Idioma:

Learning nonparametric ordinary differential equations from noisy data

Lahouel, Kamel ; Wells, Michael ; Rielly, Victor ; Lew, Ethan ; Lovitz, David ; Jedynak, Bruno M.

Journal of computational physics, 2024-06, Vol.507, Article 112971 [Periódico revisado por pares]

Texto completo disponível

Citações Citado por

Título:
Learning nonparametric ordinary differential equations from noisy data
Autor: Lahouel, Kamel ; Wells, Michael ; Rielly, Victor ; Lew, Ethan ; Lovitz, David ; Jedynak, Bruno M.
Assuntos: Amyloid accumulation ; Kernel methods ; Nonlinear dynamical systems ; Penalty method ; System identification
É parte de: Journal of computational physics, 2024-06, Vol.507, Article 112971
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: Learning nonparametric systems of Ordinary Differential Equations (ODEs) x˙=f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator. Experiments are provided for the FitzHugh–Nagumo oscillator, the Lorenz system, and for predicting the Amyloid level in the cortex of aging subjects. In all cases, we show competitive results compared with the state-of-the-art.
Editor: United States: Elsevier Inc
Idioma: Inglês

Links

Voltar para lista de resultados