Gas Source Localization Using physics Guided Neural Networks

TL;DR

This paper tackles gas source localization from concentration measurements collected by mobile agents. It introduces a physics-guided neural network (PGNN) surrogate for the steady-state advection-diffusion PDE $0=\kappa\Delta u - \boldsymbol{v}\cdot\nabla u + s_{\boldsymbol{p}}$ in $\Omega$, with Dirichlet BC and a Dirac delta source at $\boldsymbol{p}$, treating $\boldsymbol{p}$ as an input to the network. The surrogate is trained offline using a physics-guided $H_1$-loss that matches both function values and gradients while enforcing boundary conditions via a cutoff function, enabling gradient-based inversion with LBFGS-B. Results show sub-10 m localization accuracy in noise-free cases and up to ~28 m under moderate noise, with 1 s solution times, demonstrating robustness and potential for real-time, on-board gas localization on resource-limited platforms. The approach reduces reliance on expensive PDE solves and can be extended to 3D, unknown parameters, and dynamic planning, with further real-world validation planned.

Abstract

This work discusses a novel method for estimating the location of a gas source based on spatially distributed concentration measurements taken, e.g., by a mobile robot or flying platform that follows a predefined trajectory to collect samples. The proposed approach uses a Physics-Guided Neural Network to approximate the gas dispersion with the source location as an additional network input. After an initial offline training phase, the neural network can be used to efficiently solve the inverse problem of localizing the gas source based on measurements. The proposed approach allows avoiding rather costly numerical simulations of gas physics needed for solving inverse problems. Our experiments show that the method localizes the source well, even when dealing with measurements affected by noise.

Figures (3)

• Figure 1: Problem setup. The gas concentration field is shown as an example. (A ball of radius 20m around $\boldsymbol{p}$ is excluded to avoid the singularity.) The dotted black circle represents $D_\mathrm{O}$, the trajectory of the observations. The source location $\boldsymbol{p}$ is marked by a black dot and the set $\mathcal{P}$ of possible source positions by the blue hatched region.
• Figure 2: The surrogate model's performance over its training period. Blue: $H_1$-loss on training set. Orange: Mean Square Error (MSE) of function values on test set (withheld from NN-training).
• Figure 3: NN training results. Fig. (a) shows the difference between the NN-surrogate $\tilde{u}_{\boldsymbol{p}}$ and the reference solution $u_{\boldsymbol{p}}$ in $\Omega$, normalized by the maximum value of $u_{\boldsymbol{p}}$ excluding a ball of radius 20m around the source, in the situation of Fig. \ref{['fig:ProbSetup']}. Fig. (b) shows the (Euclidean) position error of the location $\boldsymbol{p}$ calculated by solving \ref{['eq:InvProb']} with our NN-surrogate approach with increasing amounts of White Gaussian Noise.