Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are derived through empirical fitting, often lack generalizability and rely heavily on expert intuition and predefined functional forms. In this work, we propose a graph - based equation discovery framework for the automated discovery of constitutive laws directly from multisourc e experimental data. This framework expresses equations as directed graphs, where nodes represent operators and variables, edges denote computational relations, and edge features encode parametric dependencies . This enables the generation and optimization of free - form symbolic expressions with undetermined material - specific parameters . Through the proposed framework, we have discovered new constitutive models for strain - rate effects in alloy steel materials and the deformation behavior of lithium metal. Com pared with conventional empirical models, these new models exhibit compact analytical structures and achieve higher accuracy. The proposed graph - based equation discovery framework provides a generalizable and interpretable approach for data - driven scientific mode l ling, particularly in contexts where traditional empirical formulations are inadequate for representing complex physical phenomena. Keywords: Constitutive model, graph, equation discovery, solid mechanics, data - driven modelling . Introduction Constitutive laws serve as fundamental elements in solid mechanics, establishing the relationship between kinematic measures and static quantities to characterize material - specific behavior. Unlike conservation principles and kinematic relations, which are derived from first principles and regarded as axiomatic foundations, constitutive models encapsulate empirical descriptions of material responses to external stimuli . Accordingly, they are typically established through phenomenological approaches, guided by systematic experimentation and theoretical generalization, to characterize nonlinear behaviors across varying conditions ( 1) . The accuracy and generality of constitutive models are critical for the reliability of mechanical analysis, directly influencing both theoretical developments and practical applications in computational mechanics and materials engineering.

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO\textsubscript{1}), faces a fundamental tradeoff between logic fidelity and computational efficiency. This work establishes a Grounding-Skolemization dichotomy to systematically analyze this challenge and motivate a paradigm shift in CQA. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemization-based methods neglect to explicitly model Skolem functions and compromise logical consistency. To address these limitations, we propose the Logic-constrained Vector Symbolic Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator, as well as a logical constraint-driven optimization protocol to harmonize geometric and logical requirements. Theoretically, LVSA guarantees universality for all EFO\textsubscript{1} queries with low computational complexity. Empirically, it outperforms state-of-the-art Skolemization-based methods and reduces inference costs by orders of magnitude compared to Grounding-based baselines.

The Transformer architecture has revolutionized the field of sequence modeling and underpins the recent breakthroughs in large language models (LLMs). However, a comprehensive mathematical theory that explains its structure and operations remains elusive. In this work, we propose a novel continuous framework that rigorously interprets the Transformer as a discretization of a structured integro-differential equation. Within this formulation, the self-attention mechanism emerges naturally as a non-local integral operator, and layer normalization is characterized as a projection to a time-dependent constraint. This operator-theoretic and variational perspective offers a unified and interpretable foundation for understanding the architecture's core components, including attention, feedforward layers, and normalization. Our approach extends beyond previous theoretical analyses by embedding the entire Transformer operation in continuous domains for both token indices and feature dimensions. This leads to a principled and flexible framework that not only deepens theoretical insight but also offers new directions for architecture design, analysis, and control-based interpretations. This new interpretation provides a step toward bridging the gap between deep learning architectures and continuous mathematical modeling, and contributes a foundational perspective to the ongoing development of interpretable and theoretically grounded neural network models.

\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database. Graph Edit Distance (GED) and Maximum Common Subgraphs (MCS) are the two commonly used domain-agnostic metrics to evaluate graph similarity in practice. Unfortunately, computing the exact GED is known to be a NP-hard problem. To solve this limitation, neural network based models have been proposed to approximate the calculations of GED/MCS. However, deep learning models are well-known ``black boxes'', thus the typically characteristic one-to-one node/subgraph alignment process in the classical computations of GED and MCS cannot be seen. Existing methods have paid attention to approximating the node/subgraph alignment (soft alignment), but the one-to-one node alignment (hard alignment) has not yet been solved. To fill this gap, in this paper we propose a novel interpretable neural node alignment model without relying on node alignment ground truth information. Firstly, the quadratic assignment problem in classical GED computation is relaxed to a linear alignment via embedding the features in the node embedding space. Secondly, a differentiable Gumbel-Sinkhorn module is proposed to unsupervised generate the optimal one-to-one node alignment matrix. Experimental results in real-world graph datasets demonstrate that our method outperforms the state-of-the-art methods in graph similarity computation and graph retrieval tasks, achieving up to 16\% reduction in the Mean Squared Error and up to 12\% improvement in the retrieval evaluation metrics, respectively.

Understanding the spatial distribution of palms within tropical forests is essential for effective ecological monitoring, conservation strategies, and the sustainable integration of natural forest products into local and global supply chains. However, the analysis of remotely sensed data in these environments faces significant challenges, such as overlapping palm and tree crowns, uneven shading across the canopy surface, and the heterogeneous nature of the forest landscapes, which often affect the performance of palm detection and segmentation algorithms. To overcome these issues, we introduce PalmDSNet, a deep learning framework for real-time detection, segmentation, and counting of canopy palms. Additionally, we employ a bimodal reproduction algorithm that simulates palm spatial propagation to further enhance the understanding of these point patterns using PalmDSNet's results. We used UAV-captured imagery to create orthomosaics from 21 sites across western Ecuadorian tropical forests, covering a gradient from the everwet Choc\'o forests near Colombia to the drier forests of southwestern Ecuador. Expert annotations were used to create a comprehensive dataset, including 7,356 bounding boxes on image patches and 7,603 palm centers across five orthomosaics, encompassing a total area of 449 hectares. By combining PalmDSNet with the bimodal reproduction algorithm, which optimizes parameters for both local and global spatial variability, we effectively simulate the spatial distribution of palms in diverse and dense tropical environments, validating its utility for advanced applications in tropical forest monitoring and remote sensing analysis.

Effective patient monitoring is vital for timely interventions and improved healthcare outcomes. Traditional monitoring systems often struggle to handle complex, dynamic environments with fluctuating vital signs, leading to delays in identifying critical conditions. To address this challenge, we propose a novel AI-driven patient monitoring framework using multi-agent deep reinforcement learning (DRL). Our approach deploys multiple learning agents, each dedicated to monitoring a specific physiological feature, such as heart rate, respiration, and temperature. These agents interact with a generic healthcare monitoring environment, learn the patients' behaviour patterns, and make informed decisions to alert the corresponding Medical Emergency Teams (METs) based on the level of emergency estimated. In this study, we evaluate the performance of the proposed multi-agent DRL framework using real-world physiological and motion data from two datasets: PPG-DaLiA and WESAD. We compare the results with several baseline models, including Q-Learning, PPO, Actor-Critic, Double DQN, and DDPG, as well as monitoring frameworks like WISEML and CA-MAQL. Our experiments demonstrate that the proposed DRL approach outperforms all other baseline models, achieving more accurate monitoring of patient's vital signs. Furthermore, we conduct hyperparameter optimization to fine-tune the learning process of each agent. By optimizing hyperparameters, we enhance the learning rate and discount factor, thereby improving the agents' overall performance in monitoring patient health status.

Machine Unlearning is an emerging field that addresses data privacy issues by enabling the removal of private or irrelevant data from the Machine Learning process. Challenges related to privacy and model efficiency arise from the use of outdated, private, and irrelevant data. These issues compromise both the accuracy and the computational efficiency of models in both Machine Learning and Unlearning. To mitigate these challenges, we introduce a novel framework, Attention-based Machine Unlearning using Federated Reinforcement Learning (FRAMU). This framework incorporates adaptive learning mechanisms, privacy preservation techniques, and optimization strategies, making it a well-rounded solution for handling various data sources, either single-modality or multi-modality, while maintaining accuracy and privacy. FRAMU's strength lies in its adaptability to fluctuating data landscapes, its ability to unlearn outdated, private, or irrelevant data, and its support for continual model evolution without compromising privacy. Our experiments, conducted on both single-modality and multi-modality datasets, revealed that FRAMU significantly outperformed baseline models. Additional assessments of convergence behavior and optimization strategies further validate the framework's utility in federated learning applications. Overall, FRAMU advances Machine Unlearning by offering a robust, privacy-preserving solution that optimizes model performance while also addressing key challenges in dynamic data environments.

Artificial Intelligence techniques can be used to classify a patient's physical activities and predict vital signs for remote patient monitoring. Regression analysis based on non-linear models like deep learning models has limited explainability due to its black-box nature. This can require decision-makers to make blind leaps of faith based on non-linear model results, especially in healthcare applications. In non-invasive monitoring, patient data from tracking sensors and their predisposing clinical attributes act as input features for predicting future vital signs. Explaining the contributions of various features to the overall output of the monitoring application is critical for a clinician's decision-making. In this study, an Explainable AI for Quantitative analysis (QXAI) framework is proposed with post-hoc model explainability and intrinsic explainability for regression and classification tasks in a supervised learning approach. This was achieved by utilizing the Shapley values concept and incorporating attention mechanisms in deep learning models. We adopted the artificial neural networks (ANN) and attention-based Bidirectional LSTM (BiLSTM) models for the prediction of heart rate and classification of physical activities based on sensor data. The deep learning models achieved state-of-the-art results in both prediction and classification tasks. Global explanation and local explanation were conducted on input data to understand the feature contribution of various patient data. The proposed QXAI framework was evaluated using PPG-DaLiA data to predict heart rate and mobile health (MHEALTH) data to classify physical activities based on sensor data. Monte Carlo approximation was applied to the framework to overcome the time complexity and high computation power requirements required for Shapley value calculations.

Reinforcement learning is well known for its ability to model sequential tasks and learn latent data patterns adaptively. Deep learning models have been widely explored and adopted in regression and classification tasks. However, deep learning has its limitations such as the assumption of equally spaced and ordered data, and the lack of ability to incorporate graph structure in terms of time-series prediction. Graphical neural network (GNN) has the ability to overcome these challenges and capture the temporal dependencies in time-series data. In this study, we propose a novel approach for predicting time-series data using GNN and monitoring with Reinforcement Learning (RL). GNNs are able to explicitly incorporate the graph structure of the data into the model, allowing them to capture temporal dependencies in a more natural way. This approach allows for more accurate predictions in complex temporal structures, such as those found in healthcare, traffic and weather forecasting. We also fine-tune our GraphRL model using a Bayesian optimisation technique to further improve performance. The proposed framework outperforms the baseline models in time-series forecasting and monitoring. The contributions of this study include the introduction of a novel GraphRL framework for time-series prediction and the demonstration of the effectiveness of GNNs in comparison to traditional deep learning models such as RNNs and LSTMs. Overall, this study demonstrates the potential of GraphRL in providing accurate and efficient predictions in dynamic RL environments.

Machine unlearning (MU) is gaining increasing attention due to the need to remove or modify predictions made by machine learning (ML) models. While training models have become more efficient and accurate, the importance of unlearning previously learned information has become increasingly significant in fields such as privacy, security, and fairness. This paper presents a comprehensive survey of MU, covering current state-of-the-art techniques and approaches, including data deletion, perturbation, and model updates. In addition, commonly used metrics and datasets are also presented. The paper also highlights the challenges that need to be addressed, including attack sophistication, standardization, transferability, interpretability, training data, and resource constraints. The contributions of this paper include discussions about the potential benefits of MU and its future directions. Additionally, the paper emphasizes the need for researchers and practitioners to continue exploring and refining unlearning techniques to ensure that ML models can adapt to changing circumstances while maintaining user trust. The importance of unlearning is further highlighted in making Artificial Intelligence (AI) more trustworthy and transparent, especially with the increasing importance of AI in various domains that involve large amounts of personal user data.