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An energy-based dee...
An energy-based deep splitting method for the nonlinear filtering problem
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- Bågmark, Kasper, 1995 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Andersson, Adam, 1979 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Larsson, Stig, 1952 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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(creator_code:org_t)
- 2023-03-20
- 2023
- Engelska.
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Ingår i: Partial Differential Equations and Applications. - : Springer Science and Business Media LLC. - 2662-2963 .- 2662-2971. ; 4:2
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Abstract
Ämnesord
Stäng
- The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on four examples, two linear in one and twenty dimensions and two nonlinear in one dimension. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Annan elektroteknik och elektronik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Other Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- stochastic partial differential equation
- energy-based method
- splitting scheme
- deep learning
- Zakai equation
- Filtering problem
- Deep learning
- Energy-based method
- Filtering problem
- Splitting scheme
- Stochastic partial differential equation
- Zakai equation
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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