While modern deep networks have demonstrated remarkable versatility, their training dynamics remain poorly understood--often driven more by empirical tweaks than architectural insight. This paper investigates how internal structural choices shape the behavior of learning systems. Building on prior efforts that introduced simple architectural constraints, we explore the broader implications of structure for convergence, generalization, and adaptation. Our approach centers on a family of enriched transformation layers that incorporate constrained pathways and adaptive corrections. We analyze how these structures influence gradient flow, spectral sensitivity, and fixed-point behavior--uncovering mechanisms that contribute to training stability and representational regularity. Theoretical analysis is paired with empirical studies on synthetic and structured tasks, demonstrating improved robustness, smoother optimization, and scalable depth behavior. Rather than prescribing fixed templates, we emphasize principles of tractable design that can steer learning behavior in interpretable ways. Our findings support a growing view that architectural design is not merely a matter of performance tuning, but a critical axis for shaping learning dynamics in scalable and trustworthy neural systems.

The Extreme Operating Conditions Search (EOCS) problem is one of the key problems in relay setting calculation, which is used to ensure that the setting values of protection relays can adapt to the changing operating conditions of power systems over a period of time after deployment. The high penetration of renewable energy and the wide application of inverter-based resources make the operating conditions of renewable power systems more volatile, which urges the adoption of the online relay setting calculation strategy. However, the computation speed of existing EOCS methods based on local enumeration, heuristic algorithms, and mathematical programming cannot meet the efficiency requirement of online relay setting calculation. To reduce the time overhead, this paper, for the first time, proposes an efficient deep learning-based EOCS method suitable for online relay setting calculation. First, the power system information is formulated as four layers, i.e., a component parameter layer, a topological connection layer, an electrical distance layer, and a graph distance layer, which are fed into a parallel graph neural network (PGNN) model for feature extraction. Then, the four feature layers corresponding to each node are spliced and stretched, and then fed into the decision network to predict the extreme operating condition of the system. Finally, the proposed PGNN method is validated on the modified IEEE 39-bus and 118-bus test systems, where some of the synchronous generators are replaced by renewable generation units. The nonlinear fault characteristics of renewables are fully considered when computing fault currents. The experiment results show that the proposed PGNN method achieves higher accuracy than the existing methods in solving the EOCS problem. Meanwhile, it also provides greater improvements in online computation time.

Vision-based object tracking is a critical component for achieving autonomous aerial navigation, particularly for obstacle avoidance. Neuromorphic Dynamic Vision Sensors (DVS) or event cameras, inspired by biological vision, offer a promising alternative to conventional frame-based cameras. These cameras can detect changes in intensity asynchronously, even in challenging lighting conditions, with a high dynamic range and resistance to motion blur. Spiking neural networks (SNNs) are increasingly used to process these event-based signals efficiently and asynchronously. Meanwhile, physics-based artificial intelligence (AI) provides a means to incorporate system-level knowledge into neural networks via physical modeling. This enhances robustness, energy efficiency, and provides symbolic explainability. In this work, we present a neuromorphic navigation framework for autonomous drone navigation. The focus is on detecting and navigating through moving gates while avoiding collisions. We use event cameras for detecting moving objects through a shallow SNN architecture in an unsupervised manner. This is combined with a lightweight energy-aware physics-guided neural network (PgNN) trained with depth inputs to predict optimal flight times, generating near-minimum energy paths. The system is implemented in the Gazebo simulator and integrates a sensor-fused vision-to-planning neuro-symbolic framework built with the Robot Operating System (ROS) middleware. This work highlights the future potential of integrating event-based vision with physics-guided planning for energy-efficient autonomous navigation, particularly for low-latency decision-making.

Vision-based object tracking is an essential precursor to performing autonomous aerial navigation in order to avoid obstacles. Biologically inspired neuromorphic event cameras are emerging as a powerful alternative to frame-based cameras, due to their ability to asynchronously detect varying intensities (even in poor lighting conditions), high dynamic range, and robustness to motion blur. Spiking neural networks (SNNs) have gained traction for processing events asynchronously in an energy-efficient manner. On the other hand, physics-based artificial intelligence (AI) has gained prominence recently, as they enable embedding system knowledge via physical modeling inside traditional analog neural networks (ANNs). In this letter, we present an event-based physics-guided neuromorphic planner (EV-Planner) to perform obstacle avoidance using neuromorphic event cameras and physics-based AI. We consider the task of autonomous drone navigation where the mission is to detect moving gates and fly through them while avoiding a collision. We use event cameras to perform object detection using a shallow spiking neural network in an unsupervised fashion. Utilizing the physical equations of the brushless DC motors present in the drone rotors, we train a lightweight energy-aware physics-guided neural network (PgNN) with depth inputs. This predicts the optimal flight time responsible for generating near-minimum energy paths. We spawn the drone in the Gazebo simulator and implement a sensor-fused vision-to-planning neuro-symbolic framework using Robot Operating System (ROS). Simulation results for safe collision-free flight trajectories are presented with performance analysis, ablation study and potential future research directions

Ensuring fairness in Recommendation Systems (RSs) across demographic groups is critical due to the increased integration of RSs in applications such as personalized healthcare, finance, and e-commerce. Graph-based RSs play a crucial role in capturing intricate higher-order interactions among entities. However, integrating these graph models into the Federated Learning (FL) paradigm with fairness constraints poses formidable challenges as this requires access to the entire interaction graph and sensitive user information (such as gender, age, etc.) at the central server. This paper addresses the pervasive issue of inherent bias within RSs for different demographic groups without compromising the privacy of sensitive user attributes in FL environment with the graph-based model. To address the group bias, we propose F2PGNN (Fair Federated Personalized Graph Neural Network), a novel framework that leverages the power of Personalized Graph Neural Network (GNN) coupled with fairness considerations. Additionally, we use differential privacy techniques to fortify privacy protection. Experimental evaluation on three publicly available datasets showcases the efficacy of F2PGNN in mitigating group unfairness by 47% - 99% compared to the state-of-the-art while preserving privacy and maintaining the utility. The results validate the significance of our framework in achieving equitable and personalized recommendations using GNN within the FL landscape.

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides researchers and engineers with a solid starting point to comprehend how to integrate different layers of physics into neural networks.

This paper introduces a novel framework for combining scientific knowledge of physics-based models with neural networks to advance scientific discovery. This framework, termed as physics-guided neural network (PGNN), leverages the output of physics-based model simulations along with observational features to generate predictions using a neural network architecture. Further, this paper presents a novel framework for using physics-based loss functions in the learning objective of neural networks, to ensure that the model predictions not only show lower errors on the training set but are also scientifically consistent with the known physics on the unlabeled set. We illustrate the effectiveness of PGNN for the problem of lake temperature modeling, where physical relationships between the temperature, density, and depth of water are used to design a physics-based loss function. By using scientific knowledge to guide the construction and learning of neural networks, we are able to show that the proposed framework ensures better generalizability as well as scientific consistency of results.