Beyond Data-Driven: How Physics-Informed Neural Networks are Reshaping Multi-Physics Design and Discovery

Abstract: Physics-informed neural networks (PINNs) constitute a rapidly maturing class of scientific machine learning models in which the governing equations of a physical system are embedded directly into the training objective as soft constraints. By enforcing partial differential equations (PDEs), conservation laws, and constitutive relationships during optimization, PINNs enable the construction of models that are simultaneously data-efficient, physically consistent, and capable of operating in regimes where measurements are sparse or indirect. In contrast to conventional deep learning, where the loss is typically defined solely in terms of data misfit, the learning task in PINNs is reformulated as a constrained optimization problem in which admissible solutions are confined to the manifold defined by the underlying physics. This review provides a comprehensive assessment of recent developments in physics-informed machine learning with an emphasis on PINN-based formulations for forward modelling, inverse design, and equation discovery across nanophotonics, fluid mechanics, astronomy, and biomedical engineering. Particular attention is devoted to how physical knowledge is injected at different stages of the modelling pipeline, including synthetic data generation, non-dimensionalization and scaling, architecture selection, loss design, and post-training regularization. We highlight emerging strategies for multi-physics coupling, transfer learning across parameter and geometry spaces, and rigorous benchmarking against established numerical solvers. Finally, the review discusses interpretability, uncertainty quantification, and hardware acceleration, and articulates how physics-informed learning is reshaping engineering practice by enabling digital twins and design workflows that combine simulation and data in a unified differentiable framework.