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Found 5 papers, 1 papers with code
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
This book aims to provide an introduction to the topic of deep learning algorithms.
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
The obtained ANN architectures and their initialization schemes are thus strongly inspired by numerical algorithms as well as by popular deep learning methodologies from the literature and in that sense we refer to the introduced ANNs in conjunction with their tailor-made initialization schemes as Algorithmically Designed Artificial Neural Networks (ADANNs).
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Such numerical simulations suggest that ANNs have the capacity to very efficiently approximate high-dimensional functions and, especially, indicate that ANNs seem to admit the fundamental power to overcome the curse of dimensionality when approximating the high-dimensional functions appearing in the above named computational problems.
Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications.
Strong error analysis for stochastic gradient descent optimization algorithms
Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications.
Numerical Analysis Probability
