Title: “Introduction to Deep Learning Algorithms”
In this book, we delve into the world of deep learning algorithms, providing a comprehensive overview of their essential components. Our aim is to equip readers with a solid foundation in deep learning, even if they have no prior knowledge on the subject. We explore various artificial neural network architectures, including fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization. Additionally, we discuss different optimization algorithms, such as stochastic gradient descent (SGD) methods, accelerated methods, and adaptive methods. The book also delves into theoretical aspects like approximation capacities of ANNs, optimization theory, and generalization errors. Lastly, we review deep learning approximation methods for PDEs, such as physics-informed neural networks (PINNs) and deep Galerkin methods. This book offers a valuable resource for both students and scientists seeking a solid foundation in deep learning, as well as practitioners aiming to deepen their mathematical understanding.
https://arxiv.org/abs/2310.20360