Science-Informed Design of Deep Learning With Applications to Wireless Systems: A Tutorial

TL;DR

This tutorial addresses the core limitations of data-driven deep learning in wireless systems by advocating Science-Informed Deep Learning (ScIDL), which integrates physics, world facts, and expert knowledge into learning pipelines. It introduces a unifying taxonomy across three dimensions—architecture, training data/output validation, and loss/optimization—and presents two representative wireless case studies to illustrate the practical benefits of science-informed design, including improved generalization and physical consistency. The paper surveys mechanisms for embedding knowledge via node/layer design, data generation, and physics-driven loss terms, while also outlining challenges such as benchmarking, data scarcity, and the need for scalable tools and theory for interpretability. By outlining future directions in ScIDL-based optimization, environment estimation, semantic communication, safety, and knowledge extraction, the authors chart a path toward robust, physically grounded DL-enabled wireless systems with broader real-world impact.

Abstract

Recent advances in computational infrastructure and large-scale data processing have accelerated the adoption of data-driven inference methods, particularly deep learning (DL), to solve problems in many scientific and engineering domains. In wireless systems, DL has been applied to problems where analytical modeling or optimization is difficult to formulate, relies on oversimplified assumptions, or becomes computationally intractable. However, conventional DL models are often regarded as non-transparent, as their internal reasoning mechanisms are difficult to interpret even when model parameters are fully accessible. This lack of transparency undermines trust and leads to three interrelated challenges: limited interpretability, weak generalization, and the absence of a principled framework for parameter tuning. Science-informed deep learning (ScIDL) has emerged as a promising paradigm to address these limitations by integrating scientific knowledge into deep learning pipelines. This integration enables more precise characterization of model behavior and provides clearer explanations of how and why DL models succeed or fail. Despite growing interest, the existing literature remains fragmented and lacks a unifying taxonomy. This tutorial presents a structured overview of ScIDL methods and their applications in wireless systems. We introduce a structured taxonomy that organizes the ScIDL landscape, present two representative case studies illustrating its use in challenging wireless problems, and discuss key challenges and open research directions. The pedagogical structure guides readers from foundational concepts to advanced applications, making the tutorial accessible to researchers in wireless communications without requiring prior expertise in AI.

Figures (6)

• Figure 1: Conceptual overview of ScIDL, showing the integration of raw data, scientific knowledge, and DL architectures. By embedding physics and domain principles into the learning pipeline, DL models improve their interpretability, domain-consistency, and generalization, and enable meta-applications such as scientific discovery and theory-guided DL design.
• Figure 2: Organizational structure of the ScIDL Tutorial to guide readers through their reading progression. The map outlines the tutorial's core sections: Introduction, Preliminary Discussion, ScIDL Taxonomy, ScIDL Case Studies, the Future of ScIDL, and Conclusion.
• Figure 3: A conceptual overview of the proposed ScIDL taxonomy, organizing science-informed DL methods into three dimensions: (1) Architecture Design, where scientific knowledge is embedded through node/layer design, parameter initialization, and pre-training strategies; (2) Training Data and Output Validation, which integrates scientific principles into data generation, processes and physics-based input and output consistency checks; and (3) Loss Function Formulation and Optimization, which incorporates scientific constraints, governing equations, and priors directly into the loss formulation and the corresponding optimization process.
• Figure 4: Sum-rate $R$ versus the number of users, comparing WMMSE, DNN, mask-aware DNN, deep unfolding, and accelerated deep unfolding.
• Figure 5: Confusion matrices of LSTM-based HAR models evaluated on (a) a distribution-like test domain and (b) a target domain.