Partial Differential Equations (PDEs) are a fundamental class of mathematical models widely used for modeling continuous systems across scientific and engineering disciplines. Physics Informed Machine Learning (PIML), which utilises both data and scientific knowledge, provides a powerful framework that bridges Artificial Intelligence (AI) and PDEs. Among PIML methods, Physics Informed Neural Networks (PINNs) have emerged as a representative and widely adopted approach. This paper offers a structured, problem-oriented review of recent developments in the use of PINNs as PDE forward solvers. We aim to help readers grasp the key trends and interrelations across methodological advances and practical applications. From a methodological perspective, we review existing approaches with a focus on Machine Learning (ML) models and representations, optimization objectives and strategies, as well as datasets and training procedures. From an application perspective, we examine the task characteristics and the applicability of PINNs in domains such as fluid dynamics, heat transfer, solid mechanics, magnetism, and highlight several practical software toolkits and benchmarks. Despite the remarkable progress made in PINN research, significant challenges remain in addressing complex real-world problems. Accordingly, we discuss current limitations in generalization capability, training efficiency, and optimization difficulty, and outline promising directions for future improvements.

Near-space hypersonic unmanned aircrafts (NHUA) encounter significant aerodynamic heating effects when flying at high velocities in extreme conditions. This leads to the generation of extremely high temperatures, reaching several thousand degrees, posing a substantial risk to the safety of NHUA. Accurate and rapid prediction of the aerothermodynamic environment is crucial for the thermal protection of NHUA. Conventional approaches exhibit some limitations, including the need for extensive pre-processing, long calculation time, inadequate precision, and reliance on expert knowledge, making them ill-suited for online intelligent prediction. This study proposes a novel “flying state-pressure and heat flux-temperature” data-driven prediction theoretical framework, considering both efficiency and accuracy. Our approach entails a prediction model for high-dimensional pressure and heat flux fields, employing principal component analysis (PCA) and multi-layer perceptron (MLP) models. A temperature time series model is also constructed using recurrent neural networks (RNN). The experimental results suggest that the prediction error falls within a narrow margin of approximately 5%. It takes around 0.1 seconds to forecast a high-dimensional field and 1 second to predict the temperature time series, which satisfies both speed and accuracy requirements.