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Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…
Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…
A new stable computational method for non-homogeneous waveguide equation with a piecewise uniform structure along the main propagation direction is constructed, based on the modified Dirichlet-to-Neumann (DtN) map of each uniform segment.…
Mapping the chemical reaction pathways and their corresponding activation barriers is a significant challenge in molecular simulation. Given the inherent complexities of 3D atomic geometries, even generating an initial guess of these paths…
We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…
Deep neural networks (DNNs) have achieved extraordinary performance in solving different tasks in various fields. However, the conventional DNN model is steadily approaching the ground-truth value through loss backpropagation. In some…
Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…
Implementing Deep Neural Networks (DNNs) on resource-constrained edge devices is a challenging task that requires tailored hardware accelerator architectures and a clear understanding of their performance characteristics when executing the…
We propose a decoupled divergence-free neural networks basis (Decoupled-DFNN) method for solving incompressible flow problems, including the Stokes and Navier-Stokes equations. To ensure the divergence free property exactly, the velocity…
Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a…
The design of advanced nuclear reactors (Gen IV) involves an array of challenging fluid-flow issues that affect its safety and performance. The calculated DNS database will be instrumental in understanding the flow behavior in the…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
This work investigates the feasibility of a post-processing-based approach for phase separation in defocusing particle tracking velocimetry for dispersed two-phase flows. The method enables the simultaneous 3D localization determination of…
We propose a fast beam orientation selection method, based on deep neural networks (DNN), capable of developing a plan comparable to those by the state-of-the-art column generation method. The novelty of Our model lies in its supervised…
On the forefront of scientific computing, Deep Learning (DL), i.e., machine learning with Deep Neural Networks (DNNs), has emerged a powerful new tool for solving Partial Differential Equations (PDEs). It has been observed that DNNs are…
Space Communication poses challenges such as severe delays, hard-to-predict routes and communication disruptions. The Delay Tolerant Network architecture, having been specifically designed keeping such scenarios in mind, is suitable to…
Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…
Simulating reactive dissolution of solid minerals in porous media has many subsurface applications, including carbon capture and storage (CCS), geothermal systems and oil & gas recovery. As traditional direct numerical simulators are…