<p>Physics-Informed Machine Learning (PIML) offers new opportunities to solve complex engineering and scientific problems by integrating physical laws into machine learning frameworks. This paper reviews recent advances in PIML, focusing on three key areas such as turbulent flow analysis, shape optimization, and convergence enhancement using temporal causality. These topics were selected based on their relevance to practical applications. Turbulent flow involves multi-scale dynamics and high computational demands. Shape optimization is directly connected to industrial design automation. Convergence enhancement, on the other hand, addresses stability issues that commonly arise in long-time simulations. First, we examine studies where PIML was used to effectively solve turbulent flow analysis problems. Next, we describe how combining PIML with optimization algorithms in shape optimization problems has reduced design time and improved efficiency. Finally, we examine the principle of the recently proposed causal Physics-Informed Neural Network (PINN) and Advanced Time-marching PINN with Hard Constraint (AT-PINN-HC) to improve convergence performance by gradually extending the initial conditions to distant time domains and learning causal relationships when learning time-dependent differential equations. These studies further extend the applicability of PIML in solving complex nonlinear problems while improving numerical stability and analytical accuracy. This paper presents the latest technological advances noted in PIML-based research, along with future research directions, and explores the potential for continued applications of PIML across engineering and scientific fields.</p> Graphical abstract <p></p>