Related papers: Adaptive deep density approximation for stochastic…

Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing. Often, this requires high-resolution or adaptive discretization grids to capture relevant spatio-temporal features in…

The paper presents a spatio-temporal wind speed forecasting algorithm using Deep Learning (DL)and in particular, Recurrent Neural Networks(RNNs). Motivated by recent advances in renewable energy integration and smart grids, we apply our…

Deep neural network (DNN)-based adaptive controllers can be used to compensate for unstructured uncertainties in nonlinear dynamic systems. However, DNNs are also very susceptible to overfitting and co-adaptation. Dropout regularization is…

A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward…

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated…

There are numerous contexts where one wishes to describe the state of a randomly evolving system. Effective solutions combine models that quantify the underlying uncertainty with available observational data to form scientifically…

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…

This work proposes a training algorithm based on adaptive random Fourier features (ARFF) with Metropolis sampling and resampling \cite{kammonen2024adaptiverandomfourierfeatures} for learning drift and diffusion components of stochastic…

The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we…

The problem of approximating smooth, multivariate functions from sample points arises in many applications in scientific computing, e.g., in computational Uncertainty Quantification (UQ) for science and engineering. In these applications,…

We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed…

Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…

Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs…

We present a dimension-reduced KRnet map approach (DR-KRnet) for high-dimensional Bayesian inverse problems, which is based on an explicit construction of a map that pushes forward the prior measure to the posterior measure in the latent…

Deep convolutional neural networks have recently shown promising results in compressive spectral reconstruction. Previous methods, however, usually adopt a single mapping function for sparse representation. Considering that different…

Deep Neural Network (DNN)-based controllers have emerged as a tool to compensate for unstructured uncertainties in nonlinear dynamical systems. A recent breakthrough in the adaptive control literature provides a Lyapunov-based approach to…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…