Related papers: Supervised and Unsupervised Neural Network Solver …
This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using…
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…
In this paper, we introduce the finite difference weighted essentially non-oscillatory (WENO) scheme based on the neural network for hyperbolic conservation laws. We employ the supervised learning and design two loss functions, one with the…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
Trained neural networks (NN) have attractive features for closing governing equations. There are many methods that are showing promise, but all can fail in cases when small errors consequentially violate physical reality, such as a solution…
We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that the approximation error can be made as small as desired with…
A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…
We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the…
In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data,…
In this work we show that semi-supervised models for vehicle trajectory prediction significantly improve performance over supervised models on state-of-the-art real-world benchmarks. Moving from supervised to semi-supervised models allows…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a…
We propose a scalable method for semi-supervised (transductive) learning from massive network-structured datasets. Our approach to semi-supervised learning is based on representing the underlying hypothesis as a graph signal with small…
The deep convolutional neural network has achieved significant progress for single image rain streak removal. However, most of the data-driven learning methods are full-supervised or semi-supervised, unexpectedly suffering from significant…
Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
A method to control results of gradient descent unsupervised learning in a deep neural network by using evolutionary algorithm is proposed. To process crossover of unsupervisedly trained models, the algorithm evaluates pointwise fitness of…