Related papers: Multi-scale Deep Neural Network (MscaleDNN) Method…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…
The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD)…
In this paper, we consider the incompressible Stokes flow problem in a perforated domain and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method…
We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…
The 3D incompressible Navier-Stokes equations model essential fluid phenomena, including turbulence and aerodynamics, but are challenging to solve due to nonlinearity and limited solution regularity. Despite extensive research, the full…
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models…
This paper studies the use of Multi-Grade Deep Learning (MGDL) for solving highly oscillatory Fredholm integral equations of the second kind. We provide rigorous error analyses of continuous and discrete MGDL models, showing that the…
Seismic datasets contain valuable information that originate from areas of interest in the subsurface; such seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden.…
Optimal transmission switching (OTS) improves optimal power flow (OPF) by selectively opening transmission lines, but its mixed-integer formulation increases computational complexity, especially on large grids. To deal with this, we propose…
The precise simulation of turbulent flows holds immense significance across various scientific and engineering domains, including climate science, freshwater science, and energy-efficient manufacturing. Within the realm of simulating…
We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connections between control theory, deep learning and theory of…
Deep neural networks (DNN) have shown promises in the lesion segmentation of multiple sclerosis (MS) from multicontrast MRI including T1, T2, proton density (PD) and FLAIR sequences. However, one challenge in deploying such networks into…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
This paper proposes a deep neural network approach for predicting multiphase flow in heterogeneous domains with high computational efficiency. The deep neural network model is able to handle permeability heterogeneity in high dimensional…
We consider the approximation of initial/boundary value problems involving, possibly high-dimensional, dissipative evolution partial differential equations (PDEs) using a deep neural network framework. More specifically, we first propose…
With recent advancing of Internet of Things (IoTs), it becomes very attractive to implement the deep convolutional neural networks (DCNNs) onto embedded/portable systems. Presently, executing the software-based DCNNs requires…
Accurate simulation of turbulent flows remains a challenge due to the high computational cost of direct numerical simulations (DNS) and the limitations of traditional turbulence models. This paper explores a novel approach to augmenting…