hanli, et al.
Published: (2026)

From LIF to QIF: Toward Differentiable Spiking Neurons for Scientific Machine Learning
by: Wan, Ruyin, et al.
Published: (2025)

Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
by: Hu, Zheyuan, et al.
Published: (2024)

A time-dependent symplectic network for non-convex path planning problems with linear and nonlinear dynamics
by: Zhang, Zhen, et al.
Published: (2024)

Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
by: Chen, Paula, et al.
Published: (2023)

Tensor neural networks for high-dimensional Fokker-Planck equations
by: Wang, Taorui, et al.
Published: (2024)

Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs
by: Brunner, Maximilian, et al.
Published: (2024)

KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
by: Toscano, Juan Diego, et al.
Published: (2024)

Randomized Forward Mode Gradient for Spiking Neural Networks in Scientific Machine Learning
by: Wan, Ruyin, et al.
Published: (2024)

Automatic selection of the best neural architecture for time series forecasting
by: Cao, Qianying, et al.
Published: (2025)

Parareal Neural Networks Emulating a Parallel-in-time Algorithm
by: Lee, Chang-Ock, et al.
Published: (2021)

A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems
by: Egger, Herbert, et al.
Published: (2025)

Safe cross-entropy-based importance sampling for rare event simulations
by: Gao, Zhiwei, et al.
Published: (2025)

ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
by: Toscano, Juan Diego, et al.
Published: (2025)

Multilevel Picard algorithm for general semilinear parabolic PDEs with gradient-dependent nonlinearities
by: Neufeld, Ariel, et al.
Published: (2023)

PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods
by: Zhang, Zhen, et al.
Published: (2026)

HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models
by: Meng, Tingwei, et al.
Published: (2024)

Unconditional full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs
by: Miraçi, Ani, et al.
Published: (2024)

Nonlinear parametrization solver for fractional Burgers equations
by: Qin, Haojun, et al.
Published: (2026)

Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions
by: Liu, Shanqing, et al.
Published: (2026)

Fast high-order spectral solvers for PDEs on triangulated surfaces with applications to deforming surfaces
by: Zavalani, Gentian
Published: (2025)

Proposal-Guided Greedy Surrogate Refinement for PDE-Driven High-Dimensional Rare-Event Estimation
by: Gao, Zhiwei, et al.
Published: (2026)

Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers
by: Zhang, Enrui, et al.
Published: (2022)

Global convergence of iterative solvers for problems of nonlinear magnetostatics
by: Egger, Herbert, et al.
Published: (2024)

$hp$-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
by: Innerberger, Michael, et al.
Published: (2022)

Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
by: Lee, Youngkyu, et al.
Published: (2024)

Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks
by: Hu, Zheyuan, et al.
Published: (2023)

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
by: Hu, Zheyuan, et al.
Published: (2024)

Adversarial Physics-Informed Machine Learning for Robust Optimal Safe Predefined-Time Stabilization: A Game-Theoretic Approach
by: Kokolakis, Nick-Marios T., et al.
Published: (2025)