Trustworthy Predictions Research Articles

MulCPred: Learning Multi-Modal Concepts for Explainable Pedestrian Action Prediction.

Pedestrian action prediction is crucial for many applications such as autonomous driving. However, state-of-the-art methods lack the explainability needed for trustworthy predictions. In this paper, a novel framework called MulCPred is proposed that explains its predictions based on multi-modal concepts represented by training samples. Previous concept-based methods have limitations, including the following: (1) they cannot be directly applied to multi-modal cases; (2) they lack the locality needed to attend to details in the inputs; (3) they are susceptible to mode collapse. These limitations are tackled accordingly through the following approaches: (1) a linear aggregator to integrate the activation results of the concepts into predictions, which associates concepts of different modalities and provides ante hoc explanations of the relevance between the concepts and the predictions; (2) a channel-wise recalibration module that attends to local spatiotemporal regions, which enables the concepts with locality; (3) a feature regularization loss that encourages the concepts to learn diverse patterns. MulCPred is evaluated on multiple datasets and tasks. Both qualitative and quantitative results demonstrate that MulCPred is promising in improving the explainability of pedestrian action prediction without obvious performance degradation. Moreover, by removing unrecognizable concepts, MulCPred shows improved cross-dataset prediction performance, suggesting its potential for further generalization.

Deployment and validation of the CLL treatment infection model adjoined to an EHR system

Research algorithms are seldom externally validated or integrated into clinical practice, leaving unknown challenges in deployment. In such efforts, one needs to address challenges related to data harmonization, the performance of an algorithm in unforeseen missingness, automation and monitoring of predictions, and legal frameworks. We here describe the deployment of a high-dimensional data-driven decision support model into an EHR and derive practical guidelines informed by this deployment that includes the necessary processes, stakeholders and design requirements for a successful deployment. For this, we describe our deployment of the chronic lymphocytic leukemia (CLL) treatment infection model (CLL-TIM) as a stand-alone platform adjoined to an EPIC-based Danish Electronic Health Record (EHR), with the presentation of personalized predictions in a clinical context. CLL-TIM is an 84-variable data-driven prognostic model utilizing 7-year medical patient records and predicts the 2-year risk composite outcome of infection and/or treatment post-CLL diagnosis. As an independent validation cohort for this deployment, we used a retrospective population-based cohort of patients diagnosed with CLL from 2018 onwards (n = 1480). Unexpectedly high levels of missingness for key CLL-TIM variables were exhibited upon deployment. High dimensionality, with the handling of missingness, and predictive confidence were critical design elements that enabled trustworthy predictions and thus serves as a priority for prognostic models seeking deployment in new EHRs. Our setup for deployment, including automation and monitoring into EHR that meets Medical Device Regulations, may be used as step-by-step guidelines for others aiming at designing and deploying research algorithms into clinical practice.

The masking technique for forced nonlinear oscillator stability behavior analysis using the non-perturbative approach

The study utilized the masking technique to explore the stability behavior of a forced nonlinear oscillator through the non-perturbative approach, with a particular focus on a Van der Pol oscillator subjected to external force, characterized by both cubic and quadratic nonlinearities. The application of the non-perturbative method (NPM) in conjunction with the masking technique was a pivotal aspect of this research, transforming the inherently non-homogeneous, nonlinear system into a homogeneous linear system. This transformation was crucial as it simplified the complex dynamics of the system, rendering it more amenable to analysis. Through this method, the research successfully established the system’s overall frequency, meticulously accounting for the impact of the periodic external force. The study also identified a distinct type of resonance response, where the system’s frequency incorporates the excited frequency in a nonlinear relationship. The masking technique proved to be an invaluable tool for examining the stability behavior of forced vibrations in oscillators via the NPM, providing profound insights into stability under external forces and enhancing the understanding and control of oscillatory behaviors in nonlinear dynamical systems. A critical confirmation of the current methodology is provided by the remarkable agreement found between the numerical solution and the provided analytical solution. This agreement shows that the analytical method produces trustworthy predictions and appropriately describes the system’s behavior. The plotted stability diagrams, which demonstrate that the model’s simulation of stability behavior is consistent with observed events, particularly resonance phenomena, offer further validity for the findings. In the resonance case, the effects of the damping coefficient and the external force’s magnitude are significant. The results of the analysis show that an increase in the damping coefficient has a destabilizing effect that causes unstable zones to expand. In contrast, in the resonance state, the quadratic and cubic nonlinearity factors both contribute to stabilization. Understanding how various system factors impact stability dynamics particularly in relation to resonance phenomena is made easier with the help of this insight.

Question Calibration and Multi-Hop Modeling for Temporal Question Answering

Many models that leverage knowledge graphs (KGs) have recently demonstrated remarkable success in question answering (QA) tasks. In the real world, many facts contained in KGs are time-constrained thus temporal KGQA has received increasing attention. Despite the fruitful efforts of previous models in temporal KGQA, they still have several limitations. (I) They adopt pre-trained language models (PLMs) to obtain question representations, while PLMs tend to focus on entity information and ignore entity transfer caused by temporal constraints, and finally fail to learn specific temporal representations of entities. (II) They neither emphasize the graph structure between entities nor explicitly model the multi-hop relationship in the graph, which will make it difficult to solve complex multi-hop question answering. To alleviate this problem, we propose a novel Question Calibration and Multi-Hop Modeling (QC-MHM) network. Specifically, We first calibrate the question representation by fusing the question and the time-constrained concepts in KG. Then, we construct the GNN layer to complete multi-hop message passing. Finally, the question representation is combined with the embedding output by the GNN to generate the final prediction. Empirical results verify that the proposed model achieves better performance than the state-of-the-art models in the benchmark dataset. Notably, the Hits@1 and Hits@10 results of QC-MHM on the CronQuestions dataset's complex questions are absolutely improved by 5.1% and 1.2% compared to the best-performing baseline. Moreover, QC-MHM can generate interpretable and trustworthy predictions.

Evidential deep learning for trustworthy prediction of enzyme commission number.

The rapid growth of uncharacterized enzymes and their functional diversity urge accurate and trustworthy computational functional annotation tools. However, current state-of-the-art models lack trustworthiness on the prediction of the multilabel classification problem with thousands of classes. Here, we demonstrate that a novel evidential deep learning model (named ECPICK) makes trustworthy predictions of enzyme commission (EC) numbers with data-driven domain-relevant evidence, which results in significantly enhanced predictive power and the capability to discover potential new motif sites. ECPICK learns complex sequential patterns of amino acids and their hierarchical structures from 20million enzyme data. ECPICK identifies significant amino acids that contribute to the prediction without multiple sequence alignment. Our intensive assessment showed not only outstanding enhancement of predictive performance on the largest databases of Uniprot, Protein Data Bank (PDB) and Kyoto Encyclopedia of Genes and Genomes (KEGG), but also a capability to discover new motif sites in microorganisms. ECPICK is a reliable EC number prediction tool to identify protein functions of an increasing number of uncharacterized enzymes.

FEMTOSAT-Based Air Quality Monitoring: Leveraging Satellite Data and LoRa Communication for Improved AQI Predictions

The exponential growth of the global population has given rise to an alarming surge in air pollution levels, casting profound repercussions on economies, ecosystems, and human well-being. The predominant method for assessing air quality involves the deployment of sensors atop buildings at regular intervals. However, this approach faces significant drawbacks, including heightened energy consumption associated with each building's sensor infrastructure and its inapplicability in sparsely populated rural areas. Addressing these limitations, the utilization of FEMTOSAT technology emerges as a solution, capitalizing on satellite data for autonomous air pollution monitoring, analysis, and mitigation. Amidst the evolving scientific landscape, the integration of Low Power Wide Area Network (LoRa) technology assumes a pivotal role within the Internet of Things (IoT), facilitating long-range data communication with minimal power consumption. In this context, LoRa communication serves as the conduit for transmitting and receiving data from satellites via RF signals. The satellite-derived environmental data, thus collected, serves as the foundation for computing the Air Quality Index (AQI) at specific locations, a critical metric that informs us about air quality conditions, whether pristine or contaminated. The AQI computation factors in various pollutants, including NO2, CO, O3, PM2.5, SO2, and PM10, all of which significantly influence air quality. This study employs a range of machine learning (ML) techniques, including time series analysis, linear regression, Support Vector Machines (SVM), and logistic regression, to predict and forecast AQI values. These models amalgamate AQI data from diverse sources, yielding robust and dependable AQI prediction models. Notably, modern sensor technology simplifies and enhances data collection accuracy. In the realm of environmental data analysis, only ML algorithms can grapple with the complexity of processing vast datasets to generate precise and trustworthy predictions. The incorporation of integrated sensors as payload in the Femto Sat mission epitomizes the mission's objectives. This system is characterized by its cost-effectiveness, lightweight design, durability, redundancy, and user-friendly interface, requiring minimal power consumption for operation.

Prediction-Uncertainty-Aware Threat Detection for ADAS: A Case Study on Lane-Keeping Assistance

Advanced driver assistance systems typically support the driver in cases where the driver is likely to fail the driving task. The challenge, from a system perspective, is to accurately detect those cases. Recently, machine learning-based prediction models that are able to estimate the prediction uncertainty in real-time have successfully been introduced for this purpose. However, very little effort has been made on using the prediction uncertainty in the decision-making logic to improve the system's robustness, especially in cases where the input data is affected by noise or anomalies that are not presented in the training data. In this work, four threat-detection methods using uncertainty estimates are proposed and evaluated using a real-world data set. The methods use different strategies for leveraging uncertainty information, where the goal is to ensure that the intervention decision is based on trustworthy predictions. The threat-detection methods' performances are evaluated, using five different learning-based prediction models, in the context of a lane-keeping assistance application.

Towards more trustworthy predictions: A hybrid evidential movie recommender system

Recommender Systems (RSs) are considered as popular tools that have revolutionized the e-commerce and digital marketing. Their main goal is predicting the users’ future preferences and providing accessible and personalized recommendations. However, uncertainty can spread at any level throughout the recommendation process, which may affect the results. In fact, the ratings given by the users are often unreliable. The final provided predictions itself may also be pervaded with uncertainty and doubt. Obviously, the reliability of the predictions cannot be fully certain and trustworthy. For the system to be effective, recommendations must inspire trust in the system and provide reliable and credible recommendations. The user may speculate about the uncertainty pervaded behind the given recommendation. He could tend to a reliable recommendation offering him a global overview about his preferences rather than an inappropriate one that contradicts his activities and objectives. While such imperfection cannot be ignored, traditional RSs are rarely able to deal with the uncertainty spreading around the prediction process, which may affect the credibility, the transparency and the trustworthiness of the current RS. Thus, in this paper, we opt for the uncertain framework of the belief function theory (BFT), which allows us to represent, quantify and manage imperfect evidence. By using the BFT, the users’ preferences and the interactions between the neighbors can be represented under uncertainty. Evidence from different information sources can then be combined leading to more reliable results. The proposed approach is a hybrid evidential movie RS that uses different data sources and delivers a personalized user-interface allowing a global overview of the possible future preferences. This representation would increase the users’ confidence towards the system as well as their satisfaction. Experiments are performed on MovieLens and their additional features provided by the Internet Movie Database (IMDb) and Rotten Tomatoes. The new approach achieves promising results compared to traditional approaches in terms of MAE, NMAE and RMSE. It also reaches interesting Precision, Recall and F-measure values of respectively, 0.782, 0.792 and 0.787.

Editorial

Dear Readers, It gives me great pleasure to announce the eighth regular issue of 2022. In this issue, various topical aspects of computer science are covered by 18 authors from 5 countries in 5 articles. As always, I would like to thank all the authors for their sound research and the editorial board for their highly valuable review effort and suggestions for improvement. These contributions, together with the generous support of the consortium members, sustain the quality of our journal. In an ongoing effort to further strengthen our journal, I would like to expand the editorial board: If you are a tenured associate professor or above with a strong publication record, you are welcome to apply to join our editorial board. We are also interested in receiving high-quality proposals for special issues on new topics and trends. Please consider yourself and encourage your colleagues to submit high-quality articles or special issue proposals for our journal. In this regular issue, I am very pleased to introduce the following 5 accepted articles: Raoua Abdelkhalek, Imen Boukhris, and Zied Elouedi from Tunisia present their research on more trustworthy predictions based on the uncertain framework of belief function theory to support the representation, quantification and management of imperfect evidence. In a research collaboration between Jordan and the USA, Abd Al-Rahman Al-Nounou, Osama Al-Khaleel, Fadi Obeidat, and Mohammad Al-Khaleel present a methodology for designing binary multipliers, in which different sizes of customized partial products generation cells are designed and used as smaller building blocks. Venilton FalvoJr, Anderson da Silva Marcolino, Nemesio Freitas Duarte Filho, Edson OliveiraJr, and Ellen Francine Barbosa present the design, development and experimental evaluation of a software product line for mobile learning applications. Ghazala Hcini, Imen Jdey, and Hela Ltifi from Tunesia introduce their research on a new and robust deep learning model for automatically classifying malaria cells as infected or uninfected, built on a convolutional neural network. And last but not least, Sercan Yalçın, Musa Eşit, and Mehmet İshak Yüce from Turkiye discuss their approach to estimating climatological parameters based on artificial intelligence techniques with particle swarm optimization and deep neural networks.

Explainable Artificial Intelligence for Bayesian Neural Networks: Toward Trustworthy Predictions of Ocean Dynamics

AbstractThe trustworthiness of neural networks is often challenged because they lack the ability to express uncertainty and explain their skill. This can be problematic given the increasing use of neural networks in high stakes decision‐making such as in climate change applications. We address both issues by successfully implementing a Bayesian Neural Network (BNN), where parameters are distributions rather than deterministic, and applying novel implementations of explainable AI (XAI) techniques. The uncertainty analysis from the BNN provides a comprehensive overview of the prediction more suited to practitioners' needs than predictions from a classical neural network. Using a BNN means we can calculate the entropy (i.e., uncertainty) of the predictions and determine if the probability of an outcome is statistically significant. To enhance trustworthiness, we also spatially apply the two XAI techniques of Layer‐wise Relevance Propagation (LRP) and SHapley Additive exPlanation (SHAP) values. These XAI methods reveal the extent to which the BNN is suitable and/or trustworthy. Using two techniques gives a more holistic view of BNN skill and its uncertainty, as LRP considers neural network parameters, whereas SHAP considers changes to outputs. We verify these techniques using comparison with intuition from physical theory. The differences in explanation identify potential areas where new physical theory guided studies are needed.

Disease risk level prediction based on knowledge driven optimized deep ensemble framework

Healthcare information in diverse formats has been steadily boosting the growth of health systems. This information covers a wide range of new sources, such as computer files, cell phones, and health monitoring gadgets. Big health data expands the additional possibilities for analyzing the health data that improve healthcare services. Deep learning can be used in collaboration with information fusion approaches to generate better comprehensive and trustworthy predictions from large healthcare information. In this study, a risk level prediction framework is established with four main stages: pre-processing, knowledge extraction, feature extraction, as well as classification and prediction. The obtained data from the Electronic Health Records (EHR) is first exposed to a pre-processing stage, where the data cleaning and tokenization operations are performed. Then, the knowledge extraction takes place via ontology-based knowledge extraction and improved semantic similarity. In addition, the statistical and information entropy features are retrieved. To forecast the health risks from HER, a novel Ensemble Classifier (EC) with Neural network (NN), optimized Deep Belief Network (DBN) & Fuzzy logic is introduced. The extracted features are utilized to train the NN, and the retrieved knowledge bases are utilized to train the fuzzy logic. The outcome from NN as well as fuzzy logic is given as a source of input to the DBN, where the final risk prediction of the disease takes place. Since DBN is the key indicator; its weight is fine-tuned utilizing a new hybrid approach known as Rain Leveraged Dynamic Butterfly Optimization (RLDBO) to improve risk level prediction accuracy.

Evaluation of parameters influencing the performance of photovoltaic-thermoelectric (PV-TE) hybrid system

Abstract This study analyzes the feasibility of the photovoltaic-thermoelectric (PV-TE) hybrid system and examines the appropriate parameters to optimize the design of the hybrid system. A new formula that sets a minimal working condition from which the output power of the hybrid system will exceed that of the PV cell alone at 298 K was developed. The experimental results showed that the hybrid system outperformed the PV cell alone at 298 K, once the minimal working condition is attained. Moreover, the results illustrated that we can enhance the performance with a slight change in the cold side temperature of the TE using PV cells with a relatively small temperature coefficient and efficiency. The results indicated also that the model can produce trustworthy predictions, consequently, it may be useful during the design of a hybrid system with optimized performance.

Uncertainty quantification by ensemble learning for computational optical form measurements

Uncertainty quantification by ensemble learning is explored in terms of an application known from the field of computational optical form measurements. The application requires solving a large-scale, nonlinear inverse problem. Ensemble learning is used to extend the scope of a recently developed deep learning approach for this problem in order to provide an uncertainty quantification of the solution to the inverse problem predicted by the deep learning method. By systematically inserting out-of-distribution errors as well as noisy data, the reliability of the developed uncertainty quantification is explored. Results are encouraging and the proposed application exemplifies the ability of ensemble methods to make trustworthy predictions on the basis of high-dimensional data in a real-world context.

Robustness to Spurious Correlations in Text Classification via Automatically Generated Counterfactuals

Spurious correlations threaten the validity of statistical classifiers. While model accuracy may appear high when the test data is from the same distribution as the training data, it can quickly degrade when the test distribution changes. For example, it has been shown that classifiers perform poorly when humans make minor modifications to change the label of an example. One solution to increase model reliability and generalizability is to identify causal associations between features and classes. In this paper, we propose to train a robust text classifier by augmenting the training data with automatically generated counterfactual data. We first identify likely causal features using a statistical matching approach. Next, we generate counterfactual samples for the original training data by substituting causal features with their antonyms and then assigning opposite labels to the counterfactual samples. Finally, we combine the original data and counterfactual data to train a robust classifier. Experiments on two classification tasks show that a traditional classifier trained on the original data does very poorly on human-generated counterfactual samples (e.g., 10%-37% drop in accuracy). However, the classifier trained on the combined data is more robust and performs well on both the original test data and the counterfactual test data (e.g., 12%-25% increase in accuracy compared with the traditional classifier). Detailed analysis shows that the robust classifier makes meaningful and trustworthy predictions by emphasizing causal features and de-emphasizing non-causal features.

Towards Trustworthy Predictions from Deep Neural Networks with Fast Adversarial Calibration

To facilitate a wide-spread acceptance of AI systems guiding decision making in real-world applications, trustworthiness of deployed models is key. That is, it is crucial for predictive models to be uncertainty-aware and yield well-calibrated (and thus trustworthy) predictions for both in-domain samples as well as under domain shift. Recent efforts to account for predictive uncertainty include post-processing steps for trained neural networks, Bayesian neural networks as well as alternative non-Bayesian approaches such as ensemble approaches and evidential deep learning. Here, we propose an efficient yet general modelling approach for obtaining well-calibrated, trustworthy probabilities for samples obtained after a domain shift. We introduce a new training strategy combining an entropy-encouraging loss term with an adversarial calibration loss term and demonstrate that this results in well-calibrated and technically trustworthy predictions for a wide range of domain drifts. We comprehensively evaluate previously proposed approaches on different data modalities, a large range of data sets including sequence data, network architectures and perturbation strategies. We observe that our modelling approach substantially outperforms existing state-of-the-art approaches, yielding well-calibrated predictions under domain drift.

Long-Term Snow Height Variations in Antarctica from GNSS Interferometric Reflectometry

Acquiring reliable estimates of the Antarctic Ice Sheet surface mass balance is essential for trustworthy predictions of its evolution and future contribution to sea level rise. Snow height variations, i.e., the net change of the surface elevation resulting from a combination of surface processes such as snowfall, ablation, and wind redistribution, can provide a unique tool to constrain the uncertainty on mass budget estimations. In this study, GNSS Interferometric Reflectometry (GNSS-IR) is exploited to assess the long-term variations of snow accumulation and ablation processes. Eight antennas belonging to the Polar Earth Observing Network (POLENET) network are considered, together with the ROB1 antenna, deployed in the east part of Antarctica by the Royal Observatory of Belgium. For ROB1, which is located on an ice rise, we highlight an annual variation of snow accumulation in April–May (~30–50 cm) and ablation during spring/summer period. A snow surface elevation velocity of +0.08 ± 0.01 ma−1 is observed in the 2013–2016 period, statistically rejecting the “no trend” null hypothesis. As the POLENET stations are all located on moving glaciers, their associated downhill motion must be corrected for using an elevation model. This induces an increased uncertainty on the snow surface elevation change determined from GNSS-IR. Among the eight stations analyzed, only three of them show a long-term snow height variation larger than the uncertainties. One is located on the Flask Galcier in the Antarctic Peninsula, with a decrease of more than 4 m between 2012 and 2014, with an uncertainty of 2.5 m. The second one is located on the Lower Thwaites Glacier where we observe, between 2010 and 2020, a snow surface drop of 10 m, with a conservative uncertainty of 1 m. The third station, located on the West Antarctic Ice Sheet (WAIS) divide, shows on the opposite an upward motion from 2005 to 2019, of 1.2 m with an uncertainty of 0.4 m. The snow surface change of the other POLENET stations analyzed is smaller than the uncertainty associated with the glacier slope.

DR|GRADUATE: Uncertainty-aware deep learning-based diabetic retinopathy grading in eye fundus images

Diabetic retinopathy (DR) grading is crucial in determining the adequate treatment and follow up of patient, but the screening process can be tiresome and prone to errors. Deep learning approaches have shown promising performance as computer-aided diagnosis (CAD) systems, but their black-box behaviour hinders clinical application. We propose DR|GRADUATE, a novel deep learning-based DR grading CAD system that supports its decision by providing a medically interpretable explanation and an estimation of how uncertain that prediction is, allowing the ophthalmologist to measure how much that decision should be trusted. We designed DR|GRADUATE taking into account the ordinal nature of the DR grading problem. A novel Gaussian-sampling approach built upon a Multiple Instance Learning framework allow DR|GRADUATE to infer an image grade associated with an explanation map and a prediction uncertainty while being trained only with image-wise labels. DR|GRADUATE was trained on the Kaggle DR detection training set and evaluated across multiple datasets. In DR grading, a quadratic-weighted Cohen's kappa (κ) between 0.71 and 0.84 was achieved in five different datasets. We show that high κ values occur for images with low prediction uncertainty, thus indicating that this uncertainty is a valid measure of the predictions' quality. Further, bad quality images are generally associated with higher uncertainties, showing that images not suitable for diagnosis indeed lead to less trustworthy predictions. Additionally, tests on unfamiliar medical image data types suggest that DR|GRADUATE allows outlier detection. The attention maps generally highlight regions of interest for diagnosis. These results show the great potential of DR|GRADUATE as a second-opinion system in DR severity grading.

The Present State of “Solid” under-Platform Damper Mechanics at AERMEC - POLITO

The numerical simulation of friction-damped blades in turbomachinery applications requires knowledge of contact parameters to be introduced in contact models. The equilibrium and kinematics of dampers are dominated by phenomena occurring at the two interfaces between the damper and the corresponding blade platforms. A precise knowledge of parameter values is vital to ensure trustworthy predictions of blades vibration frequency and of the available amount of amplitude damping. Test rigs developed at the AERMEC lab. during the last decade are presented, and reasons for their improvements are explained. These test rigs have the primary purpose to allow direct observations of contact forces and displacements, and the ensuing estimate of contact parameters. The reliability of the measurements and of their processing is demonstrated through a worked out example.

Modeling and predicting the popularity of online news based on temporal and content-related features

As the market of globally available online news is large and still growing, there is a strong competition between online publishers in order to reach the largest possible audience. Therefore an intelligent online publishing strategy is of the highest importance to publishers. A prerequisite for being able to optimize any online strategy, is to have trustworthy predictions of how popular new online content may become. This paper presents a novel methodology to model and predict the popularity of online news. We first introduce a new strategy and mathematical model to capture view patterns of online news. After a thorough analysis of such view patterns, we show that well-chosen base functions lead to suitable models, and show how the influence of day versus night on the total view patterns can be taken into account to further increase the accuracy, without leading to more complex models. Second, we turn to the prediction of future popularity, given recently published content. By means of a new real-world dataset, we show that the combination of features related to content, meta-data, and the temporal behavior leads to significantly improved predictions, compared to existing approaches which only consider features based on the historical popularity of the considered articles. Whereas traditionally linear regression is used for the application under study, we show that the more expressive gradient tree boosting method proves beneficial for predicting news popularity.

Statistical thermodynamics of thermotropic biaxial nematic liquid crystals: An effective, molecular-field based theoretical description by means of a closed approximate form of the orientational partition function

In this work, we show that the use of a molecular-field approach and of a closed, effective (even though approximate) form of the orientational partition function, leads to trustworthy predictions of order parameters and other important thermodynamic functions (as heat capacity, orientational internal energy and entropy) of real and/or virtual biaxial nematic mesophases. As a matter of fact, when the partition function Z is explicitly known, all about the thermodynamics of the studied systems becomes in principle accessible, since the thermodynamic functions can be directly calculated through the usual formulas provided by the statistical mechanics. We were successful in obtaining such an approximate expression for Z that works well and allows for almost instantaneous, reliable simulations (it is worthwhile to emphasize that, being available in the present case an analytical expression of Z, the derivatives occurring in the statistical mechanics formulas can be calculated analytically and instantaneously). Several examples of the performances of our approach are presented where, besides the second-rank order parameters, also heat capacities and changes in entropy and internal energy are quantitatively assessed, often for the first time, for the treated cases; moreover, an evaluation of some of the most important fourth-rank order parameters for the treated phases has been carried out. The results are good and our treatment proves to be suitable and promising also for future studies.