Related papers: BF-APNN: A Low-Memory Method for Accelerating the …

The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural…

We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we…

We present a novel Asymptotic-Preserving Neural Network (APNN) approach utilizing even-odd decomposition to tackle the nonlinear gray radiative transfer equations (GRTEs). Our AP loss demonstrates consistent stability concerning the small…

We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the…

This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Boltzmann equation. Our approach builds upon the…

In this paper, we develop and employ auxiliary physics-informed neural networks (APINNs) to solve forward, inverse, and coupled integro-differential problems of radiative transfer theory (RTE). Specifically, by focusing on the relevant slab…

In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation with diffusive…

The Vlasov-Poisson-Fokker-Planck (VPFP) system is a fundamental model in plasma physics that describes the Brownian motion of a large ensemble of particles within a surrounding bath. Under the high-field scaling, both collision and field…

In this paper, we develop the Asymptotic-Preserving Neural Networks (APNNs) approach to study the forward and inverse problem for the semiconductor Boltzmann equation. The goal of the neural network is to resolve the computational…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…

In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of…

To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…

With the rapid advance of Machine Learning techniques and the deep increase of availability of scientific data, data-driven approaches have started to become progressively popular across science, causing a fundamental shift in the…

Radio-Frequency (RF) imaging concerns the digital recreation of the surfaces of scene objects based on the scattered field at distributed receivers. To solve this difficult inverse scattering problems, data-driven methods are often employed…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Photonic neural networks (PNNs) are fast in-propagation and high bandwidth paradigms that aim to popularize reproducible NN acceleration with higher efficiency and lower cost. However, the training of PNN is known to be challenging, where…

Processing sequential data of variable length is a major challenge in a wide range of applications, such as speech recognition, language modeling, generative image modeling and machine translation. Here, we address this challenge by…