Related papers: Neural-Integrated Meshfree (NIM) Method: A differe…
Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…
The performance of deep neural networks is highly sensitive to the choice of the hyperparameters that define the structure of the network and the learning process. When facing a new application, tuning a deep neural network is a tedious and…
Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…
Deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM combine the smoothing effect of simple iterative methods with…
Neural image compression (NIC) has outperformed traditional image codecs in rate-distortion (R-D) performance. However, it usually requires a dedicated encoder-decoder pair for each point on R-D curve, which greatly hinders its practical…
Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…
This rapid communication devises a Neural Induction Machine (NeuIM) model, which pilots the use of physics-informed machine learning to enable AI-based electromagnetic transient simulations. The contributions are threefold: (1) a formation…
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…
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…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…
In this paper, we propose StruM, a novel structured mixed-precision-based deep learning inference method, co-designed with its associated hardware accelerator (DPU), to address the escalating computational and memory demands of deep…
Deep learning algorithms are becoming an essential component of many artificial intelligence (AI) driven applications, many of which run on resource-constrained and energy-constrained systems. For efficient deployment of these algorithms,…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…
Simultaneous Localization and Mapping (SLAM) is a fundamental task in robotics, driving numerous applications such as autonomous driving and virtual reality. Recent progress on neural implicit SLAM has shown encouraging and impressive…
Machine Unlearning (MU) aims to selectively erase the influence of specific data points from pretrained models. However, most existing MU methods rely on the retain set to preserve model utility, which is often impractical due to privacy…
Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a…
Ethical and privacy issues inherent in artificial intelligence (AI) applications have been a growing concern with the rapid spread of deep learning. Machine unlearning (MU) is the research area that addresses these issues by making a…
Missingness is a common issue for neuroimaging data, and neglecting it in downstream statistical analysis can introduce bias and lead to misguided inferential conclusions. It is therefore crucial to conduct appropriate statistical methods…