Application of artificial intelligence to solving partial differential equations. For example, such numerical techniques can be used in direct numerical simulation in fluid mechanics.

Modern techniques have been increasingly uniting the computational ability and intricate numerical procedures to address nonlinear partial differential equations in fluid mechanics. The prominence of high-order finite element methods and adaptive mesh has grown stronger in enhancing the resolution of turbulent and multiphase flows. In the same vein, the integration of conventional solvers with modern machine learning approaches has proved a significant milestone for augmenting predictive precision and computational expenses reduction. The above innovative discoveries have linked traditional solvers with contemporary data-driven approaches for more accurate modeling of the diverse nonlinear characteristics in practical problems. The research provides avenues to derive concise, unique solutions for complex paradigm interplay exemplified by environmental engineering, aerospace, and energy systems analyses.