Improved Extended Dynamic Mode Decomposition with Invertible Dictionary Learning

The Koopman operator achieves linearized representation of nonlinear systems by lifting the finite-dimensional state space of nonlinear systems to an infinite-dimensional space. While prevalent approaches typically employ neural networks for state space lifting and independently solve for approximate Koopman operators, this decoupled optimization framework tends to trap parameters in local minima. To address this limitation, this paper designs a model called the Improved Extended Dynamic Mode Decomposition with Invertible Dictionary Learning (IEDMD-IDL), which integrates parameterized representation of the Koopman operator into a unified neural network training framework, enabling joint parameter learning mechanisms under global optimization objectives. To further enhance the capacity of the model under noise, a deep regression learning module is utilized based on optimal loss functions, effectively suppressing the adverse effects of noise in the measured data on the precision of the identification. Finally, we demonstrate the IEDMD-IDL algorithm through experiments on Duffing differential equations with comparative analysis.