Live briefing
Everything about Inverse problem
Process of calculating the causal factors that produced a set of observations
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Inverse problemA 5-minute orientation
- Skim a recent paper: Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemsInfluential work since 2022
- Pick up a classic book: Introduction to Inverse Problems in ImagingThe most-reprinted book on the subject
- Read the landmark paper: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equationsCited 20,944 times
- Go sideways: Ridge regressionA closely related topic
- Go sideways: Eigendecomposition of a matrixA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems
The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
🆕 Influential since 2022
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations
Physics-informed neural networks for inverse problems in supersonic flows
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
📚 Books worth reading
- 📕Introduction to Inverse Problems in ImagingM. Bertero · 2017
Inverse Scattering Problems and Their Application to Non-Linear Integrable EquationsPham Loi Vu · 2019- 📕Inverse Problems and Related TopicsNakamura, Saburou Saitoh · 2000
Geophysical data analysisWilliam Menke · 1984
Inverse boundary spectral problemsAlexander Kachalov, Yaroslav Kurylev · 2001- 📕Bitangential direct and inverse problems for systems of integral and differential equationsDamir Z. Arov · 2012
Inverse Problems in Atmospheric Constituent TransportI. G. Enting · 2002
Parameter estimation and inverse problemsRichard C. Aster, Brian Borchers · 2005
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Ridge regression Ridge regression (also known as Tikhonov regularization, named for Andrey Tikhonov) is a method of estimating the coefficients of multiple-regression models…
- Eigendecomposition of a matrix In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A into a canonical form given by A=QDQ−𝟣…
- Regularization (mathematics) In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts…
- Landweber iteration The Landweber iteration or Landweber algorithm is an algorithm to solve ill-posed linear inverse problems, and it has been extended to solve non-linear…
- Linear seismic inversion Inverse modeling is a mathematical technique where the objective is to determine the physical properties of the subsurface of an earth region that has…
- Regularized least squares Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting…
- Moore–Penrose inverse In mathematics, and in particular linear algebra, the Moore–Penrose inverse A+ of a matrix A, often called the pseudoinverse, is the most widely known…
- Numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which…