Bidirectional machine learning-assisted sensitivity-based stochastic searching approach for groundwater DNAPL source characterization.

In this study, we designed a machine learning-based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input-output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input-output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD-PSO-MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD-PSO-MC inversion outputs was more precise than that obtained using the multichain MCMC approach.

Optimal design of groundwater pollution monitoring network based on a back-propagation neural network surrogate model and grey wolf optimizer algorithm under uncertainty.

In the optimal design of groundwater pollution monitoring network (GPMN), the uncertainty of the simulation model always affects the reliability of the monitoring network design when applying simulation-optimization methods. To address this issue, in the present study, we focused on the uncertainty of the pollution source intensity and hydraulic conductivity. In particular, we utilized simulation-optimization and Monte Carlo methods to determine the optimal layout scheme for monitoring wells under these uncertainty conditions. However, there is often a substantial computational load incurred due to multiple calls to the simulation model. Hence, we employed a back-propagation neural network (BPNN) to develop a surrogate model, which could substantially reduce the computational load. We considered the dynamic pollution plume migration process in the optimal design of the GPMN. Consequently, we formulated a long-term GPMN optimization model under uncertainty conditions with the aim of maximizing the pollution monitoring accuracy for each yearly period. The spatial moment method was used to measure the approximation degree between the pollution plume interpolated for the monitoring network and the actual plume, which could effectively evaluate the superior monitoring accuracy. Traditional methods are easily trapped in local optima when solving the optimization model. To overcome this limitation, we used the grey wolf optimizer (GWO) algorithm. The GWO algorithm has been found to be effective in avoiding local optima and in exploring the search space more effectively, especially when dealing with complex optimization problems. A hypothetical example was designed for evaluating the effectiveness of our method. The results indicated that the BPNN surrogate model could effectively fit the input-output relationship from the simulation model, as well as significantly reduce the computational load. The GWO algorithm effectively solved the optimization model and improved the solution accuracy. The pollution plume distribution in each monitoring yearly period could be accurately characterized by the optimized monitoring network. Thus, combining the simulation-optimization method with the Monte Carlo method effectively addressed the optimal monitoring network design problem under uncertainty.

Review of machine learning-based surrogate models of groundwater contaminant modeling.

Heavy computational load inhibits the application of groundwater contaminant numerical model to groundwater pollution source identification, remediation design, and uncertainty analysis, since a large number of model runs are required for these applications. Machine learning-based surrogate models are an effective approach to enhance the efficiency of the numerical models, and have recently attracted considerable attention in the field of groundwater contaminant modeling. Here, we review 120 research articles on machine learning-based surrogate models for groundwater contaminant modeling that were published between 1994 and 2022. We outline the state of the art method, identify the most significant research challenges, and suggest potential future directions. The six major applications of machine learning-based surrogate models are groundwater pollution source identification, groundwater remediation design, coastal aquifer management, uncertainty analysis of groundwater, groundwater monitoring network design, and groundwater transport parameters inversion. Together, these account for more than 90% of the studies we review. Latin hypercube sampling (LHS) is the most widely used sampling method, and artificial neural networks (ANNs) and Kriging are the two most widely used methods for constructing surrogate model. No method is universally superior, the advantages and disadvantages of different methods, as well as the applicability of these methods for different application purposes of groundwater contaminant modeling were analyzed. Some recommendations on the method selection for various application fields are given based on the reviews and experiences. Based on our review of the state-of-the-art, we suggest several future research directions to enhance the feasibility of the machine learning-based surrogate models of groundwater contaminant modeling: the alleviation of the curse of dimensionality, enhancing transferability, practical applications for real case studies, multi-source dada fusion, and real-time monitoring and prediction.

Simultaneous identification of groundwater contaminant source and hydraulic parameters based on multilayer perceptron and flying foxes optimization.

Groundwater contaminant source identification (GCSI) has practical significance for groundwater remediation and liability. However, when applying the simulation-optimization method to precisely solve GCSI, the optimization model inevitably encounters the problems of high-dimensional unknown variables to identify, which might increase the nonlinearity. In particular, to solve such optimization models, the well-known heuristic optimization algorithms might fall into a local optimum, resulting in low accuracy of inverse results. For this reason, this paper proposes a novel optimization algorithm, namely, the flying foxes optimization (FFO) to solve the optimization model. We perform simultaneous identification of the release history of groundwater pollution sources and hydraulic conductivity and compare the results with those of the traditional genetic algorithm. In addition, to alleviate the massive computational load caused by the frequent invocation of the simulation model when solving the optimization model, we utilized the multilayer perception (MLP) to establish a surrogate model of the simulation model and compared it with the method of backpropagation algorithm (BP). The results show that the average relative error of the results of FFO is 2.12%, significantly outperforming the genetic algorithm (GA); the surrogate model of MLP can replace the simulation model for calculation with fitting accuracy of more than 0.999, which is better than the commonly used surrogate model of BP.

Simultaneous identification of groundwater pollution source and important hydrogeological parameters considering the noise uncertainty of observational data.

Groundwater pollution identification is an inverse problem. When solving the inverse problem using regular methods such as simulation-optimization or stochastic statistical approaches, requires repeatedly calling the simulation model for forward calculations, which is a time-consuming process. Currently, the problem is often solved by building a surrogate model for the simulation model. However, the surrogate model is only an intermediate step in regular methods, such as the simulation-optimization method that also require the creation and solution of an optimization model with the minimum objective function, which adds complexity and time to the inversion task and presents an obstacle to achieving fast inversion. In the present study, the extreme gradient boosting (XGBoost) method and the back propagation neural network (BPNN) method were used to directly establish the mapping relationships between the output and input of the simulation model, which could directly obtain the inversion results of the variables to be identified (pollution sources release histories and hydraulic conductivities) based on actual observational data for fast inversion. In addition, to consider the uncertainty of observation data noise, the inversion accuracy of the two machine learning methods was compared, and the method with higher precision was selected for the uncertainty analysis. The results indicated that both the BPNN and XGBoost methods could perform inversion tasks well, with a mean absolute percentage error (MAPE) of 4.15% and 1.39%, respectively. Using the BPNN, with better accuracy for uncertainty analysis, when the maximum probabilistic density value was selected as the inversion result, the MAPE was 2.13%. We obtained the inversion results under different confidence levels and decision makers of groundwater pollution prevention and control can choose different inversion results according to their needs.

Groundwater contamination source identification based on Sobol sequences-based sparrow search algorithm with a BiLSTM surrogate model.

In the traditional linked simulation-optimization method, solving the optimization model requires massive invoking of the groundwater numerical simulation model, which causes a huge computational load. In the present study, a surrogate model of the origin simulation model was developed using a bidirectional long and short-term memory neural network method (BiLSTM). Compared with the surrogate models built by shallow learning methods (BP neural network) and traditional LSTM methods, the surrogate model built by BiLSTM has higher accuracy and better generalization performance while reducing the computational load. The BiLSTM surrogate model had the highest R2 of the three with 0.9910 and the lowest RMSE with 3.7732 g/d. The BiLSTM surrogate model was linked to the optimization model and solved using the sparrow search algorithm based on Sobol sequences (SSAS). SSAS enhances the diversity of the initial population of sparrows by introducing Sobol sequences and introduces nonlinear inertia weights to control the search range and search efficiency. Compared with SSA, SSAS has stronger global search ability and faster search efficiency. And SSAS identifies the contamination source location and release intensity stably and reliably. The average relative error of SSAS for the identification of source location is 9.4%, and the average relative error for the identification of source intensity is 1.83%, which are both lower than that of SSA at 11.12% and 3.03%. This study also applied the Cholesky decomposition method to establish a Gaussian field for hydraulic conductivity to evaluate the feasibility of the simulation-optimization method.

An electrochemical immunosensor for the detection of Glypican-3 based on enzymatic ferrocene-tyramine deposition reaction.

An ultrasensitive electrochemical immunosensor based on signal amplification of the deposition of the electroactive ferrocene-tyramine (Fc-Tyr) molecule, catalyzed by horseradish peroxidase (HRP), was constructed for the detection of the liver cancer marker Glypican-3 (GPC3). Functional electroactive molecule Fc-Tyr is reported to exhibit both the enzymatic cascade catalytic activity of tyramine signal amplification (TSA) and the excellent redox properties of ferrocene. In terms of design, the low matrix effects inherent in using the magnetic bead platforms, a quasi-homogeneous system, allowed capturing the target protein GPC3 without sample pretreatment, and loading HRP to trigger the TSA, which induced a large amount of Fc-Tyr deposited on the electrode surface layer by layer as a signal probe for the detection of GPC3. The concept of Fc-Tyr as an electroactive label was validated, GPC3 biosensor exhibited high selectivity and sensitivity to GPC3 in the range of 0.1 ng mL-1-1 µg mL-1. Finally, the sensor was used simultaneously with ELISA to assess GPC3 levels in the serum of clinical liver cancer patients, and the results showed consistency, with a recovery of 98.33-105.35% and a relative standard deviation (RSD) of 4.38-8.18%, providing a theoretical basis for achieving portable, rapid and point of care testing (POCT) of tumor markers.

Identification of light nonaqueous phase liquid groundwater contamination source based on empirical mode decomposition and deep learning.

The simulation optimization method was used to the identification of light nonaqueous phase liquid (LNAPL) groundwater contamination source (GCS) with the help of a hypothetical case in this study. When applying the simulation optimization method to identify GCS, it was a common technical means to establish surrogate model for the simulation model to participate in the iterative calculation to reduce the calculation load and calculation time. However, it was difficult for a single modeling method to establish surrogate model with high accuracy for the LNAPL contamination multiphase flow simulation model (MFSM). To give full play to advantages of single surrogate model and improve the accuracy of the surrogate model to the MFSM, a combination of deep belief neural network (DBNN) and long short-term memory (LSTM) neural network was used to establish artificial intelligence ensemble surrogate model (AIESM) for the MFSM. At the same time, to reduce the influence of noise in observed concentrations on the accuracy of the identification results, empirical mode decomposition (EMD) and wavelet analysis methods were used to denoise the observed concentrations, and their noise reduction effects were compared. The observed concentrations with better noise reduction effect and the observed concentrations without denoising were used to construct the objective function, and constraints of the optimization model were determined meanwhile. Then, the objective function and the constraints were integrated to build the optimization model to identify GCS and simulation model parameters. Applying the AIESM instead of the MFSM to embed in the optimization model and participate in the iterative calculation. Finally, the genetic algorithm (GA) was used to solve the optimization model to obtain the identification results of GCS and simulation model parameters. The results showed that compared with the single DBNN and LSTM surrogate models, AIESM obtained the highest accuracy and could replace the MFSM to participate in the iterative calculation, thereby reducing the calculation load and calculation time by more than 99%. Comparing with the wavelet analysis, EMD could reduce the noise in the concentrations more effectively, improved the accuracy of the approximated concentrations to the actual values, and increased the accuracy of the GCSs identification results by 1.45%.

Stochastic simulation of seawater intrusion in the Longkou area of China based on the Monte Carlo method.

Seawater intrusion is a common groundwater pollution problem, which has a great impact on ecological environment and economic development. In this paper, a numerical simulation model of variable density groundwater was constructed to simulate and predict the future seawater intrusion in Longkou city, Shandong Province of China. The influence of the sensitive parameter uncertainty of the model on the simulation results was evaluated by using the Monte Carlo method. In order to reduce the computational load from repeatedly calling the simulation model, the surrogate model was established by using the support vector regression (SVR) method. After training, the correlation coefficient R2 of the input-output relationship between the SVR surrogate model and the seawater intrusion simulation model reached 0.9957, with an average relative error of 0.2%, indicating that the surrogate model has a high fitting accuracy. Stochastic simulations of seawater intrusion showed that the seawater intrusion in the Longkou area will gradually aggravate at a slow rate, and the increase of seawater intrusion in the study area after 30 years was expected to range from - 6.03% to 7.37% at the 80% confidence level.

In Situ Silver-Based Electrochemical Oncolytic Bioreactor.

In this study, it is shown for the first time that a reduced graphene oxide (rGO) carrier has a 20-fold higher catalysis rate than graphene oxide in Ag+ reduction. Based on this, a tumor microenvironment-enabled in situ silver-based electrochemical oncolytic bioreactor (SEOB) which switched Ag+ prodrugs into in situ therapeutic silver nanoparticles with and above 95% transition rate is constructed to inhibit the growths of various tumors. In this SEOB-enabled intratumoral nanosynthetic medicine, intratumoral H2 O2 and rGO act as the reductant and the catalyst, respectively. Chelation of aptamers to the SEOB-unlocked prodrugs increases the production of silver nanoparticles in tumor cells, especially in the presence of Vitamin C, which is broken down in tumor cells to supply massive amounts of H2 O2 . Consequently, apoptosis and pyroptosis are induced to cooperatively contribute to the considerably-elevated anti-tumor effects on subcutaneous HepG2 and A549 tumors and orthotopic implanted HepG2 tumors in livers of nude mice. The specific aptamer targeting and intratumoral silver nanoparticle production guarantee excellent biosafety since it fails to elicit tissue damages in monkeys, which greatly increases the clinical translation potential of the SEOB system.

Comparative analysis of groundwater contaminant sources identification based on simulation optimization and ensemble Kalman filter.

The location and release history of groundwater contaminant sources (GCSs) are usually unknown after groundwater contamination is detected, thereby greatly hindering the design of contamination remediation schemes and contamination risk assessments. Many previous studies have used prior information such as the observed contaminant concentrations (OCC) to obtain information of GCSs, and various methods have been proposed for identifying GCSs, including simulation optimization (S/O) and ensemble Kalman filter (EnKF) methods. For the first time, the present study compared the suitability of the S/O and EnKF methods for GCSs identification based on two case studies by specifically considering the calculation time and effectiveness of GCS identification. The results showed that EnKF could reduce the calculation time required by more than 62% compared with S/O. However, the time saved did not compensate for the poor accuracy of the GCSs identification results. When the simulated contaminant concentrations (SCC) were used for GCSs identification, the MRE of the identification results with the S/O and EnKF methods were 2.79% and 5.09% in case one, respectively, and were 4.75% and 6.72% in case two. When the OCC were used for GCSs identification, the MRE of the identification results with the S/O and EnKF methods were 27.77% and 110.74% in case one, respectively, and 27.53% and 60.61% in case two. The identification results obtained using the EnKF method were not credible and the superior performance of the S/O method was obvious, thereby indicating that the EnKF method is much less suitable for actual GCSs identification compared with the S/O method.

Recognition of a linear source contamination based on a mixed-integer stacked chaos gate recurrent unit neural network-hybrid sparrow search algorithm.

Groundwater contamination source recognition involves the recovery of contamination source time series release histories from observation data. In the present study, a linear source contamination recognition task was addressed. When using a simulation-optimization inverse framework to solve the recognition task, high calculated expense and high dimensional search space always hinder the task efficiency. Moreover, traditional surrogate methods face obstacle of handling with time-sequence data. Therefore, a novel stacked chaos gate recurrent unit (SCGRU) neural network was proposed as a surrogate model to precisely emulate the sequence to sequence mapping relationship of a high computational running simulation model. To address the challenge of high dimensional search, a mixed-integer programming strategy was employed to reduce the dimension of unknown variables. Furthermore, a hybrid sparrow search algorithm (HSSA) was implemented to alleviate being trapped into local optimum. In particular, the proposed SCGRU-HSSA framework was utilized to determine the length and release intensities during the stress period of a linear source. Based on the results obtained, the following conclusions were derived: (1) SCGRU can replace the origin simulation model with high accuracy and fast running speed; (2) when using chaos sine mapping and a Cauchy mutation strategy, the SSA escaped from the local optimum, improving the search efficiency of the recognition task; and (3) SCGRU-HSSA methodology is stable and reliable in recognizing features of linear source contamination.

Groundwater contamination source identification using improved differential evolution Markov chain algorithm.

The groundwater contamination source identification (GCSI) can provide important bases for the design of pollution remediation plans. The Bayesian theory is commonly used in the GCSI problem. Usually, we use the Markov chain Monte Carlo (MCMC) method to realize the Bayesian framework. However, due to the ill-posed nature of the GCSI and the system model's complexity, the conventional MCMC algorithm is time-consuming and has low accuracy. In this study, we proposed an adaptive mutation differential evolution Markov chain (AM-DEMC) algorithm. In this algorithm, the Kent mapping chaotic sequence method, combined with differential evolution (DE) algorithm, was used to generate the initial population. In the iteration process, we introduced a hybrid mutation strategy to generate the candidate vectors. Moreover, we adaptively adjust the essential parameter F of the AM-DEMC algorithm according to the individual fitness value. For further improving the efficiency of solving the GCSI problem, the Kriging method was used to establish a surrogate model to avoid the enormous computational load associated with the numerical simulation model. Finally, a hypothetical groundwater contamination case was given to verify the effectiveness of the AM-DEMC algorithm. The results indicated that the proposed AM-DEMC algorithm successfully identified the contamination sources' characteristics and simulation model's parameters. It also exhibited stronger search-ability and higher accuracy than the MCMC and DE-MC algorithms.

Simultaneous identification of groundwater contamination source and aquifer parameters with a new weighted-average wavelet variable-threshold denoising method.

This paper first proposed a parallel heuristic search strategy for simultaneous identification of groundwater contamination source and aquifer parameters. As identification results are influenced by many factors, such as noisy contamination concentration data, data denoising is necessary. The existing wavelet threshold denoising method has unavoidable shortcomings; therefore, this paper first proposed a new weighted-average wavelet variable-threshold denoising (WWVD) method to improve the denoising effect for concentration data, which further enhanced the subsequent identification accuracy. However, frequent calls to the simulation model could produce high computational cost during likelihood calculation. Hence, single surrogate model of the simulation model was developed to reduce cost; however, it presented limitation. Thus, this paper first developed a differential evolution-tabu search (DE-TS) hybrid algorithm to construct an optimal ensemble surrogate model, which assembled Gaussian process, kernel extreme learning machine, and support vector regression. The first proposed DE-TS algorithm also improved the approximation accuracy of surrogate model to simulation model. This paper first proposed and implemented a parallel heuristic search iterative process for simultaneous identification, and the identification results were obtained when the iteration process terminated. The accuracy and efficiency of these newly proposed approaches were tested through a hypothetical case. Results showed that the WWVD method not only improved the denoising effect for concentration data but also enhanced the subsequent identification accuracy. The OES model using DE-TS hybrid algorithm improved the approximation accuracy of surrogate model to simulation model, and the parallel heuristic search strategy is helpful for simultaneous identification of groundwater contamination source and aquifer parameters.

Identification of groundwater contamination sources and hydraulic parameters based on bayesian regularization deep neural network.

Simultaneous identification of various features of groundwater contamination sources and hydraulic parameters, such as hydraulic conductivities, can result in high-nonlinear inverse problem, which significantly hinders identification. A surrogate model was proposed to relieve computational burden caused by massive callings to simulation model in identification. However, shallow learning surrogate model may show limited fitting ability to high nonlinear problem. Thus, in this study, a simulation-optimization method based on Bayesian regularization deep neural network (BRDNN) surrogate model was proposed to efficiently solve high-nonlinear inverse problem. This method identified eight variables including locations and release intensities of two pollution sources and hydraulic conductivities of two partitions. Three hidden layers were employed in the BRDNN surrogate model, which profoundly improved the fitting capacity of nonlinear mapping relationship to the simulation model. Furthermore, Bayesian regularization was applied in the training process of neural network to solve overfitting problem. The results indicated that BRDNN was capable of establishing input-output interplay of high nonlinear inverse problem, which substantially reduced computational cost while ensuring a desirable level of accuracy. The utility of simulation-optimization on the basis of BRDNN surrogate model provided stable and reliable inversion results for groundwater contamination sources and hydraulic parameters.

Groundwater contaminant source characterization with simulation model parameter estimation utilizing a heuristic search strategy based on the stochastic-simulation statistic method.

In this study, a heuristic search strategy based on stochastic-simulation statistic (S-S) approach was developed for groundwater contaminant source characterization (GCSC) with simulation model parameter estimation. First, single kernel extreme learning machine (KELM) was built as surrogate system of the numerical simulation model to reduce huge computational load while evaluating the likelihood. However, compared with single KELM, multi-kernel extreme learning machine (MK-ELM) is more flexible for large amounts of data. To improve the approximation accuracy of the surrogate system to numerical simulation model, the MK-ELM surrogate system was first developed. Then, a heuristic search iterative process was first designed for GCSC with simulation model parameter estimation. The self-adaptive sampling method was proved to be more efficient than one-time sampling. Based on this idea, a self-adaptive feedback correction step was inserted into the heuristic search iterative process to ameliorate the training samples of the surrogate system in the posterior region, which further improved accuracy of simultaneous identification results. Finally, the identification results were obtained when the iteration terminated. The proposed approaches were tested in a hypothetical case study. It was shown that the heuristic search strategy can be used to assist in groundwater contaminant source characterization with simulation model parameter estimation.

Groundwater contamination sources identification based on kernel extreme learning machine and its effect due to wavelet denoising technique.

Measurements of contaminant concentrations inevitably contain noise because of accidental and systematic errors. However, groundwater contamination sources identification (GCSI) is highly dependent on the data measurements, which directly affect the accuracy of the identification results. Thus, in the present study, the wavelet hierarchical threshold denoising method was employed to denoise concentration measurements and the denoised measurements were then used for GCSI. A 0-1 mixed-integer nonlinear programming optimization model (0-1 MINLP) based on a kernel extreme learning machine (KELM) was applied to identify the location and release history of a contamination source. The results showed the following. (1) The wavelet hierarchical threshold denoising method was not very effective when applied to concentration measurements observed every 2 months (the number of measurements is small and relatively discrete) compared with those obtained every 2 days (the number of measurements is large and relatively continuous). (2) When the concentration measurements containing noise were employed for GCSI, the identifications results were further from the true values when the measurements contained more noise. The approximation of the identification results to the true values improved when the denoised concentration measurements were employed for GCSI. (3) The 0-1 MINLP based on the surrogate KELM model could simultaneously identify the location and release history of contamination sources, as well reducing the computational load and decreasing the calculation time by 96.5% when solving the 0-1 MINLP.

Parallel heuristic search strategy based on a Bayesian approach for simultaneous recognition of contaminant sources and aquifer parameters at DNAPL-contaminated sites.

In this study, we develop a parallel heuristic search strategy based on a Bayesian approach for simultaneously recognizing groundwater contaminant sources and aquifer parameters (unknown variables) at sites contaminated with dense non-aqueous phase liquids (DNAPLs). The parallel search strategy is time-consuming because thousands of simulation models must run in order to calculate the likelihood. Various stand-alone surrogate systems for the simulation models have been established, but they also have unavoidable limitations. Thus, we develop an optimal combined surrogate system by combining Gaussian process, kernel extreme learning machine, and support vector regression methods using a differential evolution algorithm with a variable mutation rate based on the rand-to-best/1/bin strategy, thereby improving the approximation accuracy of the surrogate system to the simulation model and significantly decreasing the high computational cost. Utilizing the optimal combined surrogate system reduced the CPU time by more than 400 times. In the iterative parallel heuristic search process, each round of iteration involves determining the candidate points and state transitions. The Monte Carlo approach is used widely for selecting candidate point, but this approach does not readily converge to the posterior distribution for unknown variables when the probability density function types are complex with weak search ergodicity. In order to improve the search ergodicity, we develop a particle swarm optimization algorithm with a non-linear decreasing inertia weight and Metropolis criterion, which is more suitable for unknown variables with complex probability density functions. The recognition results are obtained simultaneously when the iterative process terminates. We assess our proposed approaches based on a hypothetical case study at a three-dimensional site contaminated with DNAPLs. The results demonstrate that the parallel heuristic search strategy is helpful for the simultaneous recognition of DNAPL contaminant sources in groundwater and aquifer parameters.