Rate Bound

Rate bounds research focuses on quantifying the approximation error of various models, particularly deep neural networks (DNNs) and deep operator networks (DONs), when approximating complex functions or operators, often arising from solving partial differential equations. Current research emphasizes establishing tight bounds for different model architectures, including those using ReLU, sigmoid, and tanh activations, and explores the impact of model size and data properties on approximation accuracy. These studies are crucial for understanding the capabilities and limitations of these models, informing their design and application in diverse scientific and engineering fields where accurate and efficient approximations are essential.