DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems

Journal Article · · Computer Methods in Applied Mechanics and Engineering

Not Available

Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
SC0019303
OSTI ID:
2216983
Journal Information:
Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 419; ISSN 0045-7825
Publisher:
ElsevierCopyright Statement
Country of Publication:
Netherlands
Language:
English

References (76)

Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network journal March 2023
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems, Part II: Stochastic Newton MCMC with Application to Ice Sheet Flow Inverse Problems journal January 2014
Reduced Operator Inference for Nonlinear Partial Differential Equations journal July 2022
High-dimensional nonlinear Bayesian inference of poroelastic fields from pressure data journal February 2023
Free Damage Propagation with Memory journal March 2018
Learning high-dimensional parametric maps via reduced basis adaptive residual networks journal December 2022
Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm journal July 2023
A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid journal August 2021
Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations journal January 2017
Estimation of Modeling Error in Computational Mechanics journal November 2002
The Newton-Kantorovich Theorem journal June 1968
Simulating Grain Shape Effects and Damage in Granular Media Using PeriDEM journal January 2023
Coupling of mechanical deformation and electromagnetic fields in biological cells journal May 2022
Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation journal December 2022
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems journal April 2022
Operator inference for non-intrusive model reduction with quadratic manifolds journal January 2023
Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth journal October 2023
Kinetic relations and local energy balance for LEFM from a nonlocal peridynamic model journal September 2020
Peridynamics-based discrete element method (PeriDEM) model of granular systems involving breakage of arbitrarily shaped particles journal June 2021
Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems journal August 2023
Numerical Analysis of Nonlocal Fracture Models in Hölder Space journal January 2018
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems journal April 2009
A feed-back approach to error control in finite element methods: application to linear elasticity journal April 1997
Mechanics of hard-magnetic soft materials journal March 2019
General Diffuse-Interface Theories and an Approach to Predictive Tumor Growth Modeling journal March 2010
Optimal design of acoustic metamaterial cloaks under uncertainty journal April 2021
A Globally Convergent Modified Newton Method for the Direct Minimization of the Ohta--Kawasaki Energy with Application to the Directed Self-Assembly of Diblock Copolymers journal January 2022
Bond-level deformation gradients and energy averaging in peridynamics journal January 2018
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture journal April 2020
On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors journal July 1999
Topology Design of Structures Subjected to Periodic Loading journal June 2002
Selection, calibration, and validation of models of tumor growth journal October 2016
On the Newton–Kantorovich Theorem journal July 2012
Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition
  • van der Zee, Kristoffer G.; Tinsley Oden, J.; Prudhomme, Serge
  • Numerical Methods for Partial Differential Equations, Vol. 27, Issue 1 https://doi.org/10.1002/num.20638
journal October 2010
Design of functionally graded composite structures in the presence of stress constraints journal May 2002
Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data journal December 2019
Model Reduction And Neural Networks For Parametric PDEs journal July 2021
Approximations of continuous functionals by neural networks with application to dynamic systems journal January 1993
Learning physics-based models from data: perspectives from inverse problems and model reduction journal May 2021
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems journal July 1995
Unified form language: A domain-specific language for weak formulations of partial differential equations journal February 2014
Optimization of vibrating structures to reduce radiated noise journal November 2011
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets journal October 2021
Direct lagrange multiplier updates in topology optimization revisited journal October 2020
A digital-twin and machine-learning framework for precise heat and energy management of data-centers journal March 2022
Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data journal December 2017
Learning Optimal Aerodynamic Designs through Multi-Fidelity Reduced-Dimensional Neural Networks conference January 2023
hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems journal October 2018
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators journal March 2021
Modeling and simulation of vascular tumors embedded in evolving capillary networks journal October 2021
POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition journal January 2022
Simulation-based optimal Bayesian experimental design for nonlinear systems journal January 2013
Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs journal January 2022
An efficient reduced-order modeling approach for non-linear parametrized partial differential equations journal October 2008
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities journal September 2009
Designing soft pyroelectric and electrocaloric materials using electrets journal January 2019
A level set-based topology optimization approach for thermally radiating structures journal May 2022
Complex Fracture Nucleation and Evolution with Nonlocal Elastodynamics journal April 2019
Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty journal May 2019
A monolithic finite-element formulation for magnetohydrodynamics journal July 2018
Non-intrusive reduced order modeling of nonlinear problems using neural networks journal June 2018
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality journal January 2002
Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth journal October 2012
Optimal design of material properties and material distribution for multiple loading conditions journal April 1995
Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network journal October 2021
Adaptive multiscale predictive modelling journal May 2018
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations journal February 2019
U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow journal May 2022
Kinetics of phase transformations in the peridynamic formulation of continuum mechanics journal September 2006
Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models journal June 2020
An introduction to structural health monitoring
  • Farrar, Charles R.; Worden, Keith
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 365, Issue 1851 https://doi.org/10.1098/rsta.2006.1928
journal December 2006
Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models journal July 2020
Goal-oriented error estimation and adaptivity for the finite element method journal March 2001
Theory of hard magnetic soft materials to create magnetoelectricity journal February 2023
Toward Predictive Multiscale Modeling of Vascular Tumor Growth: Computational and Experimental Oncology for Tumor Prediction journal June 2015
A new approach to variable-topology shape design using a constraint on perimeter journal February 1996

Similar Records

Related Subjects