Related papers: Multidimensional approximation of nonlinear dynami…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear…
Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a…
Identifying nonlinear dynamics and characterizing noise from data is critical across science and engineering for understanding and modeling the behavior of the systems accurately. The modified sparse identification of nonlinear dynamics…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and…
Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics…
Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…
Research on dynamics of robotic manipulators provides promising support for model-based control. In general, rigorous first-principles-based dynamics modeling and accurate identification of mechanism parameters are critical to achieving…