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We present a collection of MATLAB routines using discontinuous Galerkin finite elements method (DGFEM) for solving steady-state diffusion-convection-reaction equations. The code employs the sparse matrix facilities of MATLAB with…
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
Miniaturized autonomous unmanned aerial vehicles (UAVs) are gaining popularity due to their small size, enabling new tasks such as indoor navigation or people monitoring. Nonetheless, their size and simple electronics pose severe challenges…
Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer…
We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs--by three orders of magnitude--compared to industry-strength physics-based PDE solvers. This paper describes a new architectural…
Neutrino-dominated accretion flows (NDAFs) are one of the important MeV neutrino sources and significantly contribute to the cosmic diffuse neutrino background. In this paper, we investigate the spectrum of diffuse NDAF neutrino background…
Evolutional deep neural networks (EDNN) solve partial differential equations (PDEs) by marching the network representation of the solution fields, using the governing equations. Use of a single network to solve coupled PDEs on large domains…
Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only…
The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an $N$-D tensor of size $I_1\times…
A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport…
We study a novel alternative approach for the computation of transport coefficients at mesoscales. While standard nonequilibrium molecular dynamics (NEMD) approaches fix the forcing and measure the average induced flux in the system driven…
In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…
The traffic matrix estimation (TME) problem has been widely researched for decades of years. Recent progresses in deep generative models offer new opportunities to tackle TME problems in a more advanced way. In this paper, we leverage the…
Recent advances in reaction prediction have achieved near-saturated accuracy on standard benchmarks (e.g., USPTO), yet most state-of-the-art models formulate the task as a one-shot mapping from reactants to products, offering limited…
A variety of natural phenomena comprises a huge number of competing reactions and short-lived intermediates. Any study of such processes requires the discovery and accurate modeling of their underlying reaction network. However, this task…
In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…
An easily implementable path solution algorithm for 2D spatial problems, based on excitable/programmable characteristics of a specific cellular nonlinear network (CNN) model is presented and numerically investigated. The network is a single…
In plasma edge simulations, the behavior of neutral particles is often described by a Boltzmann--BGK equation. Solving this kinetic equation and estimating the moments of its solution are essential tasks, typically carried out using Monte…
A popular method to compute first-passage probabilities in continuous-time Markov chains is by numerically inverting their Laplace transforms. Past decades, the scientific computing community has developed excellent numerical methods for…