Physics-Guided Artificial Intelligence for Predictive Modeling of Complex Systems: A Comprehensive Review and Scientific Synthesis

Abstract

ABSTRACT Predictive modeling of complex multi-scale, multi-physics systems—such as turbulent fluid dynamics, geophysical climate phenomena, structural mechanics, and materials science—presents a profound challenge to modern computational science. Traditional numerical solvers based on finite element or finite difference discretizations guarantee physical conservation laws but demand prohibitive computational resources for high-dimensional or real time applications. Conversely, pure data-driven machine learning (ML) models achieve rapid inference speeds but behave as 'black-box' approximators, frequently producing physically unfeasible predictions, violating conservation laws (e.g., mass, momentum, energy), and exhibiting poor extrapolation under out-of-distribution regimes. Physics-Guided Artificial Intelligence (PGAI)—encompassing Physics-Informed Neural Networks (PINNs), Neural Operators (Fourier Neural Operators, DeepONet), and physics-regularized loss architectures—bridges this gap by directly embedding mathematical conservation principles and partial differential equations (PDEs) into deep learning representations. This review paper provides a rigorous, journal-level technical synthesis of Physics-Guided Artificial Intelligence for complex system modeling. We systematically evaluate core mathematical paradigms, loss function regularization schemes, automatic differentiation mechanisms, operator learning frameworks, and domain-specific applications across mechanics, thermal sciences, and earth systems. Drawing upon empirical benchmarks from 2019 to 2026, we demonstrate that incorporating physics-informed residual loss terms reduces predictive error norms by up to two orders of magnitude in data-sparse regimes ($N < 50$ samples) while accelerating execution speeds by 100x to 1000x compared to legacy numerical solvers. Furthermore, this paper identifies critical research gaps—including stiff PDE gradient pathologies, multi-scale stiffness, training instability in non-convex loss landscapes, and high-dimensional computational scaling—and outlines strategic future directions in neural operator foundation models and quantum-accelerated PGAI.

KEYWORDS: Physics-Guided AI (PGAI), Physics-Informed Neural Networks (PINNs), Neural Operators (FNO), Conservation Laws, Partial Differential Equations (PDEs), Automatic Differentiation, Surrogate Modeling, Out-of Distribution Extrapolation.