<![CDATA[The transition from classical numerical methods which are often hampered by mesh dependency and the curse of dimensionality to Physics-Informed Neural Networks (PINNs) has marked a new paradigm shift in scientific computing through data-physics hybrid solutions. This study aims to map the evolutionary taxonomy of PINNs over the period from 2019 to 2024, with a specific focus on analysing the methodological transition from the Point-wise Prediction paradigm towards Operator Learning. Using a Focused Narrative Review approach on 36 selected primary studies, this review synthesises technological developments from the foundational phase to the latest architectural innovations. Key findings indicate that while standard PINNs offer mesh-free flexibility for single-equation instances, Neural Operator variants such as Deep Operator Networks (DeepONet) and Fourier Neural Operators (FNO) provide transformative computational efficiency. By adopting offline training and online inference strategies, these models are capable of achieving prediction speeds up to three orders of magnitude faster than traditional numerical solvers or standard PINNs. As a unique contribution, this article emphasises the urgency of a structured future research agenda, encompassing the pressing need for benchmark standardisation (such as the Scientific Machine Learning (SciML) initiative) and the development of architectural scalability to support exascale computing. This synthesis is intended to serve as a roadmap for the development of robust, industry-oriented digital twins.]]>
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