Neural network approximation of optimal controls for stochastic reaction-diffusion equations.
Chaos
; 33(9)2023 Sep 01.
Article
em En
| MEDLINE
| ID: mdl-37703472
ABSTRACT
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the feedback function using finitely based approximations. Using structural assumptions on the finitely based approximations, rates for the approximation error of the cost can be obtained. Our algorithm significantly reduces the computational complexity of finding controls with asymptotically optimal cost. Numerical experiments using artificial neural networks as well as radial basis function networks illustrate the performance of our algorithm. Our approach can also be applied to stochastic control problems for high dimensional stochastic differential equations and more general stochastic partial differential equations.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Chaos
Assunto da revista:
CIENCIA
Ano de publicação:
2023
Tipo de documento:
Article
País de afiliação:
Alemanha