Variational Method

Variational methods are a powerful class of mathematical techniques used to approximate complex probability distributions and solve optimization problems, particularly in scenarios where exact solutions are intractable. Current research focuses on applying variational frameworks to diverse fields, including image processing (e.g., denoising using total variation methods), machine learning (e.g., Bayesian inference with diffusion models and neural networks), and physics (e.g., modeling strain localization and fluid mechanics). These methods are increasingly important for tackling high-dimensional problems and improving the interpretability and robustness of models across various scientific disciplines and practical applications, such as drug response prediction in cancer research and efficient program translation.