Estimation of effective connectivity using multi-layer perceptron artificial neural network

Neurophysiological dynamics of metacontrol states: EEG insights into conflict regulation

Understanding the neural mechanisms underlying metacontrol and conflict regulation is crucial for insights into cognitive flexibility and persistence. This study employed electroencephalography (EEG), EEG-beamforming and directed connectivity analyses to explore how varying metacontrol states influence conflict regulation at a neurophysiological level. Metacontrol states were manipulated by altering the frequency of congruent and incongruent trials across experimental blocks in a modified flanker task, and both behavioral and electrophysiological measures were analyzed. Behavioral data confirmed the experimental manipulation's efficacy, showing an increase in persistence bias and a reduction in flexibility bias during increased conflict regulation. Electrophysiologically, theta band activity paralleled the behavioral data, suggesting that theta oscillations reflect the mismatch between expected metacontrol bias and actual task demands. Alpha and beta band dynamics differed across experimental blocks, though these changes did not directly mirror behavioral effects. Post-response alpha and beta activity were more pronounced in persistence-biased states, indicating a neural reset mechanism preparing for future cognitive demands. By using a novel artificial neural networks method, directed connectivity analyses revealed enhanced inter-regional communication during persistence states, suggesting stronger top-down control and sensorimotor integration. Overall, theta band activity was closely tied to metacontrol processes, while alpha and beta bands played a role in resetting the neural system for upcoming tasks. These findings provide a deeper understanding of the neural substrates involved in metacontrol and conflict monitoring, emphasizing the distinct roles of different frequency bands in these cognitive processes.

Neural mechanisms of adaptive behavior: Dissociating local cortical modulations and interregional communication patterns

Adaptive behavior is based on flexibly managing and integrating perceptual and motor processes, and the reconfiguration thereof. Such adaptive behavior is also relevant during inhibitory control. Although research has demonstrated local activity modulations in theta and alpha frequency bands during behavioral adaptation, the communication of brain regions is insufficiently studied. Examining directed connectivity between brain regions using a machine learning approach, a generally increased activity, but decreased connectivity within a temporo-occipital theta band network was revealed during the reconfiguration of perception-action associations during inhibitory control. Additionally, a fronto-occipital alpha-theta interplay yielded a decrease in directed connectivity during reconfiguration processes, which was associated with lower error rates in behavior. Thus, adaptive behavior relies on both local increases and decreases of activity depending on the frequency band, and concomitant decreases in communication between frontal and sensory cortices. The findings reframe common conceptualizations about how adaptive behavior is supported by neural processes.

Neural connectivity patterns explain why adolescents perceive the world as moving slow

That younger individuals perceive the world as moving slower than adults is a familiar phenomenon. Yet, it remains an open question why that is. Using event segmentation theory, electroencephalogram (EEG) beamforming and nonlinear causal relationship estimation using artificial neural network methods, we studied neural activity while adolescent and adult participants segmented a movie. We show when participants were instructed to segment a movie into meaningful units, adolescents partitioned incoming information into fewer encapsulated segments or episodes of longer duration than adults. Importantly, directed communication between medial frontal and lower-level perceptual areas and between occipito-temporal regions in specific neural oscillation spectrums explained behavioral differences between groups. Overall, the study reveals that a different organization of directed communication between brain regions and inefficient transmission of information between brain regions are key to understand why younger people perceive the world as moving slow.

Exploring Brain Effective Connectivity Networks Through Spatiotemporal Graph Convolutional Models

Learning brain effective connectivity networks (ECN) from functional magnetic resonance imaging (fMRI) data has gained much attention in recent years. With the successful applications of deep learning in numerous fields, several brain ECN learning methods based on deep learning have been reported in the literature. However, current methods ignore the deep temporal features of fMRI data and fail to fully employ the spatial topological relationship between brain regions. In this article, we propose a novel method for learning brain ECN based on spatiotemporal graph convolutional models (STGCM), named STGCMEC, in which we first adopt the temporal convolutional network to extract the deep temporal features of fMRI data and utilize the graph convolutional network to update the spatial features of each brain region by aggregating information from neighborhoods, which makes the features of brain regions more discriminative. Then, based on such features of brain regions, we design a joint loss function to guide STGCMEC to learn the brain ECN, which includes a task prediction loss and a graph regularization loss. The experimental results on a simulated dataset and a real Alzheimer's disease neuroimaging initiative (ADNI) dataset show that the proposed STGCMEC is able to better learn brain ECN compared with some state-of-the-art methods.

A Survey on Brain Effective Connectivity Network Learning

Human brain effective connectivity characterizes the causal effects of neural activities among different brain regions. Studies of brain effective connectivity networks (ECNs) for different populations contribute significantly to the understanding of the pathological mechanism associated with neuropsychiatric diseases and facilitate finding new brain network imaging markers for the early diagnosis and evaluation for the treatment of cerebral diseases. A deeper understanding of brain ECNs also greatly promotes brain-inspired artificial intelligence (AI) research in the context of brain-like neural networks and machine learning. Thus, how to picture and grasp deeper features of brain ECNs from functional magnetic resonance imaging (fMRI) data is currently an important and active research area of the human brain connectome. In this survey, we first show some typical applications and analyze existing challenging problems in learning brain ECNs from fMRI data. Second, we give a taxonomy of ECN learning methods from the perspective of computational science and describe some representative methods in each category. Third, we summarize commonly used evaluation metrics and conduct a performance comparison of several typical algorithms both on simulated and real datasets. Finally, we present the prospects and references for researchers engaged in learning ECNs.

Application of Visual Recognition Based on BP Neural Network in Architectural Design Optimization

In order to establish the mapping relationship between architectural design parameters and building performance and optimize architectural design parameters, an architectural design optimization method based on BP neural network is proposed. The selected main design parameters of building ventilation include spacing coefficient, air outlet area, and height from the bottom of the window sill to the ground. Take the comprehensive performance of building ventilation design as the main optimization objective to optimize the building design. First, nine groups of samples of building optimization design are obtained through uniform experimental design. Then, based on the architectural design sample data obtained by BP neural network training, the mapping relationship between architectural design parameters and building performance is established, and based on this mapping, the optimal design parameters of the building are calculated. The research results have a certain reference value for architectural design optimization.

Investigating the discrimination of linear and nonlinear effective connectivity patterns of EEG signals in children with Attention-Deficit/Hyperactivity Disorder and Typically Developing children

BACKGROUND

Analysis of effective connectivity among brain regions is an important key to decipher the mechanisms underlying neural disorders such as Attention Deficit Hyperactivity Disorder (ADHD). We previously introduced a new method, called nCREANN (nonlinear Causal Relationship Estimation by Artificial Neural Network), for estimating linear and nonlinear components of effective connectivity, and provided novel findings about effective connectivity of EEG signals of children with autism. Using the nCREANN method in the present study, we assessed effective connectivity patterns of ADHD children based on their EEG signals recorded during a visual attention task, and compared them with the aged-matched Typically Developing (TD) subjects.

METHOD

In addition to the nCREANN method for estimating linear and nonlinear aspects of effective connectivity, the direct Directed Transfer Function (dDTF) was utilized to extract the spectral information of connectivity patterns.

RESULTS

The dDTF results did not suggest a specific frequency band for distinguishing between the two groups, and different patterns of effective connectivity were observed in all bands. Both nCREANN and dDTF methods showed decreased connectivity between temporal/frontal and temporal/occipital regions, and increased connection between frontal/parietal regions in ADHDs than TDs. Furthermore, the nCREANN results showed more left-lateralized connections in ADHDs compared to the symmetric bilateral inter-hemispheric interactions in TDs. In addition, by fusion of linear and nonlinear connectivity measures of nCREANN method, we achieved an accuracy of 99% in classification of the two groups.

CONCLUSION

These findings emphasize the capability of nCREANN method to investigate the brain functioning of neural disorders and its strength in preciously distinguish between healthy and disordered subjects.

Granger causality test with nonlinear neural-network-based methods: Python package and simulation study

BACKGROUND AND OBJECTIVE

Causality defined by Granger in 1969 is a widely used concept, particularly in neuroscience and economics. As there is an increasing interest in nonlinear causality research, a Python package with a neural-network-based causality analysis approach was created. It allows performing causality tests using neural networks based on Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), or Multilayer Perceptron (MLP). The aim of this paper is to present the nonlinear method for causality analysis and the created Python package.

METHODS

The created functions with the autoregressive (AR) and Generalized Radial Basis Functions (GRBF) neural network models were tested on simulated signals in two cases: with nonlinear dependency and with absence of causality from Y to X signal. The train-test split (70/30) was used. Errors obtained on the test set were compared using the Wilcoxon signed-rank test to determine the presence of the causality. For the chosen model, the proposed method of study the change of causality over time was presented.

RESULTS

In the case when X was a polynomial of Y, nonlinear methods were able to detect the causality, while the AR model did not manage to indicate it. The best results (in terms of the prediction accuracy) were obtained for the MLP for the lag of 150 (MSE equal to 0.011, compared to 0.041 and 0.036 for AR and GRBF, respectively). When there was no causality between the signals, none of the proposed and AR models did indicate false causality, while it was detected by GRBF models in one case. Only the proposed models gave the expected results in each of the tested scenarios.

CONCLUSIONS

The proposed method appeared to be superior to the compared methods. They were able to detect non-linear causality, make accurate forecasting and not indicate false causality. The created package enables easy usage of neural networks to study the causal relationship between signals. The neural-networks-based approach is a suitable method that allows the detection of a nonlinear causal relationship, which cannot be detected by the classical Granger method. Unlike other similar tools, the package allows for the study of changes in causality over time.

A survey of brain network analysis by electroencephalographic signals

Brain network analysis is one efficient tool in exploring human brain diseases and can differentiate the alterations from comparative networks. The alterations account for time, mental states, tasks, individuals, and so forth. Furthermore, the changes determine the segregation and integration of functional networks that lead to network reorganization (or reconfiguration) to extend the neuroplasticity of the brain. Exploring related brain networks should be of interest that may provide roadmaps for brain research and clinical diagnosis. Recent electroencephalogram (EEG) studies have revealed the secrets of the brain networks and diseases (or disorders) within and between subjects and have provided instructive and promising suggestions and methods. This review summarized the corresponding algorithms that had been used to construct functional or effective networks on the scalp and cerebral cortex. We reviewed EEG network analysis that unveils more cognitive functions and neural disorders of the human and then explored the relationship between brain science and artificial intelligence which may fuel each other to accelerate their advances, and also discussed some innovations and future challenges in the end.

A fuzzy sensitivity analysis approach to estimate brain effective connectivity and its application to epileptic seizure detection

The brain is considered to be the most complicated organ in human body. Inferring and quantification of effective (causal) connectivity among regions of the brain is an important step in characterization of its complicated functions. The proposed method is comprised of modeling multivariate time series with Adaptive Neurofuzzy Inference System (ANFIS) and carrying out a sensitivity analysis using Fuzzy network parameters as a new approach to introduce a connectivity measure for detecting causal interactions between interactive input time series. The results of simulations indicate that this method is successful in detecting causal connectivity. After validating the performance of the proposed method on synthetic linear and nonlinear interconnected time series, it is applied to epileptic intracranial Electroencephalography (EEG) signals. The result of applying the proposed method on Freiburg epileptic intracranial EEG data recorded during seizure shows that the proposed method is capable of discriminating between the seizure and non-seizure states of the brain.

Complex networks and deep learning for EEG signal analysis

Electroencephalogram (EEG) signals acquired from brain can provide an effective representation of the human's physiological and pathological states. Up to now, much work has been conducted to study and analyze the EEG signals, aiming at spying the current states or the evolution characteristics of the complex brain system. Considering the complex interactions between different structural and functional brain regions, brain network has received a lot of attention and has made great progress in brain mechanism research. In addition, characterized by autonomous, multi-layer and diversified feature extraction, deep learning has provided an effective and feasible solution for solving complex classification problems in many fields, including brain state research. Both of them show strong ability in EEG signal analysis, but the combination of these two theories to solve the difficult classification problems based on EEG signals is still in its infancy. We here review the application of these two theories in EEG signal research, mainly involving brain-computer interface, neurological disorders and cognitive analysis. Furthermore, we also develop a framework combining recurrence plots and convolutional neural network to achieve fatigue driving recognition. The results demonstrate that complex networks and deep learning can effectively implement functional complementarity for better feature extraction and classification, especially in EEG signal analysis.

Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Square (OLS) estimation, a viable alternative is to use Artificial Neural Networks (ANNs) implemented in a simple structure with one input and one output layer and trained in a way such that the weights matrix corresponds to the matrix of VAR parameters. In this work, we introduce an ANN combined with SS models for the computation of GC. The ANN is trained through the Stochastic Gradient Descent L1 (SGD-L1) algorithm, and a cumulative penalty inspired from penalized regression is applied to the network weights to encourage sparsity. Simulating networks of coupled Gaussian systems, we show how the combination of ANNs and SGD-L1 allows to mitigate the strong reduction in accuracy of OLS identification in settings of low ratio between number of time series points and of VAR parameters. We also report how the performances in GC estimation are influenced by the number of iterations of gradient descent and by the learning rate used for training the ANN. We recommend using some specific combinations for these parameters to optimize the performance of GC estimation. Then, the performances of ANN and OLS are compared in terms of GC magnitude and statistical significance to highlight the potential of the new approach to reconstruct causal coupling strength and network topology even in challenging conditions of data paucity. The results highlight the importance of of a proper selection of regularization parameter which determines the degree of sparsity in the estimated network. Furthermore, we apply the two approaches to real data scenarios, to study the physiological network of brain and peripheral interactions in humans under different conditions of rest and mental stress, and the effects of the newly emerged concept of remote synchronization on the information exchanged in a ring of electronic oscillators. The results highlight how ANNs provide a mesoscopic description of the information exchanged in networks of multiple interacting physiological systems, preserving the most active causal interactions between cardiovascular, respiratory and brain systems. Moreover, ANNs can reconstruct the flow of directed information in a ring of oscillators whose statistical properties can be related to those of physiological networks.

Frequency-specific network effective connectivity: ERP analysis of recognition memory process by directed connectivity estimators

Human memory retrieval is one of the brain's most important, and least understood cognitive mechanisms. Traditionally, research on this aspect of memory has focused on the contributions of particular brain regions to recognition responses, but the interaction between regions may be of even greater importance to a full understanding. In this study, we examined patterns of network connectivity during retrieval in a recognition memory task. We estimated connectivity between brain regions from electroencephalographic signals recorded from twenty healthy subjects. A multivariate autoregressive model (MVAR) was used to determine the Granger causality to estimate the effective connectivity in the time-frequency domain. We used GPDC and dDTF methods because they have almost resolved the previous volume conduction and bivariate problems faced by previous estimation methods. Results show enhanced global connectivity in the theta and gamma bands on target trials relative to lure trials. Connectivity within and between the brain's hemispheres may be related to correct rejection. The left frontal signature appears to have a crucial role in recollection. Theta- and gamma-specific connectivity patterns between temporal, parietal, and frontal cortex may disclose the retrieval mechanism. Old/new comparison resulted in different patterns of network connection. These results and other evidence emphasize the role of frequency-specific causal network interactions in the memory retrieval process. Graphical abstract a Schematic of processing workflow which is consists of pre-processing, sliding-window AMVAR modeling, connectivity estimation, and validation and group network analysis. b Co-registration between Geodesic Sensor Net. and 10-20 system, the arrows mention eight regions of interest (Left, Anterior, Inferior (LAI) and Right, Anterior, Inferior (RAI) and Left, Anterior, Superior (LAS) and Right, Anterior, Superior (RAS) and Left, Posterior, Inferior (LPI) and Right, Posterior, Inferior (RPI) and Left, Posterior, Superior (LPS) and Right, Posterior, Superior (RPS)).

Neural mechanism of visual information degradation from retina to V1 area

The information processing mechanism of the visual nervous system is an unresolved scientific problem that has long puzzled neuroscientists. The amount of visual information is significantly degraded when it reaches the V1 after entering the retina; nevertheless, this does not affect our visual perception of the outside world. Currently, the mechanisms of visual information degradation from retina to V1 are still unclear. For this purpose, the current study used the experimental data summarized by Marcus E. Raichle to investigate the neural mechanisms underlying the degradation of the large amount of data from topological mapping from retina to V1, drawing on the photoreceptor model first. The obtained results showed that the image edge features of visual information were extracted by the convolution algorithm with respect to the function of synaptic plasticity when visual signals were hierarchically processed from low-level to high-level. The visual processing was characterized by the visual information degradation, and this compensatory mechanism embodied the principles of energy minimization and transmission efficiency maximization of brain activity, which matched the experimental data summarized by Marcus E. Raichle. Our results further the understanding of the information processing mechanism of the visual nervous system.

Estimation of brain connectivity through Artificial Neural Networks

Among different methods available for estimating brain connectivity from electroencephalographic signals (EEG), those based on MVAR models have proved to be flexible and accurate. They rely on the solution of linear equations that can be pursued through artificial neural networks (ANNs) used as MVAR model. However, when few data samples are available, there is a lack of accuracy in estimating MVAR parameters due to the collinearity between regressors. Moreover, the assessment procedure is also affected by the lack of data points. The mathematical solution to these problems is represented by penalized regression methods based on l₁ norm, that can reduce collinearity by means of variable selection process. However, the direct application of l₁ norm during the training of an ANN does not result in an efficient learning process. With the introduction of the stochastic gradient descent-L1 (SGD-L1) it is possible to apply l₁ norm directly on the estimated weights in an efficient way. Even if ANNs has been used as MVAR model for brain connectivity estimation, the use of SGD-L1 algorithm has never been tested to this purpose when few data samples are available. In this work, we tested an approach based on ANNs and SGD-L1 on both surrogate and real EEG data. Our results show that ANNs can provide accurate brain connectivity estimation if trained with SGD-L1 algorithm even when few data samples are available.

nCREANN: Nonlinear Causal Relationship Estimation by Artificial Neural Network; Applied for Autism Connectivity Study

Quantifying causal (effective) interactions between different brain regions are very important in neuroscience research. Many conventional methods estimate effective connectivity based on linear models. However, using linear connectivity models may oversimplify the functions and dynamics of the brain. In this paper, we propose a causal relationship estimator called nonlinear Causal Relationship Estimation by Artificial Neural Network (nCREANN) that identifies both linear and nonlinear components of effective connectivity in the brain. Furthermore, it can distinguish between these two types of connectivity components by calculating the linear and nonlinear parts of the network input-output mapping. The nCREANN performance has been verified using synthesized data and then it has been applied on EEG data collected during rest in children with autism spectrum disorder (ASD) and typically developing (TD) children. The results show that overall linear connectivity in TD subjects is higher, while the nonlinear connectivity component is more dominant in ASDs. We suggest that our findings may represent different underlying neural activation dynamics in ASD and TD subjects. The results of nCREANN may provide new insight into the connectivity between the interactive brain regions.

Integrating functional connectivity and MVPA through a multiple constraint network analysis

Traditional general linear model-based brain mapping efforts using functional neuroimaging are complemented by more recent multivariate pattern analyses (MVPA) that apply machine learning techniques to identify the cognitive states associated with regional BOLD activation patterns, and by connectivity analyses that identify networks of interacting regions that support particular cognitive processes. We introduce a novel analysis representing the union of these approaches, and explore the insights gained when MVPA and functional connectivity analyses are allowed to mutually constrain each other within a single model. We explored multisensory semantic representations of concrete object concepts using a self-paced multisensory imagery task. Multilayer neural networks learned the real-world categories associated with macro-scale cortical BOLD activity patterns from the task, with some models additionally encoding regional functional connectivity. Models trained to encode functional connections demonstrated superior classification accuracy and more pronounced lesion-site appropriate category-specific impairments. We replicated these results in a data set from the openneuro.org open fMRI data repository. We conclude that mutually constrained network analyses encourage parsimonious models that may benefit from improved biological plausibility and facilitate discovery.

Frontal-temporal functional connectivity of EEG signal by standardized permutation mutual information during anesthesia

Quantifying brain dynamics during anesthesia is an important challenge for understanding the neurophysiological mechanisms of anesthetic drug effect. Several single channel Electroencephalogram (EEG) indices have been proposed for monitoring anesthetic drug effect. The most commonly used single channel commercial index is the Bispectral index (BIS). However, this monitor has shown some drawbacks. In this study, a nonlinear functional connectivity measure named Standardized Permutation Mutual Information (SPMI) is proposed to describe communication between two-channel EEG signals at frontal and temporal brain regions during a controlled propofol-induced anesthesia and recovery design from eight subjects. The SPMI index has higher correlation with estimated propofol effect-site concentration and has better ability to distinguish three anesthetic states of patient than the other functional connectivity indexes (cross-correlation, coherence, phase analysis) and also the BIS index. Moreover, the SPMI index has a faster reaction to the effect of drug concentration, less variability at the consciousness state and better robustness to noise than BIS.

Bypassing the volume conduction effect by multilayer neural network for effective connectivity estimation

Differentiation of real interactions between different brain regions from spurious ones has been a challenge in neuroimaging researches. While using electroencephalographic data, those spurious interactions are mostly caused by the volume conduction (VC) effect between the recording sites. In this study, we address the problem by jointly modeling the causal relationships among brain regions and the mixing effects of volume conduction. The VC effect is formulated with a time-invariant linear equation, and the causal relationships between the brain regions are modeled with a nonlinear multivariate autoregressive process. These two models are simultaneously implemented by a multilayer neural network. The internal hidden layers represent the interactions among the regions, while the external layers are devoted for the relationship between the source activities and observed EEG measurements at the scalp. The causal interactions are estimated by the causality coefficient measure, which is based on the information (weights and parameters) embedded in the network. The proposed method is verified using various simulated data. It is then applied to the real EEG signals collected from a memory retrieval test. The results showed that the method is able to eliminate the volume conduction interferences and consequently leads to higher accuracy in identification of true causal interactions. Graphical abstract The proposed network structure used to simultaneously model the volume conduction and source interactions. By this special structure, we first move from the sensor space to the source space at the first layer. Then, within internal hidden layers, the interactions between the sources are represented in the form of a general (nonlinear) multivariate autoregressive (nMVAR) model. Finally, we return from the source space to the sensor space at the last layer of the network. The proposed method bypasses the effect of volume conduction and causes more accurate connectivity estimation.

Prediction of epilepsy seizure from multi-channel electroencephalogram by effective connectivity analysis using Granger causality and directed transfer function methods

Epilepsy is a chronic disorder, which causes strange perceptions, muscle spasms, sometimes seizures, and loss of awareness, associated with abnormal neuronal activity in the brain. The goal of this study is to investigate how effective connectivity (EC) changes effect on unexpected seizures prediction, as this will authorize the patients to play it safe and avoid risk. We approve the hypothesis that EC variables near seizure change significantly so seizure can be predicted in accordance with this variation. We introduce two time-variant coefficients based on standard deviation of EC on Freiburg EEG dataset by using directed transfer function and Granger causality methods and compare index changes over the course of time in five different frequency bands. Comparison of the multivariate and bivariate analysis of factors is implemented in this investigation. The performance based on the suggested methods shows the seizure occurrence period is approximately 50 min that is expected onset stated in, the maximum value of sensitivity approaching ~ 80%, and 0.33 FP/h is the false prediction rate. The findings revealed that greater accuracy and sensitivity are obtained by the designed system in comparison with the results of other works in the same condition. Even though these results still are not sufficient for clinical applications. Based on the conclusions, it can generally be observed that the greater results by DTF method are in the gamma and beta frequency bands.

Accelerated Exploration for Long-Term Urban Water Infrastructure Planning through Machine Learning

In this study, the neural network method (Multi-Layer Perceptron, MLP) was integrated with an explorative model, to study the feasibility of using machine learning to reduce the exploration time but providing the same support in long-term water system adaptation planning. The specific network structure and training pattern were determined through a comprehensive statistical trial-and-error (considering the distribution of errors). The network was applied to the case study in Scotchman’s Creek, Melbourne. The network was trained with the first 10% of the exploration data, validated with the following 5% and tested on the rest. The overall root-mean-square-error between the entire observed data and the predicted data is 10.5722, slightly higher than the validation result (9.7961), suggesting that the proposed trial-and-error method is reliable. The designed MLP showed good performance dealing with spatial randomness from decentralized strategies. The adoption of MLP-supported planning may overestimate the performance of candidate urban water systems. By adopting the safety coefficient, a multiplicator or exponent calculated by observed data and predicted data in the validation process, the overestimation problem can be controlled in an acceptable range and have few impacts on final decision making.