Related papers: Effective Filtering on a Random Slow Manifold
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous…
We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the…
Existing fast algorithms for bilateral and nonlocal means filtering mostly work with grayscale images. They cannot easily be extended to high-dimensional data such as color and hyperspectral images, patch-based data, flow-fields, etc. In…
We propose a novel method of efficient upsampling of a single natural image. Current methods for image upsampling tend to produce high-resolution images with either blurry salient edges, or loss of fine textural detail, or spurious noise…
In this paper, we present a novel low rank representation (LRR) algorithm for data lying on the manifold of square root densities. Unlike traditional LRR methods which rely on the assumption that the data points are vectors in the Euclidean…
Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure,…
We introduce a method for constructing reduced-order models directly from videos of dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user-selected part in the video of an autonomous dynamical system. In…
This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul…
In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…
3D single-photon LiDAR imaging plays an important role in numerous applications. However, long acquisition times and significant data volumes present a challenge to LiDAR imaging. This paper proposes a task-optimized adaptive sampling…
When signals are measured through physical sensors, they are perturbed by noise. To reduce noise, low-pass filters are commonly employed in order to attenuate high frequency components in the incoming signal, regardless if they come from…
Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…