GMRF-wind

A lightweight, training-free, physics-informed 2D indoor airflow field estimation using Gaussian Markov Random Fields (GMRF).

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Overview

GMRF-wind provides a real-time, training-free spatial estimation framework to reconstruct continuous 2D wind velocity maps ($\mathbf{W}$) from a set of sparse, noisy wind vector observations ($\mathbf{Z}$) and occupancy grid geometries.

Instead of relying on heavy Computational Fluid Dynamics (CFD) solvers or data-intensive machine learning models, this package formulates wind field estimation as a Maximum A Posteriori (MAP) inference problem on a Gaussian Markov Random Field graph. By minimizing a total energy function $E(\mathbf{W}, \mathbf{Z})$, the algorithm efficiently solves a linear sparse system to deliver macro-scale wind maps in milliseconds.

This repository provides the official ROS 2 wrapper and C++ core implementation of the methodology presented in:

A Physics-Informed Gaussian Markov Random Field Framework for Indoor Airflow Field Estimation
Javier Monroy, Pepe Ojeda, and Javier Gonzalez-Jimenez
Building and Environment, Vol. 288, 2026.
🔗 Read Full Paper (Open Access)

The Code

The repository is organized as a ROS 2 workspace-style package collection: one small message package for custom interfaces (gmrf_msgs) and one main mapping package that contains the C++ solver, launch/config files, scripts, and data assets for estimating 2D indoor airflow fields. The code is essentially divided into the core library (in the subpackage gmrf_wind_core) and a ROS-wrapper node (gmrf_wind_mapping).

Whitin it, there are two ROS executables, the main “nodes” you should care about:

1. gmrf_wind_mapping_node implemented in gmrf_node.cpp: this is the main runtime node for online wind mapping.

• accepts an environment occupancy map (from MapServer)
• receives sparse wind observations from anemometers (via topic subscription)
• converts sensor measurements into map-frame coordinates using TF
• inserts those observations into a CGMRF_map (the core class, ROS-independent)
• solves the MAP estimation repeatedly
• publishes the result as RViz markers (for visualization and debug)
• exposes two services: WindEstimation: returns U/V velocity components, can query either the whole grid or specific points. AddWindObservation: lets clients add additional sensor observations directly, useful for external sources or debugging.

This is the node used in the standard launch file gmrf_wind_launch.py.

2. gmrf_validation implemented in gmrf_validation.cpp: this is an evaluation/benchmark node designed to operate offline for numerical testing.

• it loads an occupancy map and CFD ground-truth dataset (from file)
• runs the estimator after "simulating" measurements
• compares prediction quality using metrics like MAE/RMSE or similar optimization criteria
• it is designed for validation experiments rather than real-time deployment

This is the node launched by gmrf_validation_launch.py.

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Key Features

• ⚡ Real-Time & Computational Efficiency: Solves spatial estimates in milliseconds on CPU, suitable for low-power onboard robotic processors.
• 🚫 Training-Free & Zero Setup: Requires no offline datasets, neural network training, or parameter tuning per environment.
• 🛡️ Physics-Grounded Constraints: Embeds fundamental fluid transport mechanics directly into the graph precision matrix:
  • Incompressibility / Continuity Constraint: $\nabla \cdot \mathbf{w} = 0$
  • Advection-Diffusion Momentum Proxy: Smooths flow direction along streamlines while preserving spatial gradients.
  • No-Penetration Boundary Conditions: Prevents unphysical airflow through walls and solid obstacles ($\mathbf{w} \cdot \mathbf{n}_{\text{obs}} = 0$).
• 🤖 Robotics Ready: Native ROS 2 integration accepting live OccupancyGrid maps and point wind observations (e.g., from anemometers mounted on mobile robots).

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How It Works

The framework embeds simplified physical constraints derived from the Navier–Stokes equations—including mass conservation, advection, and viscous diffusion—into the estimation process, ensuring physically consistent flow reconstruction at a fraction of the computational cost of CFD. It defines specialized energy factors encoding geometric spatial priors, physical conservation laws, and sensor observation models:

$$E(\mathbf{W}, \mathbf{Z}) = E_{\text{z}}(\mathbf{W}, \mathbf{Z}) + E_{\text{o}}(\mathbf{W}) + E_{\text{physics}}(\mathbf{W})$$

1. Observation Factor ($E_{\text{z}}$): Pulls the local velocity vector towards incoming anemometer measurements.
2. Spatial Prior ($E_{\text{o}}$): enforces a boundary condition without penetration at obstacles.
3. Physics Factors ($E_{\text{physics}}$): Constrains neighbor-to-neighbor transitions according to indoor mass continuity, advection and diffusion.

The resulting sparse Gaussian precision matrix ($\mathbf{Q}$) allows solving the linear system $\mathbf{Q}\mathbf{W} = \mathbf{b}$ continuously, as new measurements arrive.

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Intended Applications

GMRF-wind is designed for operational robotics and environmental monitoring applications where fast, macro-scale flow awareness is required:

• Robot-Assisted Gas Source Localization (GSL): Guiding mobile inspection robots toward hazardous gas leaks by tracking active wind corridors.
• Indoor Air Quality (IAQ) & HVAC Optimization: Rapid mapping of ventilation patterns, stagnation zones, and pollutant dispersion routes.

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Quick Start

Prerequisites

• ROS 2 (Humble / Iron / Jazzy)
• Eigen3
• OpenCV / PCL (for map handling)

Although GMRF-W is a self-contained pkg, the implementation considers anemometer sensor readings which depends on an external pkg defining some "olfaction" related msgs. This pkg is available in a different repository named olfaction_msgs (https://github.com/MAPIRlab/olfaction_msgs).

Citation

If it is relevant to your research, you can cite the paper with the following BibTex:

@ARTICLE{monroy_bae_2026,
    author = {Monroy, Javier and Ojeda, Pepe and Gonzalez-Jimenez, Javier},
     title = {A Physics-Informed Gaussian Markov Random Field Framework for Indoor Airflow Field Estimation},
   journal = {Building and Environment},
      year = {2026},
       url = {https://doi.org/10.1016/j.buildenv.2026.114957},
       doi = {10.1016/j.buildenv.2026.114957}
}