Related papers: Studying First Passage Problems using Neural Netwo…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often…
Modern deep learning enabled artificial neural networks, such as Deep Neural Network (DNN) and Convolutional Neural Network (CNN), have achieved a series of breaking records on a broad spectrum of recognition applications. However, the…
Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…
Spiking neural networks (SNNs) exhibit superior energy efficiency but suffer from limited performance. In this paper, we consider SNNs as ensembles of temporal subnetworks that share architectures and weights, and highlight a crucial issue…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
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…
We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (or…
Dedicated analog neurocomputing circuits are promising for high-throughput, low power consumption applications of machine learning (ML) and for applications where implementing a digital computer is unwieldy (remote locations; small, mobile,…
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…
The probabilistic power flow (PPF) problem is essential to quantifying the distribution of the nodal voltages due to uncertain injections. The conventional PPF problem considers a fixed topology, and the solutions to such a PPF problem are…
In order to ease the analysis of error propagation in neuromorphic computing and to get a better understanding of spiking neural networks (SNN), we address the problem of mathematical analysis of SNNs as endomorphisms that map spike trains…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…
We study the first passage time processes of anomalous diffusion on self similar curves in two dimensions. The scaling properties of the mean square displacement and mean first passage time of the ballistic motion, fractional Brownian…
The recent deep learning revolution has created an enormous opportunity for accelerating compute capabilities in the context of physics-based simulations. Here, we propose EikoNet, a deep learning approach to solving the Eikonal equation,…
Neural network methods are increasingly applied to solve phase transition problems, particularly in identifying critical points in non-equilibrium phase transitions, offering more convenience compared to traditional methods. In this paper,…
We consider the neural representation to solve the Boltzmann-BGK equation, especially focusing on the application in microscopic flow problems. A new dimension reduction model of the BGK equation with the flexible auxiliary distribution…