Stochastic Approach

Stochastic approaches are increasingly used to model and solve complex problems across diverse scientific and engineering domains, primarily aiming to account for inherent uncertainties and variability within systems. Current research focuses on developing and analyzing efficient stochastic algorithms, such as stochastic gradient descent and its variants, for optimization problems, variational inequalities, and machine learning applications, often incorporating neural networks or other machine learning models for improved efficiency and accuracy. These methods are proving valuable for tackling computationally challenging problems in areas ranging from material science and robotics to risk assessment and AI safety, offering more robust and efficient solutions than traditional deterministic approaches.