Related papers: Modeling Nonlinear Dynamics from Videos
Monocular dynamic reconstruction is a challenging and long-standing vision problem due to the highly ill-posed nature of the task. Existing approaches depend on templates, are effective only in quasi-static scenes, or fail to model 3D…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific,…
This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce…
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…
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 use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow in the permanently chaotic regime studied by Kreilos & Eckhardt (2012). Our three-dimensional model is obtained by…
Video motion magnification techniques allow us to see small motions previously invisible to the naked eyes, such as those of vibrating airplane wings, or swaying buildings under the influence of the wind. Because the motion is small, the…
This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…
A natural approach to generative modeling of videos is to represent them as a composition of moving objects. Recent works model a set of 2D sprites over a slowly-varying background, but without considering the underlying 3D scene that gives…
This paper presents a new self-supervised system for learning to detect novel and previously unseen categories of objects in images. The proposed system receives as input several unlabeled videos of scenes containing various objects. The…
We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe…
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
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…
Synthesizing realistic animations of humans, animals, and even imaginary creatures, has long been a goal for artists and computer graphics professionals. Compared to the imaging domain, which is rich with large available datasets, the…
Data-driven learning approaches for physics simulation, sometimes referred to as world models, have emerged as promising alternatives to traditional physics simulators due to their differentiable nature. Prior work has demonstrated…
The objective of this paper is a model that is able to discover, track and segment multiple moving objects in a video. We make four contributions: First, we introduce an object-centric segmentation model with a depth-ordered layer…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
Spectral submanifolds (SSMs) have emerged as accurate and predictive model reduction tools for dynamical systems defined either by equations or data sets. While finite-elements (FE) models belong to the equation-based class of problems,…