Numerical Approximation

Numerical approximation focuses on developing efficient and accurate methods for representing complex mathematical objects, such as solutions to differential equations or conditional expectations, using simpler, computationally tractable forms. Current research emphasizes leveraging neural networks, particularly in physics-informed machine learning and variational inference contexts, alongside established techniques like the splitting-up method and low-rank approximations, to improve accuracy and efficiency. These advancements are crucial for tackling high-dimensional problems in diverse fields, ranging from fluid dynamics and finance to Bayesian statistics, enabling more realistic simulations and improved decision-making.