Many wrong models approach to localize an odor source in turbulence with static sensors

Abstract: The problem of locating an odor source in turbulent flows is central to key applications such as environmental monitoring and disaster response. We address this challenge by designing an algorithm based on Bayesian inference, which uses odor measurements from an ensemble of static sensors to estimate the source position through a stochastic model of the environment. The problem is difficult because of the multiscale and out-of-equilibrium properties of turbulent transport, which lack accurate analytical and phenomenological modeling, thus preventing a guaranteed convergence for Bayesian approaches. To overcome the risk of relying on a single unavoidably wrong model approximation, we propose a method to rank ``many wrong models'' and to blend their predictions. We evaluated our \emph{weighted Bayesian update} algorithm by its ability to estimate the source location with predefined accuracy and/or within a specified time frame and compare it to standard Monte Carlo sampling methods. To demonstrate the robustness and potential applications of both approaches under realistic environmental conditions, we use high-quality direct numerical simulations of the Navier-Stokes equations to mimic the turbulent transport of odors in presence of a strong mean wind. Despite minimal prior information on the source and environmental conditions, our proposed approach consistently proves to be more accurate, reliable, and robust than Monte Carlo methods, thus showing promise as a new tool for addressing the odor source localization problem in real-world scenarios.