Abstract
In this work, the construction of adaptive one-dimensional computational grids is considered using a numerical method and physics-informed neural networks (PINNs). The grid adaptation process is described by the diffusion equation, which allows for the redistribution of nodes based on a control function. The numerical method employs an iterative scheme that adjusts the node positions according to the solution gradients, ensuring local refinement in key regions. In the PINN approach, the governing equation is incorporated into the loss function, enabling the neural network model to generate the grid based on physical constraints. To evaluate the performance of both methods, tests are conducted with different control function parameters, and the influence of diffusion coefficients on grid adaptation is analyzed. The results show that the numerical method leads to sharper variations in node spacing, while PINNs produce a smoother grid distribution. A comparative analysis of the deviations between the methods is performed. The obtained data allow for assessing the characteristics of grid adaptation in both approaches and for identifying possible directions for their further application in numerical modeling tasks.