A tutorial on the adjoint method for inverse problems

DOI10.1016/j.cma.2021.113810zbMath1506.74494OpenAlexW3154995791MaRDI QIDQ2236941

Dan Givoli

Publication date: 26 October 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2021.113810

zbMATH Keywords

identificationinverse problemgradientreviewadjoint methodtutorial

Mathematics Subject Classification ID

Inverse problems in equilibrium solid mechanics (74G75) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical and other methods in solid mechanics (74S99) Inverse problems in dynamical solid mechanics (74H75)

Related Items (14)

Shape identification of scatterers using a time-dependent adjoint method ⋮ Bayesian inversion with α-stable priors ⋮ A domain decomposition strategy for mCRE-based model updating in dynamics ⋮ Full-waveform inversion using level set and cut elements for sharp-interface problems ⋮ On the use of neural networks for full waveform inversion ⋮ Finite element interpolated neural networks for solving forward and inverse problems ⋮ HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions ⋮ Single‐field identification of inclusions and cavities in an elastic medium ⋮ Adjoint-based optimal control of contractile elastic bodies. Application to limbless locomotion on frictional substrates ⋮ Immersed boundary parametrizations for full waveform inversion ⋮ A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems ⋮ Isogeometric multi-resolution full waveform inversion based on the finite cell method ⋮ Comparison of the FWI-Adjoint and Time Reversal Methods for the Identification of Elastic Scatterers ⋮ A physically-informed deep-learning model using time-reversal for locating a source from sparse and highly noisy sensors data

Uses Software

• revolve
• hIPPYlib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inverse problems. Basics, theory and applications in geophysics
• Aerodynamic design via control theory
• An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems
• Numerical Methods for Inverse Problems
• Adjoint Methods for Shape Optimization
• The Art of Differentiating Computer Programs
• A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion
• A fully equivalent global pressure formulation for three-phases compressible flows
• Algorithm 799: revolve
• On optimum design in fluid mechanics
• Discrete Inverse Problems
• Optical tomography as a PDE-constrained optimization problem

This page was built for publication: A tutorial on the adjoint method for inverse problems