A Tensor-based Volterra Series Black-box Nonlinear System Identification and Simulation Framework

Tensors are a multi-linear generalization of matrices to their d-way counterparts, and are receiving intense interest recently due to their natural representation of high-dimensional data and the availability of fast tensor decomposition algorithms. Given the input-output data of a nonlinear system/circuit, this paper presents a nonlinear model identification and simulation framework built on top of Volterra series and its seamless integration with tensor arithmetic. By exploiting partially-symmetric polyadic decompositions of sparse Toeplitz tensors, the proposed framework permits a pleasantly scalable way to incorporate high-order Volterra kernels. Such an approach largely eludes the curse of dimensionality and allows computationally fast modeling and simulation beyond weakly nonlinear systems. The black-box nature of the model also hides structural information of the system/circuit and encapsulates it in terms of compact tensors. Numerical examples are given to verify the efficacy, efficiency and generality of this tensor-based modeling and simulation framework.