Probabilistic Learning Research Articles

An applied deep reinforcement learning approach to control active networked microgrids in smart cities with multi-level participation of battery energy storage system and electric vehicles

This study proposed an intelligent energy management strategy for islanded networked microgrids (NMGs) in smart cities considering the renewable energy sources uncertainties and power fluctuations. Energy management of active power and frequency control approach is based on the intelligent probabilistic wavelet fuzzy neural network-deep reinforcement learning algorithm (IPWFNN-DRLA). The control strategy is formulated with deep reinforcement learning approach based on the Markov decision process and solved by the soft actor-critic algorithm. The NMG local controller (NMGLC) provides information such as the frequency, active power, power generation data, and status of the electric vehicle's battery energy storage system to the NMG central controller (NMGCC). Then the NMGCC calculates active power and frequency support based on the IPWFNN-DRLA approach and sends the results to the NMGLC. The proposed model is developed in a continuous problem-solving space with two structures of offline training and decentralized distributed operation. For this purpose, each NMG has a control agent (NMGCA) based on the IPWFNN algorithm, and the NMGCA learning model is formulated based the online back-propagation learning algorithm. The proposed approach demonstrates a computation accuracy exceeding 98%, along with a 7.82% reduction in computational burden and a 61.1% reduction in computation time compared to alternative methods.

Hyperbolic Secant representation of the logistic function: Application to probabilistic Multiple Instance Learning for CT intracranial hemorrhage detection

Multiple Instance Learning (MIL) is a weakly supervised paradigm that has been successfully applied to many different scientific areas and is particularly well suited to medical imaging. Probabilistic MIL methods, and more specifically Gaussian Processes (GPs), have achieved excellent results due to their high expressiveness and uncertainty quantification capabilities. One of the most successful GP-based MIL methods, VGPMIL, resorts to a variational bound to handle the intractability of the logistic function. Here, we formulate VGPMIL using Pólya-Gamma random variables. This approach yields the same variational posterior approximations as the original VGPMIL, which is a consequence of the two representations that the Hyperbolic Secant distribution admits. This leads us to propose a general GP-based MIL method that takes different forms by simply leveraging distributions other than the Hyperbolic Secant one. Using the Gamma distribution we arrive at a new approach that obtains competitive or superior predictive performance and efficiency. This is validated in a comprehensive experimental study including one synthetic MIL dataset, two well-known MIL benchmarks, and a real-world medical problem. We expect that this work provides useful ideas beyond MIL that can foster further research in the field.

Increased methane emissions from oil and gas following the Soviet Union’s collapse

Global atmospheric methane concentrations rose by 10 to 15 ppb/y in the 1980s before abruptly slowing to 2 to 8 ppb/y in the early 1990s. This period in the 1990s is known as the "methane slowdown" and has been attributed in part to the collapse of the former Soviet Union (USSR) in December 1991, which may have decreased the methane emissions from oil and gas operations. Here, we develop a methane plume detection system based on probabilistic deep learning and human-labeled training data. We use this method to detect methane plumes from Landsat 5 satellite observations over Turkmenistan from 1986 to 2011. We focus on Turkmenistan because economic data suggest it could account for half of the decline in oil and gas emissions from the former USSR. We find an increase in both the frequency of methane plume detections and the magnitude of methane emissions following the collapse of the USSR. We estimate a national loss rate from oil and gas infrastructure in Turkmenistan of more than 10% at times, which suggests the socioeconomic turmoil led to a lack of oversight and widespread infrastructure failure in the oil and gas sector. Our finding of increased oil and gas methane emissions from Turkmenistan following the USSR's collapse casts doubt on the long-standing hypothesis regarding the methane slowdown, begging the question: "what drove the 1992 methane slowdown?"

Dysfunctional feedback processing in male methamphetamine abusers: Evidence from neurophysiological and computational approaches

Methamphetamine use disorder (MUD) as a major public health risk is associated with dysfunctional neural feedback processing. Although dysfunctional feedback processing in people who are substance dependent has been explored in several behavioral, computational, and electrocortical studies, this mechanism in MUDs requires to be well understood. Furthermore, the current understanding of latent components of their behavior such as learning speed and exploration-exploitation dilemma is still limited. In addition, the association between the latent cognitive components and the related neural mechanisms also needs to be explored. Therefore, in this study, the underlying neurocognitive mechanisms of feedback processing of such impairment, and age/gender-matched healthy controls are evaluated within a probabilistic learning task with rewards and punishments. Mathematical modeling results based on the Q-learning paradigm suggested that MUDs show less sensitivity in distinguishing optimal options. Additionally, it may be worth noting that MUDs exhibited a slight decrease in their ability to learn from negative feedback compared to healthy controls. Also through the lens of underlying neural mechanisms, MUDs showed lower theta power at the medial-frontal areas while responding to negative feedback. However, other EEG measures of reinforcement learning including feedback-related negativity, parietal-P300, and activity flow from the medial frontal to lateral prefrontal regions, remained intact in MUDs. On the other hand, the elimination of the linkage between value sensitivity and medial-frontal theta activity in MUDs was observed. The observed dysfunction could be due to the adverse effects of methamphetamine on the cortico-striatal dopamine circuit, which is reflected in the anterior cingulate cortex activity as the most likely region responsible for efficient behavior adjustment. These findings could help us to pave the way toward tailored therapeutic approaches.

Aspmc: New frontiers of algebraic answer set counting

In the last decade, there has been increasing interest in extensions of answer set programming (ASP) that cater for quantitative information such as weights or probabilities. A wide range of quantitative reasoning tasks for ASP and logic programming, among them probabilistic inference and parameter learning in the neuro-symbolic setting, can be expressed as algebraic answer set counting (AASC) tasks, i.e., weighted model counting for ASP with weights calculated over some semiring, which makes efficient solvers for AASC desirable. In this article, we present ▪, a new solver for AASC that pushes the limits of efficient solvability. Notably, ▪ provides improved performance compared to the state of the art in probabilistic inference by exploiting three insights gained from thorough theoretical investigations in our work. Namely, we consider the knowledge compilation step in the AASC pipeline, where the underlying logical theory specified by the answer set program is converted into a tractable circuit representation, on which AASC is feasible in polynomial time. First, we provide a detailed comparison of different approaches to knowledge compilation for programs, revealing that translation to propositional formulas followed by compilation to sd-DNNF seems favorable. Second, we study how the translation to propositional formulas should proceed to result in efficient compilation. This leads to the second and third insight, namely a novel way of breaking the positive cyclic dependencies in a program, called TP-Unfolding, and an improvement to the Clark Completion, the procedure used to transform programs without positive cyclic dependencies into propositional formulas. Both improvements are tailored towards efficient knowledge compilation. Our empirical evaluation reveals that while all three advancements contribute to the success of ▪, TP-Unfolding improves performance significantly by allowing us to handle cyclic instances better.

Prediction and correlations estimation of seismic capacities of pier columns: Extended Gaussian process regression models

Assessing the seismic capacity of pier columns is a crucial element in the performance-based seismic design of bridges. Such assessment necessitates a probabilistic approach to accurately determine the marginal probability distributions of seismic capacities and to characterize the dependencies among these variables. In response to this need, this paper employs Multi-Output Gaussian Process Regression (MO-GPR), a probabilistic machine learning method, to jointly model the multiple seismic capacities of pier columns. We initially introduce a probabilistic seismic capacity model that utilizes MO-GPR for pier columns and validate its predictive accuracy in comparison to Bayesian linear regression and existing empirical methods. Subsequently, the methodology is augmented by the integration of hierarchical modeling within the MO-GPR framework, resulting in a Multi-Output Hierarchical Gaussian Process Regression (MO-HGPR) model that effectively estimates intraclass correlation coefficients for specific types of datasets. It is postulated that these correlation coefficients also reflect correlations associated with multiple components of the real structure. This study employs MO-HGPR and MO-GPR separately to investigate the potential correlations of seismic capacities among pier columns and distinct limit states. The results demonstrate that the MO-GPR model exhibits superior prediction accuracy and more effectively portrays uncertainty compared to existing empirical models. Moreover, the correlations of seismic capacities among piers and limit states are both robust and significantly impact the seismic fragility of bridges. This finding highlights the essential nature of considering capacities correlations in seismic fragility or risk assessment processes.

Probabilistic neural network-based flexible estimation of lithium-ion battery capacity considering multidimensional charging habits

As the adoption of electric vehicles (EVs) continues to rise due to increasing environmental concerns and policy support, the accurate estimation of battery capacity becomes crucial for efficient vehicle management and prolonging battery life. This study presents a framework for capacity estimation under real-world electric vehicle charging scenarios, reflecting a variety of driving habits. A novel CNN-LSTM neural network architecture featuring a probabilistic regression layer (CLPNN) is developed, utilizing short time interval data to provide accurate, reliable capacity and uncertainty estimates for diverse charging situations. The adaptability of the proposed method is evaluated by intercepting real-vehicle statistics to simulate charging events. We introduce two result fusion strategies for refining capacity estimations: the Trimmed Mean Strategy and the Uncertainty Screening Strategy. Their performances are meticulously compared to establish the most effective approach. Moreover, probabilistic layer transfer learning is employed to address the challenge of insufficient labeled data in the target domain, thereby improving the transfer and generalization performance of the model. The findings of this study underscore the potential of the proposed methods in accurately evaluating battery capacity and dealing with uncertainties in real-world EV operations.

Probabilistic machine learning for enhanced chiller sequencing: A risk-based control strategy

Multiple-chiller systems are widely adopted in large buildings due to their high flexibility and efficiency in providing cooling capacity. A reliable and robust chiller sequencing control strategy is crucial to ensure the energy efficiency and stability of the multiple-chiller systems. However, conventional chiller sequencing control strategies are usually based on real-time measured cooling load without considering the cooling load changes in the following hours. Conventional rule-based strategy may result in unnecessary switching on and off, leading to energy waste and impairing system stability. Therefore, this study proposes a robust chiller sequencing control strategy that utilizes probabilistic cooling load predictions. 1h-ahead probabilistic cooling load prediction in the form of the normal distribution is made using natural gradient boosting (NGBoost). Compared to conventional machine learning algorithms, NGBoost can predict not only the future cooling load but also the uncertainty of the predicted cooling load, which enables the load prediction to handle the uncertainties associated with the data/measurements adequately. A novel risk-based sequencing strategy is developed based on the probabilistic cooling load predictions. The data experiment shows that the proposed strategy can significantly improve the stability and reliability of the chiller plant by reducing the total switching number by up to 43.6 %.

Reliable Prostate Cancer Risk Mapping From MRI Using Targeted and Systematic Core Needle Biopsy Histopathology.

To compute a dense prostate cancer risk map for the individual patient post-biopsy from magnetic resonance imaging (MRI) and to provide a more reliable evaluation of its fitness in prostate regions that were not identified as suspicious for cancer by a human-reader in pre- and intra-biopsy imaging analysis. Low-level pre-biopsy MRI biomarkers from targeted and non-targeted biopsy locations were extracted and statistically tested for representativeness against biomarkers from non-biopsied prostate regions. A probabilistic machine learning classifier was optimized to map biomarkers to their core-level pathology, followed by extrapolation of pathology scores to non-biopsied prostate regions. Goodness-of-fit was assessed at targeted and non-targeted biopsy locations for the post-biopsy individual patient. Our experiments showed high predictability of imaging biomarkers in differentiating histopathology scores in thousands of non-targeted core-biopsy locations (ROC-AUCs: 0.85-0.88), but also high variability between patients (Median ROC-AUC [IQR]: 0.81-0.89 [0.29-0.40]). The sparseness of prostate biopsy data makes the validation of a whole gland risk mapping a non-trivial task. Previous studies i) focused on targeted-biopsy locations although biopsy-specimens drawn from systematically scattered locations across the prostate constitute a more representative sample to non-biopsied regions, and ii) estimated prediction-power across predicted instances (e.g., biopsy specimens) with no patient distinction, which may lead to unreliable estimation of model fitness to the individual patient due to variation between patients in instance count, imaging characteristics, and pathologies. This study proposes a personalized whole-gland prostate cancer risk mapping post-biopsy to allow clinicians to better stage and personalize focal therapy treatment plans.

Probabilistic Brain Extraction in MR Images via Conditional Generative Adversarial Networks.

Brain extraction, or the task of segmenting the brain in MR images, forms an essential step for many neuroimaging applications. These include quantifying brain tissue volumes, monitoring neurological diseases, and estimating brain atrophy. Several algorithms have been proposed for brain extraction, including image-to-image deep learning methods that have demonstrated significant gains in accuracy. However, none of them account for the inherent uncertainty in brain extraction. Motivated by this, we propose a novel, probabilistic deep learning algorithm for brain extraction that recasts this task as a Bayesian inference problem and utilizes a conditional generative adversarial network (cGAN) to solve it. The input to the cGAN's generator is an MR image of the head, and the output is a collection of likely brain images drawn from a probability density conditioned on the input. These images are used to generate a pixel-wise mean image, serving as the estimate for the extracted brain, and a standard deviation image, which quantifies the uncertainty in the prediction. We test our algorithm on head MR images from five datasets: NFBS, CC359, LPBA, IBSR, and their combination. Our datasets are heterogeneous regarding multiple factors, including subjects (with and without symptoms), magnetic field strengths, and manufacturers. Our experiments demonstrate that the proposed approach is more accurate and robust than a widely used brain extraction tool and at least as accurate as the other deep learning methods. They also highlight the utility of quantifying uncertainty in downstream applications. Additional information and codes for our method are available at: https://github.com/bmri/bmri.

Probabilistic learning approach for the liquid holdup analysis of high-viscosity intermittent flows

A Gaussian mixture model (GMM) was implemented to investigate the relationship between the liquid holdup (in various parts of the flow) and the pressure for different experimental realizations of high-viscosity gas–liquid flows. We considered a Newtonian fluid with a constant viscosity of 6 Pa s (600 cP) under a laboratory-controlled temperature. Because the pressure and the holdup do not exhibit a clear-cut relationship in the time domain, a supervised classification algorithm and a “deep” neural network (DNN) were first applied to classify the data points and predict average holdup values. Then, the GMM was applied to determine the holdup in various liquid aggregation structures of the flow as a function of the pressure. The growth rates of the cumulative lengths of the liquid structures (i.e., slug body, mixing front, and liquid film) and the gas bubbles were obtained. The GMM predicted holdup values were in close agreement with the experimental data.

Prefrontal theta—gamma transcranial alternating current stimulation improves non-declarative visuomotor learning in older adults

The rise in the global population of older adults underscores the significance to investigate age-related cognitive disorders and develop early treatment modalities. Previous research suggests that non-invasive transcranial Alternating Current Stimulation (tACS) can moderately improve cognitive decline in older adults. However, non-declarative cognition has received relatively less attention. This study investigates whether repeated (16-day) bilateral theta—gamma cross-frequency tACS targeting the Dorsolateral Prefrontal Cortex (DLPFC) enhances non-declarative memory. Computerized cognitive training was applied alongside stimulation to control for the state-of-the-brain. The Alternating Serial Reaction Time (ASRT) task was employed to assess non-declarative functions such as visuomotor skill and probabilistic sequence learning. Results from 35 participants aged 55–82 indicated that active tACS led to more substantial improvements in visuomotor skills immediately after treatment, which persisted 3 months later, compared to sham tACS. Treatment benefit was more pronounced in older adults of younger age and those with pre-existing cognitive decline. However, neither intervention group exhibited modulation of probabilistic sequence learning. These results suggest that repeated theta—gamma tACS can selectively improve distinct non-declarative cognitive aspects when targeting the DLPFC. Our findings highlight the therapeutic potential of tACS in addressing deficits in learning and retaining general skills, which could have a positive impact on the quality of life for cognitively impaired older individuals by preserving independence in daily activities.

Virtual brain twins: from basic neuroscience to clinical use.

Virtual brain twins are personalized, generative and adaptive brain models based on data from an individual's brain for scientific and clinical use. After a description of the key elements of virtual brain twins, we present the standard model for personalized whole-brain network models. The personalization is accomplished using a subject's brain imaging data by three means: (1) assemble cortical and subcortical areas in the subject-specific brain space; (2) directly map connectivity into the brain models, which can be generalized to other parameters; and (3) estimate relevant parameters through model inversion, typically using probabilistic machine learning. We present the use of personalized whole-brain network models in healthy ageing and five clinical diseases: epilepsy, Alzheimer's disease, multiple sclerosis, Parkinson's disease and psychiatric disorders. Specifically, we introduce spatial masks for relevant parameters and demonstrate their use based on the physiological and pathophysiological hypotheses. Finally, we pinpoint the key challenges and future directions.

An explainable machine learning-based probabilistic framework for the design of scaffolds in bone tissue engineering.

Recently, 3D-printed biodegradable scaffolds have shown great potential for bone repair in critical-size fractures. The differentiation of the cells on a scaffold is impacted among other factors by the surface deformation of the scaffold due to mechanical loading and the wall shear stresses imposed by the interstitial fluid flow. These factors are in turn significantly affected by the material properties, the geometry of the scaffold, as well as the loading and flow conditions. In this work, a numerical framework is proposed to study the influence of these factors on the expected osteochondral cell differentiation. The considered scaffold is rectangular with a 0/90 lay-down pattern and a four-layered strut made of polylactic acid with a 5% steel particle content. The distribution of the different types of cells on the scaffold surface is estimated through a scalar stimulus, calculated by using a mechanobioregulatory model. To reduce the simulation time for the computation of the stimulus, a probabilistic machine learning (ML)-based reduced-order model (ROM) is proposed. Then, a sensitivity analysis is performed using the Shapley additive explanations to examine the contribution of the various parameters to the framework stimulus predictions. In a final step, a multiobjective optimization procedure is implemented using genetic algorithms and the ROM, aiming to identify the material parameters and loading conditions that maximize the percentage of surface area populated by bone cells while minimizing the area corresponding to the other types of cells and the resorption condition. The results of the performed analysis highlight the potential of using ROMs for the scaffold design, by dramatically reducing the simulation time while enabling the efficient implementation of sensitivity analysis and optimization procedures.

Automated experimental design of safe rampdowns via probabilistic machine learning

Typically the rampdown phase of a shot consists of a decrease in current and injected power and optionally a change in shape, but there is considerable flexibility in the rate, sequencing, and duration of these changes. On the next generation of tokamaks it is essential that this is done safely as the device could be damaged by the stored thermal and electromagnetic energy present in the plasma. This works presents a procedure for automatically choosing experimental rampdown designs to rapidly converge to an effective rampdown trajectory. This procedure uses probabilistic machine learning methods paired with acquisition functions taken from Bayesian optimization. In a set of 2022 experiments at DIII-D, the rampdown designs produced by our method maintained plasma control down to substantially lower current and energy levels than are typically observed. The actions predicted by the model significantly improved as the model was able to explore over the course of the experimental campaign.

Analyzing entropy features in time-series data for pattern recognition in neurological conditions

In the field of medical diagnosis and patient monitoring, effective pattern recognition in neurological time-series data is essential. Traditional methods predominantly based on statistical or probabilistic learning and inference often struggle with multivariate, multi-source, state-varying, and noisy data while also posing privacy risks due to excessive information collection and modeling. Furthermore, these methods often overlook critical statistical information, such as the distribution of data points and inherent uncertainties. To address these challenges, we introduce an information theory-based pipeline that leverages specialized features to identify patterns in neurological time-series data while minimizing privacy risks. We incorporate various entropy methods based on the characteristics of different scenarios and entropy. For stochastic state transition applications, we incorporate Shannon’s entropy, entropy rates, entropy production, and the von Neumann entropy of Markov chains. When state modeling is impractical, we select and employ approximate entropy, increment entropy, dispersion entropy, phase entropy, and slope entropy. The pipeline’s effectiveness and scalability are demonstrated through pattern analysis in a dementia care dataset and also an epileptic and a myocardial infarction dataset. The results indicate that our information theory-based pipeline can achieve average performance improvements across various models on the recall rate, F1 score, and accuracy by up to 13.08 percentage points, while enhancing inference efficiency by reducing the number of model parameters by an average of 3.10 times. Thus, our approach opens a promising avenue for improved, efficient, and critical statistical information-considered pattern recognition in medical time-series data.

Using Probabilistic Machine Learning Methods to Improve Beef Cattle Price Modeling and Promote Beef Production Efficiency and Sustainability in Canada

Accurate agricultural commodity price models enable efficient allocation of limited natural resources, leading to improved sustainability in agriculture. Because of climate change, price volatility and uncertainty in the sector are expected to increase in the future, increasing the need for improved price modeling. With the emergence of machine learning (ML) algorithms, novel tools are now available to enhance the modeling of agricultural commodity prices. This research explores both univariate and multivariate ML techniques to perform probabilistic price prediction modeling for the Canadian beef industry, taking into account beef production, commodity markets, and international trade features to enhance accuracy. We model Alberta fed steer prices using three multivariate ML algorithms (support vector regression (SVR), random forest (RF), and Adaboost (AB)) and three univariate ML algorithms (autoregressive integrated moving average (ARIMA), seasonal ARIMA (SARIMA), and the seasonal autoregressive integrated moving average with exogenous factors (SARIMAX)). We apply these models to monthly fed steer price data between January 2005 and September 2023 and compare predicted prices with observed prices using several validation metrics. The outcomes indicate that both random forest (RF) and Adaboost (AB) show superior overall performance in accurately predicting Alberta fed steer prices in comparison to other algorithms. To better account for the variance of the best model performance, we subsequently adopted a probabilistic approach by considering uncertainty in our best-selected ML model. The beef industry can use these improved price models to minimize resource waste and inefficiency in the sector and improve the long-term sustainability prospects for beef producers in Canada.

On the use of a new probabilistic model and machine learning methods with applications to reliability and music engineering

In this paper, we considered a new probability distribution with new applications in the field of engineering, in particular, in music engineering. The new probability distribution is mainly based on the Weibull distribution and cosine function. We call this the weighted cosine flexible Weibull distribution. The point estimators for the new distribution are obtained. We evaluate these point estimators for three sets of parameter values. The illustration of the weighted cosine flexible Weibull distribution is provided for two practical data set which are drawn from the reliability and music engineering. In addition, to dual robust machine learning approaches, we implement the Lasso (Least Absolute Shrinkage and Selection Operator) and Elastic Net (ENet) to improve the predictive performance of the data. This was done in response to the existence of outliers in the same datasets. We provide comparative analysis to see how well these approaches performed in comparison to the Step Indicator Saturation (SIS) method.

Damage identification for railway tracks using ultrasound guided wave and hybrid probabilistic deep learning

Rails are often damaged by train extrusion and other external forces, which seriously affects track safety. Although deep learning is widely used in rail damage recognition, its usual inability to understand own uncertainty that is critical in engineering application. Hence, this paper proposes a hybrid probabilistic deep learning for rail damage identification. It combines the hierarchical representation capabilities of deep learning with probability distributions. The posterior distribution provides support for the uncertainty quantification in identification results. Firstly, ultrasonic guided waves were used to sense the rail damage and time-frequency feature map dataset was obtained by analysing its time-domain signal using wavelet transform. Then, two different weight perturbation methods are used for comparative study. The reparameterization method performs more consistently and efficiently in this task, with a recognition accuracy of 0.9400. Subsequently, the effect of the number of probabilistic and non-probabilistic layers in the hybrid network on recognition results was analysed. Experimental results showed that hybrid probabilistic deep learning achieved the highest testing accuracy of 0.9900. The uncertainty quantification metrics of recognition results from hybrid probabilistic deep learning are mostly less than 0.2, demonstrating favourable reliability.

Digital imaging-in-flow (FlowCAM) and probabilistic machine learning to assess the sonolytic disinfection of cyanobacteria in sewage wastewater

Assessing the cyanobacteria disinfection in sewage and its compliance with international-standards requires determining the concentration and viability, which can be achieve using Imaging Flow Cytometry device called FlowCAM. The objective is to thoroughly investigate the sonolytic morphological changes and disinfection-performance towards toxic cyanobacteria existing in sewage using the FlowCAM. After optimizing the process conditions, over 80% decline in cyanobacterial cell counts was observed, accompanied by an additional 10–15% of cells exhibiting injuries, as confirmed through morphological investigation. Moreover, for the first time, the experimentally collected data was utilized to build deep-learning probabilistic-neural-networks (PNN) and natural-gradient-boosting (NGBoost) models for predicting disinfection efficiency and ABD area as target outputs. The findings suggest that the NGBoost model exhibited superior prediction performance for both targets, with high test coefficient of determination (R2 > 0.87) and lower test errors (RMSE < 7.10, MAE < 4.14). The confidence interval examination in NGBoost prediction performance showed a minute variation from the experimentally calculated values, suggesting a high accuracy in model prediction. Finally, SHAP analysis suggests the sonolytic time alone contributes around 50% to the cyanobacteria disinfection. Overall, the findings demonstrate the effectiveness of the FlowCAM device and the potential of machine-learning modeling in predicting disinfection outcomes.