Deep Probabilistic Indoor Gas Source Localization via Physical Dependency-Guided Sequential Inference

Seunghwan Kim; Hyungjin Kim; Junhee Lee; Hyondong Oh

cs.ROAug 17, 2026

Deep Probabilistic Indoor Gas Source Localization via Physical Dependency-Guided Sequential Inference

Authors: Seunghwan Kim, Hyungjin Kim, Junhee Lee, Hyondong Oh

Organizations: Department of Mechanical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea · Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea

Abstract

Reliable gas source localization (GSL) is critical to safety in industrial and urban environments, yet remains challenging indoors because walls and obstacles interact with airflow to create complex gas dispersion. High-fidelity models such as computational fluid dynamics and filament models can capture these effects, but their computational cost limits online use. We propose a deep probabilistic framework that infers the source posterior from sparse and noisy measurements collected by a mobile robot. Unlike end-to-end models that directly infer source estimates from measurements, the proposed method incorporates physical dependencies of indoor gas transport, where wind and source location govern the concentration field. These dependencies are embedded through sequential conditional inference, in which inferred wind and concentration fields guide source posterior estimation. This structure improves localization under sparse and noisy observations. Evaluations show that the proposed method outperforms representative GSL baselines and enables accurate and efficient active GSL in simulations. Real-robot experiments demonstrate the feasibility of online operation on an embedded GPU.

Figures & tables

Fig. 1: Network architectures for deep probabilistic gas source estimation (DGSE). (a) DGSE-O directly predicts the source posterior from sparse wind and gas observations and the map. (b) DGSE-P shares an encoder across wind-field (WF), concentration-field (CF), and source-localization (SL) decoders. (c) DGSE-S implements physical dependency-guided sequential inference by conditioning CF estimation on the inferred WF and SL estimation on the inferred WF and CF.

Fig. 2: Bayesian network representing the physical dependencies used to derive the conditional inference sequence in DGSE-S.

Sensor	Model	Parameters
Gas conc.	$z_{\text{raw}}^{c}\sim\mathcal{N}(c,\,\sigma_{g}^{2})$	$\sigma_{g}=\alpha_{g}c+\sigma_{env}$
		$\alpha_{g}\in[0,\,1.0]$
		$\sigma_{env}\in[0,\,0.5]\times\bar{c}$
Wind speed	$z^{w,m}\sim\mathcal{N}(w^{m},\,\sigma_{w,m}^{2})$	$\sigma_{w,m}=\alpha_{w}w^{m}$
		$\alpha_{w}\in[0,\,0.5]$
Wind dir.	$z^{w,a}\sim\mathcal{N}(w^{a},\,\sigma_{w,a}^{2})$	$\sigma_{w,a}\in[0^{\circ},\,15^{\circ}]$

TABLE I: Sensor noise models and parameter ranges.

Fig. 3: Data generation pipeline. Computational fluid dynamics (CFD) simulations generate ground-truth wind fields, concentration fields, and source locations from randomized indoor layouts and boundary conditions. Sparse wind and gas observations are then produced by adding randomized sensor noise before rasterizing the inputs for DGSE training.

Fig. 4: Quantitative comparison of DGSE-O, DGSE-P, and DGSE-S across 1,000 test environments with varying numbers of observations. The three prediction tasks are evaluated: wind-field (WF) prediction, concentration-field (CF) prediction, and source-localization (SL) prediction. Black lines denote RMSE for WF/CF and localization error for SL, while red lines denote Gaussian NLL for WF/CF and cross-entropy (CE) for SL.

Fig. 5: Comparison of DGSE-S and baseline gas distribution mapping (GDM) methods in terms of concentration-field root mean square error (RMSE) and negative log-likelihood (NLL) across five test environments.

Fig. 6: Representative gas distribution mapping (GDM) results for the case of 100 observations across the five test environments, each with a different inlet velocity $v_{\mathrm{in}}$ and release rate $q$ . Each environment compares DGSE-S with KDM+V/W, GaBP+, G-GMRF, and GW-GMRF; GT denotes the ground-truth concentration field. The predicted concentration-field mean $\mu_{c}$ is visualized as the estimated gas distribution map, and the predicted wind-field mean $\mu_{w}$ is shown to indicate the corresponding airflow estimate. Error maps show $\tilde{e}_{c}=\|\mu_{c}-c_{\text{true}}\|$ , and uncertainty maps show the predicted standard deviation $\sigma_{c}$ .

Fig. 7: Computation times of gas distribution mapping (GDM) methods for the case of 100 observations. Times are reported as deployment latencies under the method-specific hardware described in the text.

Fig. 8: Test environments used for source localization and active GSL evaluations. The red dots denote simulated clusters of ethanol gas molecules.

Fig. 9: Source-localization performance from sparse random observations. SL error denotes source-localization error, and CE denotes the cross-entropy of the estimated source posterior. Each method was evaluated using 50 randomly sampled sensing locations over 20 trials in each environment.

Environment	Method	SR [ $\%$ ]	Error [ $m$ ]	ST [ $s$ ]	TD [ $m$ ]	One-step Computation Time [ $s$ ]
	Dual-mode planner	55	2.100 (1.717)	437.84 (293.11)	37.22 (18.80)	0.331 (0.150)
1	GrGSL	–	–	–	–	–
inlet velocity: 0.5 $\mathrm{m/s}$	PMFS	80	1.368 (1.404)	535.59 (189.27)	53.78 (26.79)	7.795 (1.372)
release rate: 0.06 $\mathrm{g/s}$	DGSE-S (Ours)	100	0.197 (0.076)	65.69 (7.12)	11.42 (0.54)	0.108 (0.0105)
	Dual-mode planner	20	2.693 (1.536)	366.83 (201.68)	34.48 (16.07)	0.360 (0.123)
2	GrGSL	–	–	–	–	–

TABLE II: Results of active GSL

Fig. 10: Search paths of DGSE-S and the comparison methods in Environments 5 and 6.

Fig. 11: Illustrative results of DGSE-S source search in Environment 4. The black line represents the robot trajectory, while the orange circles indicate the locations where gas concentrations were measured. The circle sizes are proportional to the measured concentration. The panels show how the predicted wind field, concentration field, and source-location probability evolve over the search steps. The index $k$ denotes the step number, where each step corresponds to one sensing location visited by the robot.

Fig. 12: Setup for real-world experiments. The mobile robot carries LiDAR, gas, and wind sensors, while a fan establishes a structured indoor airflow and CO 2 is released as the gas source.

Fig. 13: Illustrative results of real-world Experiment 1. The figure shows the robot trajectory, gas measurement locations, predicted concentration field, and source-location probability during downstream-to-upstream source search.

Fig. 14: Illustrative results of real-world Experiment 2. The figure shows the robot trajectory, gas measurement locations, predicted concentration field, and source-location probability during upstream-to-downstream source search.

	Method	SR [ $\%$ ]	Error [ $m$ ]	ST [ $s$ ]	TD [ $m$ ]
	Dual-mode planner	40	2.353 (0.653)	367.64 (69.47)	19.31 (4.35)
Experiment 1	PMFS	0	1.620 (0.476)	500.00 (0.00)	54.00 (3.18)
	DGSE-S (Ours)	100	0.818 (0.341)	90.48 (38.78)	11.97 (4.06)
	Dual-mode planner	60	1.293 (0.430)	371.29 (169.47)	25.57 (5.80)
Experiment 2	PMFS	60	1.024 (0.344)	402.49 (109.55)	55.89 (2.05)
	DGSE-S (Ours)	100	0.459 (0.277)	99.65 (19.92)	19.21 (1.82)

TABLE III: Results of active GSL in real-world experiments

Fig. 15: Concentration map and source probability map of DGSE-S in real-world Experiment 1, obtained via manual teleoperation. The maps illustrate how the continuous concentration estimate supports a source posterior despite secondary gas accumulation away from the primary transport stream.

Fig. 16: Gas hit map and source probability map of PMFS in real-world Experiment 1 for two representative trials. The binary hit maps show how thresholding can either miss the main transport stream or include secondary concentration regions.

Fig. 17: Illustrative results of the dual-mode planner in real-world Experiment 1. The path and concentration observations show convergence toward a high-concentration transport region rather than the true source under airflow-driven dispersion.

Fig. A.1: Source-localization (SL) loss over 100 epochs on the training and validation sets for DGSE-O, DGSE-P, and DGSE-S under different source-task weights.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

$S_{c}=S_{s}$	1	2	5	10	50
CF loss	$-$ 3.724	$-$ 3.725	$-$ 3.725	$-$ 3.725	$-$ 3.725
SL loss	5.153	5.104	5.090	5.092	5.091

Appendix

TABLE B.1: MC-estimated original losses on the validation set at the final epoch for varying

S_{c}

and

S_{s}

Fig. B.1: Comparison between the surrogate loss and the MC-estimated original losses over 2,000 validation environments (60,000 data points) during training, expressed in terms of losses. (a) Concentration-field (CF) validation loss. (b) Source-localization (SL) validation loss.

Fig. C.1: Effect of sample-based marginalization in DGSE-S. (a) Relative reduction of source CE and concentration-field NLL compared with single-sample inference. Black, red, and blue curves denote all validation samples, sparse-observation cases ( $\leq 50$ observations), and dense-observation cases ( $\geq 200$ observations), respectively. (b) Inference latency of the concentration field (CF) and source-localization (SL) modules on an NVIDIA Jetson AGX Orin.

Fig. D.1: Illustrative DGSE-S active GSL results in OOD Environment 4. The panels show the accumulated search path together with the predicted wind field, concentration field, and source posterior.

Fig. D.2: Out-of-domain environments used for the additional active GSL evaluation. The red dots denote simulated clusters of ethanol gas molecules.

Environment (inlet velocity, release rate)	SR [ $\%$ ]	Error [ $m$ ]	ST [ $s$ ]	TD [ $m$ ]	One-step Computation Time [ $s$ ]	PER
1 (3.0 $\mathrm{m/s}$ , 0.03 $\mathrm{g/s}$ )	100	0.851 (0.155)	151.65 (30.76)	27.82 (3.08)	0.104 (0.0534)	3.16
2 (3.0 $\mathrm{m/s}$ , 0.03 $\mathrm{g/s}$ )	100	0.881 (0.212)	184.87 (76.20)	18.39 (5.13)	0.0966 (0.0444)	3.64
3 (1.5 $\mathrm{m/s}$ , 0.09 $\mathrm{g/s}$ )	100	0.540 (0.259)	103.46 (20.53)	14.41 (2.30)	0.0858 (0.00239)	3.59
4 (2.5 $\mathrm{m/s}$ , 0.06 $\mathrm{g/s}$ )	100	0.593 (0.445)	194.89 (76.65)	26.94 (12.97)	0.110 (0.0515)	3.00
5 (2.5 $\mathrm{m/s}$ , 0.09 $\mathrm{g/s}$ )	100	0.952 (0.277)	139.07 (85.02)	21.36 (11.91)	0.0943 (0.00307)	3.37
6 (1.5 $\mathrm{m/s}$ , 0.01 $\mathrm{g/s}$ )	100	0.643 (0.391)	374.78 (115.39)	71.12 (17.63)	0.135 (0.00621)	4.67

Appendix

TABLE D.1: Results of active GSL in out-of-domain environments.

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Calibration-Free Gas Source Localization with Mobile Robots: Source Term Estimation Based on Concentration Measurement Ranking

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Distributed Intelligent Systems and Algorithms Laboratory, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

Mobile Robotics Robot Localization

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Efficient Gas Source Localization (GSL) in real-world settings is crucial, especially in emergency scenarios. Mobile robots equipped with low-cost, in-situ gas sensors offer a safer alternative to human inspection in hazardous environments. Probabilistic algorithms enhance GSL efficiency with scattered gas measurements by comparing gas concentration measurements gathered by robots to physical dispersion models. However, accurately deriving gas concentrations from data acquired with low-cost sensors is challenging due to the nonlinear sensor response, environmental dependencies (e.g., humidity, temperature, and other gas influences), and robot motion. Mitigating these disturbance factors requires frequent sensor calibration in controlled environments, which is often impractical for real-world deployments. To overcome these issues, we propose a novel feature extraction algorithm that leverages the relative ranking of gas measurements within the dynamically accumulated dataset. By comparing the rank differences between gathered and modeled values, we estimate the probabilistic distribution of source locations across the entire environment. We validate our approach in high-fidelity simulations and physical experiments, demonstrating consistent localization accuracy with uncalibrated gas sensors. Compared to existing methods, our technique eliminates the need for gas sensor calibration, making it well-suited for real-world applications.

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