Nonlinear Map

Nonlinear maps are mathematical functions describing transformations where the output is not directly proportional to the input, crucial for modeling complex systems across diverse fields. Current research focuses on analyzing the stability and convergence properties of these maps, employing techniques like Physics-Informed Neural Networks (PINNs) for learning nonlinear transformations and developing novel algorithms such as algorithmic boosting to accelerate fixed-point computations. These advancements have significant implications for various applications, including robotics (e.g., inverse kinematics), machine learning (e.g., algorithm convergence analysis), and the solution of systems of equations. The development of robust and efficient methods for analyzing and computing with nonlinear maps continues to be a key area of investigation.