In inverse problem theory, the identification of nonlinear spatiotemporal systems is still an underdeveloped topic [1] . This work aims to introduce a means for spatiotemporal system identification based on spectral methods. To achieve this goal, a continuous black-box model class is proposed and parameterized to obtain a model structure whose proper discretization yields a regression form, giving the unknown parameters based on the maximum likelihood estimation. An orthogonal system

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... ion algorithm is devised to eliminate the redundant parameters. Spectral differentiation operators are extended to inverse problems for proper discretization of the continuous model structure. Trigonometric and algebraic spectral operators are introduced for periodic and non-periodic system identifications and for their practical implementation, wavenumber reordering and roundoff attenuation methods are proposed.