Cover Image

An analysis of the derivative-free loss method for solving PDEs

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Han, Jihun, Lee, Yoonsang
Format:	Preprint
Published:	2023
Subjects:	Numerical Analysis Machine Learning 65N15, 65N75, 65C05, 60G46
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

A probabilistic approach to spectral analysis of Cauchy-type inverse problems: Convergence and stability analysis
by: Cîmpean, Iulian, et al.
Published: (2025)

Numerical spectral analysis of Cauchy-type inverse problems: A probabilistic approach
by: Cîmpean, Iulian, et al.
Published: (2024)

A derivative-free localized stochastic method for very high-dimensional semilinear parabolic PDEs
by: Fang, Shuixin, et al.
Published: (2025)

Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates
by: Feng, Jiaying, et al.
Published: (2025)

Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
by: Ding, Xinwen, et al.
Published: (2025)

A posteriori analysis of neural network approximations
by: Führer, Thomas, et al.
Published: (2025)

A posteriori error analysis, Pod-Deim reduced order geometrically parametrized models and unfitted FEMs
by: Karatzas, Efthymios N.
Published: (2026)

Error-rate and decision-theoretic methods of multiple testing: Which genes have high objective probabilities of differential expression?
by: Bickel, David R.
Published: (2002)

A Multilevel Monte Carlo Virtual Element Method for Uncertainty Quantification of Elliptic Partial Differential Equations
by: Antonietti, Paola F., et al.
Published: (2026)

Stochastic approach for elliptic problems in perforated domains
by: Han, Jihun, et al.
Published: (2024)

Regularization effect of noise on fully discrete approximation for stochastic reaction-diffusion equation near sharp interface limit
by: Cui, Jianbo
Published: (2023)

Structure-preserving Kernel-based methods for solving dissipative PDEs on surfaces
by: Sun, Zhengjie, et al.
Published: (2023)

Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
by: Chen, Yifan, et al.
Published: (2023)

Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
by: Bringmann, Philipp, et al.
Published: (2025)

FEALPy: A Cross-platform Intelligent Numerical Simulation Engine
by: Zheng, Yangyang, et al.
Published: (2025)

Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces
by: Reusken, Arnold, et al.
Published: (2024)

A low-cost, parameter-free, and pressure-robust enriched Galerkin method for the Stokes equations
by: Lee, Seulip, et al.
Published: (2022)

A parallel batch greedy algorithm in reduced basis methods: Convergence rates and numerical results
by: Reich, Niklas, et al.
Published: (2024)

An Adaptive Algorithm Based on Stochastic Discontinuous Galerkin for Convection Dominated Equations with Random Data
by: Çiloğlu, Pelin, et al.
Published: (2023)

Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals
by: Bespalov, Alex, et al.
Published: (2022)

Optimal $L^2$ error estimates of mass- and energy-conserved FE schemes for a nonlinear Schrödinger-type system
by: Zhang, Zhuoyue, et al.
Published: (2023)

Nonasymptotic Convergence Rate of Quasi-Monte Carlo: Applications to Linear Elliptic PDEs with Lognormal Coefficients and Importance Samplings
by: Liu, Yang, et al.
Published: (2023)

Deep BSDE Solver on Bounded Domains Part I: General Loss Rate
by: Würschmidt, Maximilian
Published: (2025)

Energy norm error estimates of a hybrid high-order method for the linear parabolic integro-differential equations on general meshes
by: Mohapatra, Achyuta Ranjan Dutta
Published: (2026)

Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
by: Sousedík, Bedřich, et al.
Published: (2022)

Goal-Oriented Adaptive Finite Element Multilevel Quasi-{M}onte {C}arlo
by: Beck, Joakim, et al.
Published: (2025)

Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions
by: Bansal, Aparna, et al.
Published: (2026)

Arbitrary order approximations at constant cost for Timoshenko beam network models
by: Hauck, Moritz, et al.
Published: (2024)

A Certified Goal-Oriented A Posteriori Defeaturing Error Estimator for Elliptic PDEs
by: Weder, Philipp, et al.
Published: (2025)

Embedded Trefftz DG method for the Helmholtz equation
by: Stocker, Paul, et al.
Published: (2026)

Adaptive boundary element methods for regularized combined field integral equations
by: Chaumont-Frelet, Théophile, et al.
Published: (2025)

Nitsche method for the Stokes-Poisson-Boltzmann equation with Navier slip boundary condition
by: Agrawal, Ayush, et al.
Published: (2026)

The coupling of mixed and primal finite element methods for the coupled body-plate problem
by: Hu, Jun, et al.
Published: (2025)

Linearized Localized Orthogonal Decomposition for Quasilinear Nonmonotone Elliptic PDE
by: Khrais, Maher, et al.
Published: (2025)

A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian
by: Barker, Mary, et al.
Published: (2022)

A High-Order Fast Direct Solver for Surface PDEs on Triangles
by: Zavalani, Gentian
Published: (2026)

Key challenges and bridges among convergence analysis techniques for polytopal methods
by: da Veiga, Lourenço Beirão, et al.
Published: (2026)

Bayesian parameter identification in impedance boundary conditions for Helmholtz problems
by: Wulbusch, Nick, et al.
Published: (2023)

Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models
by: Ankur, et al.
Published: (2024)

An inverse random diffraction grating problem for the Helmholtz equation
by: Sun, Zhiqi, et al.
Published: (2025)