Learning low-dimensional separable decompositions of MIMO non-linear systems

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We present a new internal structure exploration method developed for the multiple-input multiple-output (MIMO) dynamical systems with finite memory and almost arbitrary non-linear characteristic. The proposed Double Separation Algorithm applies distance correlation screening for pre-selection of those system inputs that contribute to the consecutive outputs and, based on the first-stage inference outcomes, estimates projection coefficients sensitive to the existence of additive system sub-characteristics. In effect, the proposed approach allows for effective exploration of the internal system structure. A numerical experiment on an MIMO nonlinear finite impulse response (NFIR) system illustrates the ability of the proposed approach to indicate which of the system inputs contribute to which of the system outputs. The experiment also illustrates the ability of the approach to detect which of the nonlinear sub-characteristics, recovered in the first stage of the approach, can be separated into a sum of lower-dimensional sub-characteristics.