Related papers: TRENDy: Temporal Regression of Effective Nonlinear…
A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state…
This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to…
In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…
The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements…
In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…
Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives…
Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about…
Sensing is a universal task in science and engineering. Downstream tasks from sensing include inferring full state estimates of a system (system identification), control decisions, and forecasting. These tasks are exceptionally challenging…
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…
Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…
Understanding and predicting complex dynamics in accelerators is necessary for their successful operation. A grand challenge in accelerator physics is to develop predictive virtual accelerators that mitigate design cost and schedule risk.…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
Territoriality is a phenomenon exhibited throughout nature. On the individual level, it is the processes by which organisms exclude others of the same species from certain parts of space. On the population level, it is the segregation of…
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…
Vortex-induced vibrations (VIV) remain a canonical yet complex manifestation of fluid-structure interactions, where coupled nonlinear dynamics govern the motion of bluff bodies. For several years, we have relied on traditional reduced-order…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
The data-driven discovery of dynamics via machine learning is currently pushing the frontiers of modeling and control efforts, and it provides a tremendous opportunity to extend the reach of model predictive control. However, many leading…