Related papers: Studying First Passage Problems using Neural Netwo…
We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher…
Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from…
Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation.…
Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…
The rapid advancement of embedded multicore and many-core systems has revolutionized computing, enabling the development of high-performance, energy-efficient solutions for a wide range of applications. As models scale up in size, data…
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…
There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…
Recently, the interpretability of deep learning has attracted a lot of attention. A plethora of methods have attempted to explain neural networks by feature visualization, saliency maps, model distillation, and so on. However, it is hard…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
Since the original algorithm by John Vidale in 1988 to numerically solve the isotropic eikonal equation, there has been tremendous progress on the topic addressing an array of challenges including improvement of the solution accuracy,…
The high-pressure transportation process of pipeline necessitates an accurate hydraulic transient simulation tool to prevent slack line flow and over-pressure, which can endanger pipeline operations. However, current numerical solution…
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…
Deep neural networks are strongly over-parameterized, often containing far more weights than required for their task. Although such redundancy can aid optimization, it leads to inefficient deployment and high computational cost, motivating…
Nowadays, shallow and deep Neural Networks (NNs) have vast applications including biomedical engineering, image processing, computer vision, and speech recognition. Many researchers have developed hardware accelerators including…
Stochastic spiking neural networks based on nanoelectronic spin devices can be a possible pathway to achieving "brainlike" compact and energy-effcient cognitive intelligence. The computational model attempt to exploit the intrinsic device…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…