Related papers: Automatic Differentiation to Simultaneously Identi…
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is a necessary step to draw conclusions from these data, and it often becomes quite essential to construct dynamical models using these…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…
We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number $N$ and offering robustness to either intrinsic or extrinsic…
The performance of estimated models is often evaluated in terms of their predictive capability. In this study, we investigate another important aspect of estimated model evaluation: the disparity between the statistical and dynamical…
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…
The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…
We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations…
Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
The quasi-potential is a key concept in stochastic systems as it accounts for the long-term behavior of the dynamics of such systems. It also allows us to estimate mean exit times from the attractors of the system, and transition rates…
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
We consider a setting, where the output of a linear dynamical system (LDS) is, with an unknown but fixed probability, replaced by noise. There, we present a robust method for the prediction of the outputs of the LDS and identification of…
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…
In this study, we investigate the performance of the sparse identification of nonlinear dynamics (SINDy) algorithm and the neural ordinary differential equations (ODEs) in identification of the underlying mechanisms of open ocean Lagrangian…
Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For…
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…
Our ability to predict, control, and ultimately understand complex systems rests on discovering the equations that govern their dynamics. Identifying these equations directly from noisy, limited observations has therefore become a central…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…