Sparse Source Identification in Transient Advection-Diffusion Problems with a Primal-Dual-Active-Point Strategy

Abstract

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 evacuation planning following contaminant release. In such scenarios, timely and reliable decision-making is essential, despite limited observation data. To identify contaminant sources, we formulate an inverse problem governed by an advection-diffusion equation. Given the problem's underdetermined nature, we further employ a variational regularization ansatz and model the unknown contaminant sources as distribution over the spatial domain. To efficiently solve the arising inverse problem, we employ a problem-specific variant of the Primal-Dual-Active-Point (PDAP) algorithm which efficiently approximates sparse minimizers of the inverse problem by alternating between greedy location updates and source intensity optimization. The approach is demonstrated on two- and three-dimensional test cases involving both instantaneous and continuous contaminant sources and outperforms state-of-the-art techniques with $L^2$-regularization. Its effectiveness is further illustrated in complex domains with real-world building geometries imported from OpenStreetMap.

References in corpus (13)

• The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy
• Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems
• Sparsity of solutions for variational inverse problems with finite-dimensional data
• Model-Based Active Source Identification in Complex Environments
• Emergency Response Inference Mapping (ERIMap): A Bayesian network-based method for dynamic observation processing
• A sparse control approach to optimal sensor placement in PDE-constrained parameter estimation problems
• Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems
• A two-stage numerical approach for the sparse initial source identification of a diffusion-advection equation
• A Low-rank Solver for the Stochastic Unsteady Navier-Stokes Problem
• Model Order Reduction for Deforming Domain Problems in a Time-Continuous Space-Time Setting
• Elasto-acoustic modelling and simulation for the seismic response of structures: The case of the Tahtalı dam in the 2020 İzmir earthquake
• Towards optimal sensor placement for inverse problems in spaces of measures
• On extremal points for some vectorial total variation seminorms