Few-Shot-Learning-Like Neural Dynamics for Time-Dependent Multilinear $\mathcal {M}$-Tensor Equation

In recent years, many discrete neural dynamics models are presented based on continuous models to solve the multilinear tensor equation. However, these existing discrete models all depend on numerical algorithms, such as Euler difference formula and Taylor-type difference formula, which may suffer from the problem of fixed selections with limited feasible parameters. In this article, a few-shot-learning-like neural dynamics (FLLND) model is constructed to find the solution to the time-dependent multilinear tensor equation (TMTE), which opens a new road in constructing the discrete computing model from its continuous counterpart. Specifically, to keep the consistency and better generalization of the constructed model, a few-shot-learning-like method is leveraged to learn parameters from a small dataset. Then, theoretical analyses are conducted to demonstrate the convergence and robustness of the constructed FLLND model in solving the TMTE problem. Finally, several TMTE examples are provided to illustrate the effectiveness and practicality of the FLLND model.