Two-step AI-aided Bayesian source identification of urban-scale pollution

Identifying urban air pollution sources is essential for public health and environmental sustainability. In this study, we propose a novel hierarchical method for urban air pollution source identification, leveraging deep learning (DL) within an efficient Bayesian inference framework. We rely on observations in the form of two‐dimensional (2D) pollutant concentration distributions, and adopt the Wasserstein distance to model the likelihood probability distribution. The hierarchical nature of the framework stems from the integration of two neural networks (NNs). The first one acts as an emulator that replicates the physical dispersion model to predict future pollution observations recursively over a defined timeframe. These predictions are then used as inputs for the second NN that approximates the distance between predicted and observed pollutant concentration distributions to rapidly compute the likelihood probability. The approach adopts a multi‐model strategy to mitigate the accumulation of errors, particularly those arising from the recursive prediction steps across multiple time intervals, ensuring the reliability of predictions over extended periods. The proposed framework is implemented on graphics processing units (GPUs), enabling scalable computations for real‐world applications and rapid decision making. Through extensive numerical experiments, we demonstrate the suggested method's effectiveness in accurately estimating pollution source parameters, including location, emission rate, and duration, using synthetic observational data. Sensitivity analyses further explore the impact of observational horizons and sampling on solution convergence and accuracy. Numerical results demonstrate robust performances and computational efficiency compared to the conventional approach, particularly in scenarios with limited computational resources and observations availability.

Bayesian Markov-chain Monte Carlo (McMC) techniques are increasingly being used in geophysical estimation of hydrogeologic processes due to their ability to produce multiple estimates that enable comprehensive assessment of uncertainty. Standard McMC sampling methods can, however, become computationally intractable for spatially distributed, high-dimensional problems. We have developed a novel basis-constrained Bayesian McMC difference inversion framework for time-lapse geophysical imaging. The strategy parameterizes the Bayesian inversion model space in terms of sparse, hydrologic-process-tuned bases, leading to dimensionality reduction while accounting for the physics of the target hydrologic process. We evaluate the algorithm on cross-borehole electrical resistivity tomography (ERT) field data acquired during a heat-tracer experiment. We validate the ERT-estimated temperatures with direct temperature measurements at two locations on the ERT plane. We also perform the inversions using the conventional smoothness-constrained inversion (SCI). Our approach estimates the heat plumes without excessive smoothing in contrast with the SCI thermograms. We capture most of the validation temperatures within the 90% confidence interval of the mean. Accounting for the physics of the target process allows the detection of small temperature changes that are undetectable by the SCI. Performing the inversion in the reduced-dimensional model space results in significant gains in computational cost.

BackgroundTranslating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made.ResultsWe compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogenous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations.ConclusionWe present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.

This paper develops a Bayesian inverse modelling framework for the in-situ characterisation of walls' thermal performance in the presence of thermal anomalies subject to uncertainty. For any given wall, the proposed framework uses in-situ contact measurements of temperature and heat flux in order to approximate the (posterior) distribution of a set of parameters which are inputs of a 3D heat transfer model of the wall that accounts for the presence of unknown anomalies. The set of inputs that we infer include (i) the geometry of the thermal anomaly as well was its material properties, (ii) the as-built thermophysical properties of the clear part (i.e. without anomaly) of the wall (iii) surface resistances and (iv) modelling errors that arise from unaccounted sources of uncertainty in the boundary conditions. The geometry of the unknown thermal anomaly is parameterised with a level-set function that is inferred within the proposed Bayesian approach. In order to incorporate prior statistical information of the thermal anomaly, a Gaussian process conditioned on measurements from thermal images is employed to build a prior on the level-set function. The posterior distribution of inferred inputs is approximated via the implementation of an Ensemble Kalman Inversion algorithm that provides stable and accurate approximations of the posterior. This paper also proposes a methodology that uses the inferred 3D model to derive a thermally equivalent 1D model of the wall that is suitable for its integration with existing building energy performance software. The proposed inverse modelling technique is experimentally validated by characterising the thermal performance of an insulation panel in the presence of a thermal anomaly. Our computations show that the proposed approach produces a 3D model that accurately describes thermal performance, and a derived equivalent 1D model that effectively reproduces the dynamic thermal performance of the insulation panel in the presence of the thermal anomaly.

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

Despite their apparent high dimensionality, spatially distributed reservoir properties can often be compactly (sparsely) described in a properly designed basis. Hence estimation of high-dimensional reservoir flow properties from dynamic performance data, a.k.a. history matching, can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models. Sparse inverse problems have been mainly formulated as a deterministic inverse problem. Given the uncertainty in describing the reservoir properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion framework to enable uncertainty quantification. We use sparse geologic dictionaries to compactly represent uncertain reservoir properties and develop a sparse Bayesian approach for effective data integration and uncertainty quantification. In formulating the Bayesian inversion, commonly used Gaussian distributions are not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, Laplace (or double exponential) probability distributions are appropriate for representing sparse parameters. However, combining Laplace priors with frequently used Gaussian likelihood functions leads to neither Laplace nor Gaussian posterior distributions, thereby complicating the analytical characterization of the posterior distribution. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors, and then, as a practical approximation, use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to sample from the derived posterior distribution for uncertainty quantification. The Sparse RML (SpRML) realizations are approximate samples from the posterior distribution and provide a mechanism for assessing the uncertainty in the calibrated reservoir model with a relatively modest computational complexity. We demonstrate the suitability and effectiveness of the proposed SpRML formulation with a synthetic dataset and the model adapted from the PUNQ-S3 benchmark reservoir.

An autoregressive moving average (ARMA) is a time series model that is applied in everyday life for pattern recognition and forecasting. The ARMA model contains a noise which is assumed to have a specific distribution. The noise is often considered to have a Gaussian distribution. However in applications, the noise is sometimes found that does not have a Gaussian distribution. The first objective is to develop the ARMA model in which noise has a Laplacian distribution. The second objective is to estimate the parameters of the ARMA model. The ARMA model parameters include ARMA model orders, ARMA model coefficients, and noise variance. The parameter estimation of the ARMA model is carried out in the Bayesian framework. In the Bayesian framework, the ARMA model parameters are treated as a variable that has a prior distribution. The prior distribution for the ARMA model parameters is combined with the likelihood function for the data to get the posterior distribution for the parameter. The posterior distribution for parameters has a complex form so that the Bayes estimator cannot be determined analytically. The reversible jump Markov chain Monte Carlo (MCMC) algorithm was adopted to determine the Bayes estimator. The first result, the ARMA model can be developed by assuming Laplacian distribution noise. The second result, the performance of the algorithm was tested using simulation studies. The simulation shows that the reversible jump MCMC algorithm can estimate the parameters of the ARMA model correctly.

Positron Emission Tomography (PET) is a valuable imaging method for studying molecular-level processes in the body, such as hyperphosphorylated tau (p-tau) protein aggregates, a hallmark of several neurodegenerative diseases including Alzheimer's disease. P-tau density and cerebral perfusion can be quantified from PET data using tracer kinetic modeling techniques. However, noise in PET images leads to uncertainty in the estimated kinetic parameters. This can be quantified in a Bayesian framework by the posterior distribution of kinetic parameters given PET measurements. Markov Chain Monte Carlo (MCMC) techniques can be employed to estimate the posterior distribution, although with significant computational needs. In this paper, we propose to leverage deep learning inference efficiency to infer the posterior distribution. A novel approach using denoising diffusion probabilistic model (DDPM) is introduced. The performance of the proposed method was evaluated on a [18F]MK6240 study and compared to an MCMC method. Our approach offered significant reduction in computation time (over 30 times faster than MCMC) and consistently predicted accurate (< 0.8 % mean error) and precise (< 5.77 % standard deviation error) posterior distributions.

Binarization of gray scale document images is one of the most important steps in automatic document image processing. In this paper, we present a two-stage document image binarization approach, which includes a top-down region-based binarization at the first stage and a neural network based binarization technique for the problematic blocks at the second stage after a feedback checking. Our two-stage approach is particularly effective for binarizing text images of highlighted or marked text. The region-based binarization method is fast and suitable for processing large document images. However, the block effect and regional edge noise are two unavoidable problems resulting in poor character segmentation and recognition. The neural network based classifier can achieve good performance in two-class classification problem such as the binarization of gray level document images. However, it is computationally costly. In our two-stage binarization approach, the feedback criteria are employed to keep the well binarized blocks from the first stage binarization and to re-binarize the problematic blocks at the second stage using the neural network binarizer to improve the character segmentation quality. Experimental results on a number of document images show that our two-stage binarization approach performs better than the single-stage binarization techniques tested in terms of character segmentation quality and computational cost.

Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non‐linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic framework, in which uncertainty is represented by a so‐called posterior probability distribution. Recently, variational inference has emerged as an efficient method to estimate Bayesian solutions. By seeking the closest approximation to the posterior distribution within any chosen family of distributions, variational inference yields a fully probabilistic solution. It is important to define expressive variational families so that the posterior distribution can be represented accurately. We introduce boosting variational inference (BVI) as a computationally efficient means to construct a flexible approximating family comprising all possible finite mixtures of simpler component distributions. We use Gaussian mixture components due to their fully parametric nature and the ease with which they can be optimized. We apply BVI to seismic travel time tomography and full waveform inversion, comparing its performance with other methods of solution. The results demonstrate that BVI achieves reasonable efficiency and accuracy while enabling the construction of a fully analytic expression for the posterior distribution. Samples that represent major components of uncertainty in the solution can be obtained analytically from each mixture component. We demonstrate that these samples can be used to solve an interrogation problem: to assess the size of a subsurface target structure. To the best of our knowledge, this is the first method in geophysics that provides both analytic and reasonably accurate probabilistic solutions to fully non‐linear, high‐dimensional Bayesian full waveform inversion problems.

The Bayesian framework is commonly used to quantify uncertainty in seismic inversion. To perform Bayesian inference, Markov chain Monte Carlo (MCMC) algorithms are regarded as the gold standard technique for sampling from the posterior probability distribution. Consistent MCMC methods have trouble for complex, high-dimensional models, and most methods scale poorly to large datasets, such as those arising in seismic inversion. As an alternative, approximate MCMC methods based on unadjusted Langevin dynamics offer scalability and more rapid sampling at the cost of biased inference. However, when assessing the quality of approximate MCMC samples for characterizing the posterior distribution, most diagnostics fail to account for these biases. In this work, we introduce the kernel Stein discrepancy (KSD) as a diagnostic tool to determine the convergence of MCMC samples for Bayesian seismic inversion. We demonstrate the use of the KSD for measuring sample quality and selecting the optimal Langevin MCMC algorithm for two Gaussian Bayesian inference problems.

&amp;lt;p&amp;gt;Corresponding author: PhD student RV Chiritescu chiritescu.robert.valentin@gmail.com&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;&amp;amp;#160;&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Abstract:&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Air pollution in general and urban air pollution in particular have significant influences on atmosphere composition and hence on climate, environment, and human health. Although ground-based measurements have been performed for some decades and many observational studies were reported, information on air quality in some areas in East Europe are sparsely distributed. Romania represents the largest country at the crossroads of Central, Southeastern and Eastern Europe, and experience rapid economic growth since 2000s. It has a terrain distributed relatively equally between mountains, hills, and plains, and various regional climates (from alpine climate, to cold or wet warm continental, to warm oceanic due to proximity of Black Sea, in Koeppen classification). Various levels of development generate more by-products, including air pollution, deteriorating therefore the air quality at regional levels. Meteorology and topography also may influence the air pollution.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;The aim of present study was to comparatively assess the air pollution levels in 15 urban area spread out over Romania in 2019 and 2020, as the first pandemic year of COVID-19. The selected cities have different level of economic development, have various climate and topographic conditions, and they are expected to be impacted by manifold pollution sources. A special attention was paid to the evaluation of the impact of different levels of social restrictions that were taken in order to diminish the spread of SARS-CoV-2 virus.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Using the ground-based measurements from the Romanian National Air Quality Network, two observational data sets were constructed with particulate matter with an aerodynamic diameter below 10&amp;amp;#160;&amp;amp;#956;m (PM&amp;lt;sub&amp;gt;10&amp;lt;/sub&amp;gt;) and below 2.5&amp;amp;#160;&amp;amp;#956;m (PM&amp;lt;sub&amp;gt;2.5&amp;lt;/sub&amp;gt;) and with major gaseous air pollutants (CO, NO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, SO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, O&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;) mass concentrations for 2019 and 2020. Air pollutants variations were statistical analyzed for each season for each site.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;The largest contributor to the pollution was Bucharest, the most developed city. Lowest air pollution levels were measured during the lockdown period in spring, as main traffic and non-essential activities were severely restricted. The reductions of air pollution mass concentrations due to the imposed social restrictions were found to be urban area-dependent.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Outcomes of present research contribute to scientific knowledge regarding temporal and spatial variation of major air pollutants at the country scale, can help for identification of air pollution sources and in air quality modeling at urban scale.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;&amp;amp;#160;&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Acknowledgment&amp;lt;/strong&amp;gt;&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;The research leading to these results has received funding from the NO Grants 2014-2021, under Project contract no. 31/2020, EEA-RO-NO-2019-0423 project. Data regarding ground-based air pollutants and local meteorology were extracted from the public available Romanian National Air Quality Database, www.calitateaer.ro, last accessed in December 2021. BM was supported by the University of Bucharest, PhD research grant.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;&amp;amp;#160;&amp;lt;/p&amp;gt;

Occupational exposure assessment is important in preventing occupational coal worker’s diseases. Methods have been proposed to assess compliance with exposure limits which aim to protect workers from developing diseases. A Bayesian framework with informative prior distribution obtained from historical or expert judgements has been highly recommended for compliance testing. The compliance testing is assessed against the occupational exposure limits (OEL) and categorization of the exposure, ranging from very highly controlled to very poorly controlled exposure groups. This study used a Bayesian framework from historical and expert elicitation data to compare the posterior probabilities of the 95th percentile (P95) of the coal dust exposures to improve compliance assessment and decision-making. A total of 10 job titles were included in this study. Bayesian framework with Markov chain Monte Carlo (MCMC) simulation was used to draw a full posterior probability of finding a job title to an exposure category. A modified IDEA (“Investigate”, “Discuss”, “Estimate”, and “Aggregate”) technique was used to conduct expert elicitation. The experts were asked to give their subjective probabilities of finding coal dust exposure of a job title in each of the exposure categories. Sensitivity analysis was done for parameter space to check for misclassification of exposures. There were more than 98% probabilities of the P95 exposure being found in the poorly controlled exposure group when using expert judgments. Historical data and non-informative prior tend to show a lower probability of finding the P95 in higher exposure categories in some titles unlike expert judgments. Expert judgements tend to show some similarity in findings with historical data. We recommend the use of expert judgements in occupational risk assessment as prior information before a decision is made on current exposure when historical data are unavailable or scarce.

Air pollution is responsible for various health issues, including respiratory and cardiovascular diseases, among individuals. However, previous studies have not successfully identified the sources of air pollution that contribute to the acceleration of climate change. To address this gap, a novel approach known as the Adaptive Exponential Sigmoid Fuzzy Tsallis Entropy Interference System (AES-FTEIS) is proposed for identifying air pollution sources. Datasets from remote sensing and ground-level air pollution measurements are collected, temporally aligned using the Prior Distribution Regularized Kalman Filter (PDRKF), and imputed using Cross-Entropy Minimization Spline Interpolation (CEMSI). Additionally, aerosol particles such as PM2.5 and PM10 are extracted from the dataset and incorporated into the analysis. Subsequently, the data are organized by location and time using Transfer Entropy Spectral Clustering (TESC), and their correlation are analysed using Spearman Rank Correlation (SRC). An exploratory data analysis is conducted on the time-based grouped results through Box plots, leading to feature extraction. Finally, the AES-FTEIS is utilized to identify the pollution sources based on the levels of aerosol particle concentrations. The experimental results show that the proposed WOLSTM-ASLRCNN classifier achieves 97.56% of accuracy and 98.5% of precision, outperforming existing models such as CNN (95.3%), LSTM (93.84%), GRU (92.57%), and RNN (89.66%). The proposed TESC clustering method obtained a silhouette score of 0.9721, higher than SC (0.9687), AC (0.9428), HC (0.9271) and KMC (0.9087). Moreover, the AES-FTEIS source identification approach reduced the rule generation time to 1483 ms, demonstrating the effectiveness of the proposed framework.

A Bayesian parameter estimation method applied to a marine ecosystem model for the coastal Gulf of Alaska