Related papers: Solving Traveltime Tomography with Deep Learning
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…
Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order…
We investigate the application of deep learning to the retrieval of the internuclear distance in the two-dimensional H$_2^{+}$ molecule from the momentum distribution of photoelectrons produced by strong-field ionization. We study the…
Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…
Deep learning techniques have been used to build velocity models (VMs) for seismic traveltime tomography and have shown encouraging performance in recent years. However, they need to generate labeled samples (i.e., pairs of input and label)…
Electrical Impedance Tomography (EIT) is a promising noninvasive imaging technique that reconstructs the spatial conductivity distribution from boundary voltage measurements. However, it poses a highly nonlinear and ill-posed inverse…
We present a machine learning approach that allows to characterize the disorder potential of a two-dimensional electronic system from its quantum transport properties. Numerically simulated transport data for a large number of disorder…
Due to the rapid development of Internet of Things (IoT) technologies, many online web apps (e.g., Google Map and Uber) estimate the travel time of trajectory data collected by mobile devices. However, in reality, complex factors, such as…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Recently deep neural networks have been widely and successfully applied in computer vision tasks and attracted growing interests in medical imaging. One barrier for the application of deep neural networks to medical imaging is the need of…
We study the travel time tomography problem for transversely isotropic media using the artificial boundary method used in works in X-ray tomography and boundary rigidity problems. The analysis involved requires a modification of the…
This paper focuses on how to approximate traveling wave solutions for various kinds of partial differential equations via artificial neural networks. A traveling wave solution is hard to obtain with traditional numerical methods when the…
While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions have low regularity or singularities. To address these issues,…
Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and…
We consider transportation networks that are modeled by dynamic graphs, and introduce the possibility for traveling agents to use Backward Time-Travel (BTT) devices at any node to go back in time (to some extent, and with some appropriate…