Abstract/Summary

In numerical weather prediction (NWP), determining states and reconstructing model parameters or the underlying structural functions of dynamical models are essential and crucial components of the modelling and simulation process. In addition, it is gaining prominence in emerging application areas. In light of this, we examine the estimate of an unknown model M or the F function that determines the rate of change of x, which represents the dynamical system model of the type x˙ = F(x) using a high-dimensional nonlinear approach based on Ansatz functions such as Polynomial or Gaussian functions. The focus of this thesis is to propose specific iterative learning methods developed for estimating a dynamical system of interest using data assimilation (DA) techniques, as opposed to the traditional approaches typically used for parameter estimation, reduced order model approximation and the current approaches of machine learning (ML) and artificial intelligence (AI) techniques in general. This is initially evaluated using two models of dynamical systems with increasing complexity: Lorenz ’63 and Lorenz ’96. Then, we examine the reconstruction strategy based on a variety of basis functions, including Polynomial and Radial Basis Functions (RBF). As generic application issues, we examine the reconstruction of the dynamics of Lorenz ’63 with implicitly applied RBF under the assumption that the L 2 metric in coefficient space corresponds to a Gaussian prior in coefficient space. In addition, we employ the Amari Neural Field model for kernel reconstruction as a simulation test case for brain neural activity. Using the Lorenz ’96 model, we examine a Taylor series technique to express the forcing function F(x) with regard to the state variables. This was utilised for the rebuilding of models via ensemble data assimilation. Using the variational data assimilation method and the Kalman filter technique, our Model Reconstruction for Dynamical Systems primary objective is to study a general method for resolving this problem with little or some specific understanding of the underlying dynamical system. The models are then supplemented with a reaction-diffusion system. We demonstrate that learning a reaction-diffusion model’s fundamental partial differential equation is doable and produces good results when the learnt model is utilised as a propagator. Thus, we notice that the general iterative model reconstruction is competitive for the specific inverse issue under study for a broad range of initial conditions. Included are numerical examples demonstrating the practicability of the method