Kernel Modelling of Fading Memory Systems
The paper is a follow-up of the recently introduced kernel-based framework to identify nonlinear input-output systems regularized by desirable input-output incremental properties. Assuming that the system has fading memory, we propose to learn the functional that maps the past input to the present output rather than the operator mapping input trajectories to output trajectories. While retaining the benefits of the previously proposed framework, this modification simplifies the selection of the kernel, enforces causality, and enables temporal simulation.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Fading memory and the convolution theorem
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolutio…
Modelling the Memory of Turbulence-Induced Beam Wander
One of the major challenges for long range, high speed Free-Space Optical (FSO) communication is turbulence induced beam wander. Beam wander causes fluctuations in the received intensity as well as crosstalk in mode divi…
Reservoir kernels and Volterra series
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using …
tensor algebraUniversal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems
A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts ar…
A Fully Probabilistic Tensor Network for Regularized Volterra System Identification
Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BT…