# Sensor optimization for urban wind estimation with cluster-based probabilistic framework

arXiv: https://arxiv.org/abs/2509.25222 · HTML: https://mlsanity.com/paper/2509.25222/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 23 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 2 of 2)

- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Modeling Multivariable High-resolution 3D Urban Microclimate Using Localized Fourier Neural Operator](https://mlsanity.com/paper/2411.11348/) (2024)

## Abstract (arXiv)

We propose a physics-informed machine-learned framework for sensor-based flow estimation for drone trajectories in complex urban terrain. The input is a rich set of flow simulations at many wind conditions. The outputs are velocity and uncertainty estimates for a target domain and subsequent sensor optimization for minimal uncertainty. The framework has three innovations compared to traditional flow estimators. First, the algorithm scales proportionally to the domain complexity, making it suitable for flows that are too complex for any monolithic reduced-order representation. Second, the framework extrapolates beyond the training data, e.g., smaller and larger wind velocities. Last, and perhaps most importantly, the sensor location is a free input, significantly extending the vast majority of the literature. The key enablers are (1) a Reynolds number-based scaling of the flow variables, (2) a physics-based domain decomposition, (3) a cluster-based flow representation for each subdomain, (4) an information entropy correlating the subdomains, and (5) a multi-variate probability function relating sensor input and targeted velocity estimates. This framework is demonstrated using drone flight paths through a three-building cluster as a simple example. We anticipate adaptations and applications for estimating complete cities and incorporating weather input.