Related papers: Source Reconstruction for Spatio-Temporal Physical…

We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…

Inferring the source information of greenhouse gases, such as methane, from spatially sparse sensor observations is an essential element in mitigating climate change. While it is well understood that the complex behavior of the atmospheric…

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty…

We consider the problem of Active Source Identification (ASI) in steady-state Advection-Diffusion (AD) transport systems. Unlike existing bio-inspired heuristic methods, we propose a model-based method that employs the AD-PDE to capture the…

Discharge of hazardous substances into the marine environment poses a substantial risk to both public health and the ecosystem. In such incidents, it is imperative to accurately estimate the release strength of the source and reconstruct…

In the face of growing needs for water and energy, a fundamental understanding of the environmental impacts of human activities becomes critical for managing water and energy resources, remedying water pollution, and making regulatory…

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…

In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, moving according to a prescribed stochastic process,…

In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…

This work presents a mathematical model to enable rapid prediction of airborne contaminant transport based on scarce sensor measurements. The method is designed for applications in critical infrastructure protection (CIP), such as…

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on…

In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…

In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types, the resulting measurements thus give only…

Refraction by the atmosphere causes the positions of sources to depend on the airmass through which an observation was taken. This shift is dependent on the underlying spectral energy of the source and the filter or bandpass through which…

The Water Residence Time distribution is the equivalent of the impulse response of a linear system allowing the propagation of water through a medium, e.g. the propagation of rain water from the top of the mountain towards the aquifers. We…

We provide an example of a distribution preserving source separation method, which aims at addressing perceptual shortcomings of state-of-the-art methods. Our approach uses unconditioned generative models of signal sources. Reconstruction…

Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…