Deep Learning for Solving High Dimensional Hamilton Jacobi B

<!doctype html> <html lang="pt"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <title>Deep Learning for Solving High Dimensional Hamilton Jacobi B | 108555</title> <meta name="keywords" content="Reuther Benjamin*, "/> <meta name="description" content="Traditional methods for solving HJB equations face challenges, especially when dealing with high-dimensional spaces. However, deep learning offers a pr..108555"/> <meta name="citation_publisher" content="Hilaris SRL" /> <meta name="citation_journal_title" content="Revista de Matemática Aplicada e Computacional"> <meta name="citation_title" content="Deep Learning for Solving High Dimensional Hamilton Jacobi Bellman Equations"> <meta name="citation_author" content="Reuther Benjamin" /> <meta name="citation_year" content=""> <meta name="citation_volume" content="13"> <meta name="citation_issue" content="3"> <meta name="citation_abstract" content="Traditional methods for solving HJB equations face challenges, especially when dealing with high-dimensional spaces. However, deep learning offers a promising approach to overcome these limitations. The HJB equation, named after William Rowan Hamilton, Carl Gustav Jacob Jacobi, and Richard Bellman, provides a necessary condition for optimality. It is a partial differential equation (PDE) that characterizes the value function of the control problem, essentially describing the evolution of the optimal cost as a function of time and state. Solving the HJB equation is crucial for determining the optimal policy or strategy in various applications. However, as the dimensionality of the problem increases, traditional numerical methods like finite difference methods or finite element methods become computationally infeasible due to the curse of dimensionality. 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However, deep learning offers a promising approach to overcome these limitations. The HJB equation, named after William Rowan Hamilton, Carl Gustav Jacob Jacobi, and Richard Bellman, provides a necessary condition for optimality. It is a partial differential equation (PDE) that characterizes the value function of the control problem, essentially describing the evolution of the optimal cost as a function of time and state. Solving the HJB equation is crucial for determining the optimal policy or strategy in various applications. However, as the dimensionality of the problem increases, traditional numerical methods like finite difference methods or finite element methods become computationally infeasible due to the curse of dimensionality. This is where deep learning techniques, particularly neural networks, come into play.</p></p> <div class="alert alert-info text-left"><b>Isen莽茫o de responsabilidade:</b> Este resumo foi traduzido usando ferramentas de intelig锚ncia artificial e ainda n茫o foi revisado ou verificado</div> <div class="row mt-3"> <div class="col-12 col-sm-auto"> <p class="lead">Compartilhe este artigo</p> </div> <div class="col-12 col-sm-auto"> <div class="nav social-icons"> <a title="Clique aqui" target="_blank" href="https://www.facebook.com/sharer.php?u=https://portuguese.hilarispublisher.com/abstract/deep-learning-for-solving-high-dimensional-hamilton-jacobi-bellman-equations-108555.html" class="nav-link bg-facebook fab fa-facebook-f text-white"> </a> <a title="Clique aqui" target="_blank" href="https://twitter.com/share?url=https://portuguese.hilarispublisher.com/abstract/deep-learning-for-solving-high-dimensional-hamilton-jacobi-bellman-equations-108555.html" class="nav-link bg-twitter fab fa-twitter 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