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The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. The adjoint state space is chosen to simplify the physical interpretation of equation constraints. Adjoint state techniques allow the use of integration by parts, resulting in a form which explicitly contains the physically interesting quantity. An adjoint state equation is introduced, including a new unknown variable.

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rdfs:label	Adjoint state method (en)
rdfs:comment	The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. The adjoint state space is chosen to simplify the physical interpretation of equation constraints. Adjoint state techniques allow the use of integration by parts, resulting in a form which explicitly contains the physically interesting quantity. An adjoint state equation is introduced, including a new unknown variable. (en)
dcterms:subject	Numerical analysis
Wikipage page ID	23879584 (xsd:integer)
Wikipage revision ID	1118743482 (xsd:integer)
Link from a Wikipage to another Wikipage	Weak formulation Numerical method Operator (mathematics) Function (mathematics) Functional (mathematics) Gateaux derivative Geophysics Gradient Constraint (mathematics) LU decomposition Stationary point Backpropagation Adjoint equation Landweber iteration Linear programming Numerical analysis Partial differential equation Tensor contraction Tensor Chain rule Lagrange multiplier Lagrange multipliers Inner product Integration by parts Self-adjoint operator Photonics Shape optimization Neural networks Dual problem Dyadic product Adjoint matrix Numerical optimization problem Seismic imaging
Link from a Wikipage to an external page	http://cs.stanford.edu/~ambrad/adjoint_tutorial.pdf https://doi.org/10.1111/j.1365-246X.2006.02978.x https://dx.doi.org/10.1175/1520-0477(1997)078%3C2577:WIAAM%3E2.0.CO;2 https://web.archive.org/web/20150906095132/http:/ocw.mit.edu/courses/mathematics/18-325-topics-in-applied-mathematics-waves-and-imaging-fall-2012/lecture-notes/MIT18_325F12_Chapter4.pdf http://math.mit.edu/~stevenj/18.336/adjoint.pdf
sameAs	Adjoint state method Adjoint state method Adjoint state method
dbp:wikiPageUsesTemplate	dbt:Primary_sources dbt:Short_description dbt:Mathapplied-stub
has abstract	The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. The adjoint state space is chosen to simplify the physical interpretation of equation constraints. Adjoint state techniques allow the use of integration by parts, resulting in a form which explicitly contains the physically interesting quantity. An adjoint state equation is introduced, including a new unknown variable. The adjoint method formulates the gradient of a function towards its parameters in a constraint optimization form. By using the dual form of this constraint optimization problem, it can be used to calculate the gradient very fast. A nice property is that the number of computations is independent of the number of parameters for which you want the gradient.The adjoint method is derived from the dual problem and is used e.g. in the Landweber iteration method. The name adjoint state method refers to the dual form of the problem, where the adjoint matrix is used. When the initial problem consists of calculating the product and must satisfy , the dual problem can be realized as calculating the product, where must satisfy . And is called the adjoint state vector. (en)
prov:wasDerivedFrom	wikipedia-en:Adjoint_state_method?oldid=1118743482&ns=0
page length (characters) of wiki page	11275 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Adjoint_state_method
is Link from a Wikipage to another Wikipage of	List of numerical analysis topics Adjoint equation Shape optimization
is foaf:primaryTopic of	wikipedia-en:Adjoint_state_method

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