Related papers: Modeling Nonlinear Dynamics from Videos

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves…

This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…

Videos provide a rich source of information, but it is generally hard to extract dynamical parameters of interest. Inferring those parameters from a video stream would be beneficial for physical reasoning. Robots performing tasks in dynamic…

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…

Data-driven discovery of governing equations has kindled significant interests in many science and engineering areas. Existing studies primarily focus on uncovering equations that govern nonlinear dynamics based on direct measurement of the…

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Multi-body mechanical systems have rich internal dynamics, whose solutions can be exploited as efficient control targets. Yet, solutions non-trivially depend on system parameters, obscuring feasible properties for use as target…

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow…

Extracting and predicting object structure and dynamics from videos without supervision is a major challenge in machine learning. To address this challenge, we adopt a keypoint-based image representation and learn a stochastic dynamics…

In this paper, we propose a computationally tractable and theoretically supported non-linear low-dimensional generative model to represent real-world data in the presence of noise and sparse outliers. The non-linear low-dimensional manifold…

In this paper, we consider the task of unsupervised object discovery in videos. Previous works have shown promising results via processing optical flows to segment objects. However, taking flow as input brings about two drawbacks. First,…

This paper proposes a new method for Non-Rigid Structure-from-Motion (NRSfM) from a long monocular video sequence observing a non-rigid object performing recurrent and possibly repetitive dynamic action. Departing from the traditional idea…

Appearance features have been widely used in video anomaly detection even though they contain complex entangled factors. We propose a new method to model the normal patterns of human movements in surveillance video for anomaly detection…

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

Estimating the pose of a moving camera from monocular video is a challenging problem, especially due to the presence of moving objects in dynamic environments, where the performance of existing camera pose estimation methods are susceptible…

Disentangled representations support a range of downstream tasks including causal reasoning, generative modeling, and fair machine learning. Unfortunately, disentanglement has been shown to be impossible without the incorporation of…