Nonlinear optimization (NOPT) is a meaningful tool for solving complex tasks in fields like engineering, economics, and operations research, among others. However, NOPT has problems when it comes to dealing with data variability and noisy input measurements that lead to incorrect solutions. Furthermore, nonlinear constraints may result in outcomes that are either infeasible or suboptimal, such as nonconvex optimization. This paper introduces a novel regularized physics-informed neural network (RPINN) framework as a new NOPT tool for both supervised and unsupervised data-driven scenarios. Our RPINN is threefold: By using custom activation functions and regularization penalties in an artificial neural network (ANN), RPINN can handle data variability and noisy inputs. Furthermore, it employs physics principles to construct the network architecture, computing the optimization variables based on network weights and learned features. In addition, it uses automatic differentiation training to make the system scalable and cut down on computation time through batch-based back-propagation. The test results for both supervised and unsupervised NOPT tasks show that our RPINN can provide solutions that are competitive compared to state-of-the-art solvers. In turn, the robustness of RPINN against noisy input measurements makes it particularly valuable in environments with fluctuating information. Specifically, we test a uniform mixture model and a gas-powered system as NOPT scenarios. Overall, with RPINN, its ANN-based foundation offers significant flexibility and scalability.

Modern medium-voltage (MV) distribution networks face increasing reliability challenges driven by aging assets, climate variability, and evolving operational demands. In Colombia and across Latin America, reliability metrics, such as the System Average Interruption Frequency Index (SAIFI), standardized under IEEE 1366, serve as key indicators for regulatory compliance and service quality. However, existing analytical approaches struggle to jointly deliver predictive accuracy, interpretability, and traceability required for regulated environments. Here, we introduce CRITAIR (Criticality Analysis through Interpretable Artificial Intelligence-based Recommendations), an integrated framework that combines predictive modeling, explainable analytics, and regulation-aware reasoning to enhance reliability management in MV networks. CRITAIR unifies three components: (i) a TabNet-based predictive module that estimates SAIFI using outage, asset, and meteorological data while producing global and local attributions; (ii) an agentic retrieval-and-reasoning stage that grounds recommendations in regulatory evidence from RETIE and NTC 2050; and (iii) interpretable reasoning graphs that map decision pathways. Evaluations conducted on real operational data demonstrate that CRITAIR achieves competitive predictive performance—comparable to Random Forest and XGBoost—while maintaining transparency through sparse attention and sequential feature explainability. Also, our regulation-aware reasoning module exhibits coherent and verifiable recommendations, achieving high semantic alignment scores (BERTScore) and expert-rated interpretability. Overall, CRITAIR bridges the gap between predictive analytics and regulatory governance, offering a transparent, auditable, and deployment-ready solution for digital transformation in electric distribution systems.

Modern medium-voltage (MV) distribution networks face increasing reliability challenges driven by aging assets, climate variability, and evolving operational demands. In Colombia and across Latin America, reliability metrics such as the system average interruption frequency index (SAIFI), standardized under IEEE 1366, serve as key indicator for regulatory compliance and service quality. However, existing analytical approaches struggle to jointly deliver predictive accuracy, interpretability, and traceability required for regulated environments. Here, we introduces CRITAIR (Criticality Analysis through Interpretable Artificial Intelligence-based Recommendations), an integrated framework that combines predictive modeling, explainable analytics, and regulation-aware reasoning to enhance reliability management in MV networks. CRITAIR unifies three components: (i) a TabNet-based predictive module that estimates SAIFI using outage, asset, and meteorological data while producing global and local attributions; (ii) an agentic retrieval-and-reasoning layer that grounds recommendations in regulatory evidence from RETIE and NTC 2050; and (iii) interpretable reasoning graphs that map decision pathways for full auditability. Evaluations conducted on real operational data demonstrate that CRITAIR achieves competitive predictive performance—comparable to Random Forest and XGBoost—while maintaining transparency through sparse attention and sequential feature explainability. Also, our regulation-aware reasoning module exhibits coherent and verifiable recommendations, achieving high semantic alignment scores (BERTScore) and expert-rated interpretability. Overall, CRITAIR bridges the gap between predictive analytics and regulatory governance, offering a transparent, auditable, and deployment-ready solution for digital transformation in electric distribution systems.

Addressing unemployment is essential for formulating effective public policies. In particular, socioeconomic and monetary variables serve as essential indicators for anticipating labor market trends, given their strong influence on employment dynamics and economic stability. However, effective unemployment rate prediction requires addressing the non-stationary and non-linear characteristics of labor data. Equally important is the preservation of interpretability in both samples and features to ensure that forecasts can meaningfully inform public decision-making. Here, we provide an explainable framework integrating unsupervised and supervised machine learning to enhance unemployment rate prediction and interpretability. Our approach is threefold: (i) we gather a dataset for Colombian unemployment rate prediction including monetary and socioeconomic variables. (ii) Then, we used a Local Biplot technique from the widely recognized Uniform Manifold Approximation and Projection (UMAP) method along with local affine transformations as an unsupervised representation of non-stationary and non-linear data patterns in a simplified and comprehensible manner. (iii) A Gaussian Processes regressor with kernel-based feature relevance analysis is coupled as a supervised counterpart for both unemployment rate prediction and input feature importance analysis. We demonstrated the effectiveness of our proposed approach through a series of experiments conducted on our customized database focused on unemployment indicators in Colombia. Furthermore, we carried out a comparative analysis between traditional statistical techniques and modern machine learning methods. The results revealed that our framework significantly enhances both clustering and predictive performance, while also emphasizing the importance of input samples and feature selection in driving accurate outcomes.

Domain adaptation is a key approach to ensure that artificial intelligence models maintain reliable performance when facing distributional shifts between training (source) and testing (target) domains. However, existing methods often struggle to simultaneously preserve domain-invariant representations and discriminative class structures, particularly in the presence of complex covariate shifts and noisy pseudo-labels in the target domain. In this work, we introduce Conditional Rényi $\alpha$-Entropy Domain Adaptation, named CREDA, a novel deep learning framework for domain adaptation that integrates kernel-based conditional alignment with a differentiable, matrix-based formulation of Rényi’s quadratic entropy. The proposed method comprises three main components: (i) a deep feature extractor that learns domain-invariant representations from labeled source and unlabeled target data; (ii) an entropy-weighted approach that down-weights low-confidence pseudo-labels, enhancing stability in uncertain regions; and (iii) a class-conditional alignment loss, formulated as a Rényi-based entropy kernel estimator, that enforces semantic consistency in the latent space. We validate CREDA on standard benchmark datasets for image classification, including Digits, ImageCLEF-DA, and Office-31, showing competitive performance against both classical and deep learning-based approaches. Furthermore, we employ nonlinear dimensionality reduction and class activation maps visualizations to provide interpretability, revealing meaningful alignment in feature space and offering insights into the relevance of individual samples and attributes. Experimental results confirm that CREDA improves cross-domain generalization while promoting accuracy, robustness, and interpretability.

Domain adaptation is a key approach to ensure that artificial intelligence models maintain reliable performance when facing distributional shifts between training (source) and testing (target) domains. However, existing methods often struggle to simultaneously preserve domain-invariant representations and discriminative class structures, particularly in the presence of complex covariate shifts and noisy pseudo-labels in the target domain. In this work, we introduce Conditional Rényi α-Entropy Domain Adaptation, named CREDA, a novel deep learning framework for domain adaptation that integrates kernel-based conditional alignment with a differentiable, matrix-based formulation of Rényi’s quadratic entropy. The proposed method comprises three main components: (i) a deep feature extractor that learns domain-invariant representations from labeled source and unlabeled target data; (ii) an entropy-weighted approach that down-weights low-confidence pseudo-labels, enhancing stability in uncertain regions; and (iii) a class-conditional alignment loss, formulated as a Rényi-based entropy kernel estimator, that enforces semantic consistency in the latent space. We validate CREDA on standard benchmark datasets for image classification, including Digits, ImageCLEF-DA, and Office-31, showing competitive performance against both classical and deep learning-based approaches. Furthermore, we employ nonlinear dimensionality reduction and class activation maps visualizations to provide interpretability, revealing meaningful alignment in feature space and offering insights into the relevance of individual samples and attributes. Experimental results confirm that CREDA improves cross-domain generalization while promoting accuracy, robustness, and interpretability.