Related papers: Deep learning of parameterized equations with appl…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable…

This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field.…

Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…

Deep neural networks (DNNs) have received tremendous attention and achieved great success in various applications, such as image and video analysis, natural language processing, recommendation systems, and drug discovery. However, inherent…

We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually…

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…

Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems. A remarkable feature of FML is that it is capable of producing accurate predictive models…

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…

Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic…

Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by…

There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based…

During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the…

Training deep feature hierarchies to solve supervised learning tasks has achieved state of the art performance on many problems in computer vision. However, a principled way in which to train such hierarchies in the unsupervised setting has…

Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…

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…

Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…

Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…