Related papers: Physics Constrained Deep Learning For Turbulence M…

As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…

Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…

Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…

Turbulent-flow control aims to develop strategies that effectively manipulate fluid systems, such as the reduction of drag in transportation and enhancing energy efficiency, both critical steps towards reducing global CO$_2$ emissions. Deep…

We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…

Turbulence in fluids, gases, and plasmas remains an open problem of both practical and fundamental importance. Its irreducible complexity usually cannot be tackled computationally in a brute-force style. Here, we combine Large Eddy…

Recently, deep learning has emerged as a promising tool for statistical downscaling, the set of methods for generating high-resolution climate fields from coarse low-resolution variables. Nevertheless, their ability to generalize to climate…

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…

Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers.…

Numerical models based on Reynolds-Averaged Navier-Stokes (RANS) equations are widely used in engineering turbulence modeling. However, the RANS predictions have large model-form uncertainties for many complex flows. Quantification of these…

With the advent of improved computational resources, aerospace design has testing-based process to a simulation-driven procedure, wherein uncertainties in design and operating conditions are explicitly accounted for in the design under…

The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…

Reduced quasilinear (QL) and nonlinear (gradient-driven) models with scale separations, commonly used to interpret experiments and to forecast turbulent transport levels in magnetised plasmas are tested against nonlinear models without…

In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3D heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…

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…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…