Related papers: Solving the inverse problem of noise-driven dynami…

We introduce Linearly Constrained Diffusion Implicit Models (CDIM), a fast and accurate approach to solving noisy linear inverse problems using diffusion models. Traditional diffusion-based inverse methods rely on numerous projection steps…

Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal…

This work is concerned with a direct sampling method (DSM) for inverse acoustic scattering problems using far-field data. The method characterizes some unknown obstacles, inhomogeneous media or cracks, directly through an indicator function…

Diffusion models (DMs) have rapidly emerged as a powerful framework for image generation and restoration. However, existing DMs are primarily trained in a supervised manner by using a large corpus of clean images. This reliance on clean…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by…

We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…

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…

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…

Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of models. We assess the strengths and weaknesses of the method by varying coupling strength and noise levels in coupled logistic maps. We…

We analytically determine the correlation functions of the stochastic response of a generic mapping system driven by colored noise. We also address the issue of noise cascading in coupled-element systems, particularly in a uni-directionally…

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…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…

Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…

The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…