Related papers: Model discovery for dynamical systems with complex…
This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach uses deep neural networks to learn uncertain…
Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…
A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these…
Developing and fielding complex systems requires proof that they are reliably correct with respect to their design and operating requirements. Especially for autonomous systems which exhibit unanticipated emergent behavior, fully…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…
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…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…
Identifying the main features and learning the causal relationships of a dynamic system from time-series of sensor data are key problems in many real-world robot applications. In this paper, we propose an extension of a state-of-the-art…
Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine…
A novel approach is presented for discovering PDEs that govern the motion of satellites in space. The method is based on SINDy, a data-driven technique capable of identifying the underlying dynamics of complex physical systems from time…
The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the…
We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…