A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics (SINDy) algorithm is developed. First, the Akaike information criterion (AIC) is integrated to enforce model selection by hierarchically ranking the most informative model from several manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations (ODEs) to partial differential equations (PDEs), while group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to treat noise separate from signals and tends to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the Van der Pol , Rössler , Burgers’ and Kuramoto–Sivashinsky equations , can be identified correctly with the introduction of noise. Furthermore, except for normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possesses robustness.
A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon the partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics(SINDy) algorithm is developed. First, Akaike information criterion(AIC), which is based on information criterion is integrated to enforce model selection via hierarchically ranking the most informative model from a manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations(ODEs) to partial differential equations(PDEs) when the group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to make noise separate from signals and inclines to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the duffing oscillator, Lotka-Volterra, Rössler, Burgers’ equation and Kuramoto-Sivashinsky equation can be identified correctly with the introduction of noise. Furthermore, except for the normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possess robustness.
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