Related papers: Acceleration of Radiation Transport Solves Using A…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

Scanning transmission electron microscopy (STEM) is a powerful tool to reveal the morphologies and structures of materials, thereby attracting intensive interests from the scientific and industrial communities. The outstanding spatial…

In this paper, we propose a coupled Discrete Empirical Interpolation Method (DEIM) and Generalized Multiscale Finite element method (GMsFEM) to solve nonlinear parabolic equations with application to the Allen-Cahn equation. The Allen-Cahn…

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…

Emerging intelligent embedded devices rely on Deep Neural Networks (DNNs) to be able to interact with the real-world environment. This interaction comes with the ability to retrain DNNs, since environmental conditions change continuously in…

The thesis focuses on various techniques to find an alternate approximation method that could be universally used for a wide range of CFD problems but with low computational cost and low runtime. Various techniques have been explored within…

Neuroevolution is an active and growing research field, especially in times of increasingly parallel computing architectures. Learning methods for Artificial Neural Networks (ANN) can be divided into two groups. Neuroevolution is mainly…

Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration…

In this paper, we study the least-squares finite element methods (LSFEM) for the linear hyperbolic transport equations. The linear transport equation naturally allows discontinuous solutions and discontinuous inflow conditions, while the…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

We have modeled transport properties of nanostructures using the Green's function method within the framework of the density-functional theory. The scheme is computationally demanding so that numerical methods have to be chosen carefully. A…

Finite Element Analysis (FEA) is a powerful but computationally intensive method for simulating physical phenomena. Recent advancements in machine learning have led to surrogate models capable of accelerating FEA. Yet there are still…

The generative learning phase of Autoencoder (AE) and its successor Denosing Autoencoder (DAE) enhances the flexibility of data stream method in exploiting unlabelled samples. Nonetheless, the feasibility of DAE for data stream analytic…

Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than…

Electromagnetic Navigation Systems (eMNS) can be used to control a variety of multiscale devices within the human body for remote surgery. Accurate modeling of the magnetic fields generated by the electromagnets of an eMNS is crucial for…

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may…

Modeling gas flow through fractures of subsurface rock is a particularly challenging problem because of the heterogeneous nature of the material. High-fidelity simulations using discrete fracture network (DFN) models are one methodology for…

Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by…

Accurate prediction of structural displacements under external loading is fundamental to structural health monitoring and seismic safety assessment. Although the finite element method (FEM) remains the prevailing approach because of its…

This paper proposes a new extension to Deep Evolutionary Network Structured Evolution (DENSER), called Fast-DENSER++ (F-DENSER++). The vast majority of NeuroEvolution methods that optimise Deep Artificial Neural Networks (DANNs) only…