An improved sparse identification of nonlinear dynamics with Akaike information criterion and group sparsity

Abstract

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.

Analyzing Russia–Ukraine War Patterns Based on Lanchester Model Using SINDy Algorithm

“…Moreover, SINDy can be used to reduce the complexity of a model by identifying a subset of terms essential for capturing the dynamics of the system, allowing for more efficient simulation and analysis. Numerous applications and variants of the SINDy algorithm in modeling dynamical systems can be observed, encompassing recent works such as [18][19][20][21][22][23][24]. The Lanchester model is a nonlinear dynamical system, and for some models, the dynamical equations are difficult to solve analytically.…”

Adaptive Uncertainty-Penalized Model Selection for Data-Driven PDE Discovery

“…In the model selection from a finite set of potential PDEs, Akaike information criterion (AIC) [16]- [18] and Bayesian information criterion (BIC) [19] are commonly adopted as metrics evaluating point estimates of model parameters. However, when changing the number of nonzero terms in a linear model fitted on an overcomplete candidate library, the AIC and BIC values tend to decrease as the model complexity increases.…”

Governing equation discovery based on causal graph for nonlinear dynamic systems

“…Modern machine learning methods have made significant progress in the black box prediction performance of many tasks, but the simplified closed form of the internal governing equations of the systems is still unclear or partially unknown. Therefore, it is necessary to study how to explore the governing equations of systems, which contain the underlying governing equation, from the observed data [1][2][3].…”