Related papers: Supervised and Unsupervised Neural Network Solver …
In this paper, we consider a nonlinear and nonlocal parabolic model for multi-species ionic fluids and introduce a semi-implicit finite volume scheme, which is second order accurate in space, first order in time and satisfies the following…
From higher computational efficiency to enabling the discovery of novel and complex structures, deep learning has emerged as a powerful framework for the design and optimization of nanophotonic circuits and components. However, both…
Accurately modeling robot dynamics is crucial to safe and efficient motion control. In this paper, we develop and apply an iterative learning semi-parametric model, with a neural network, to the task of autonomous racing with a Model…
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…
In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method that approximates numerical solutions of partial differential equations (PDEs) using neural network…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…
Convolutional Neural Networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation…
This paper introduces a new method for safety-aware robot learning, focusing on repairing policies using predictive models. Our method combines behavioral cloning with neural network repair in a two-step supervised learning framework. It…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
We identify configurational phases and structural transitions in a polymer nanotube composite by means of machine learning. We employ various unsupervised dimensionality reduction methods, conventional neural networks, as well as the…
Perimeter control maintains high traffic efficiency within protected regions by controlling transfer flows among regions to ensure that their traffic densities are below critical values. Existing approaches can be categorized as either…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
In this paper, a new scheme of arbitrary high order accuracy in both space and time is proposed to solve hyperbolic conservative laws. Based on the idea of flux vector splitting(FVS) scheme, we split all the space and time derivatives in…
Despite rapid improvements in the performance of central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks…
In this work, we propose a novel framework for unsupervised learning for event cameras that learns motion information from only the event stream. In particular, we propose an input representation of the events in the form of a discretized…
We develop new more efficient A-WENO schemes for both hyperbolic systems of conservation laws and nonconservative hyperbolic systems. The new schemes are a very simple modification of the existing A-WENO schemes: They are obtained by a more…