In pure and practical mathematics, solving nonlinear partial differential equations (PDEs) in high-dimensional environments is challenging due to the curse of dimensionality, which exponentially increases processing needs Complex problems require alternative numerical methods since conventional methods often lack accuracy and computational feasibility. Numerical solvers have disadvantages, but neural networks, Physics-Informed Neural Networks (PINNs), and kernel approaches can accurately approximate nonlinear PDE solutions. Several investigations show that machine learning reduces L2-norm faults and convergence rates, improving accuracy and processing efficiency. Machine learning models like PINNs solved Burgers' equation with L2-norm errors of 0.050, while older numerical techniques had 0.120. PINNs can converge on complex PDEs like the Navier-Stokes equation in 2,000 epochs, compared to 10,000 iterations for standard methods. This study found that machine learning can improve mathematical modelling accuracy and efficiency for solving high-dimensional nonlinear partial differential equations (PDEs). Machine learning enhances numerical analytic theory in fluid dynamics, finance, and engineering, where complex and high-dimensional PDEs are common. The findings also show that machine learning methods may solve these equations' computational issues, enabling mathematical modelling and simulation research that improves outcomes. Machine learning technology can help mathematicians solve more complicated problems that were previously intractable using classical numerical methods in addition to theoretical breakthroughs. This study improves computer mathematics theory and practice by solving high-dimensional PDEs faster. As researchers improve machine learning techniques, mathematical modelling and cross-disciplinary collaboration will arise to answer scientific and engineering problems.