Related papers: Enhancing model identification with SINDy via null…
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of…
We present a three-step method to perform system identification and optimal control of non-linear systems. Our approach is mainly data driven and does not require active excitation of the system to perform system identification. In…
Inferring physical laws from data is a central challenge in science and engineering, including but not limited to healthcare, physical sciences, biosciences, social sciences, sustainability, climate, and robotics. Deep networks offer…
Uncertainty quantification during atmospheric chemistry modeling is computationally expensive as it typically requires a large number of simulations using complex models. As large-scale modeling is typically performed with simplified…
This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…
dentifying accurate and yet interpretable low-order models from data has gained a renewed interest over the past decade. In the present work, we illustrate how the combined use of dimensionality reduction and sparse system identification…
Deriving constitutive models (CMs) from numerical data has been an attractive approach as a systematic CM building method. One recent study is Rheo-SINDy, which extended the sparse identification of nonlinear dynamics (SINDy) method to…
The control of complex dynamical systems remains a fundamental challenge in science and engineering, where strong nonlinearities, the presence of noise, and computational constraints often pose significant obstacles in traditional control…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase-amplitude reduction techniques, leveraging an analytical…
In this work, a new two-stage identification method based on dynamic programming and sparsity inducing is proposed for switched linear systems. Our method achieves sparsity inducing in the identification of switched linear systems by the…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…
Accurate estimation of thermospheric mass density is a prerequisite for orbit prediction and space situational awareness, where the upper atmosphere responds nonlinearly to solar and geomagnetic forcing across several orders of magnitude.…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…
The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…
We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
System identification is a common tool for estimating (linear) plant models as a basis for model-based predictive control and optimization. The current challenges in process industry, however, ask for data-driven modelling techniques that…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…