Solution of time-dependent convection diffusion reaction equations in 2- and 3-dimensional space with a physics-informed neural network

Many engineering and physics problems can be mathematically modeled by convection-diffusion-reaction (CDR) equations. In this thesis, Physics-Informed Neural Networks (PINN), a mesh-free method, is employed to solve one-, two-, and three-dimensional nonlinear CDR equations.The numerical solutions obtained are compared with analytical solutions and evaluated using L2 error norm, RMS error, and maximum absolute error metrics.The results demonstrate that the PINN method can produce accurate and efficient solutions, particularly for high-dimensional and convection-dominant problems. This study provides an original contribution to the literature by presenting a PINN-based 3D CDR solution.