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LEARNING DISCONTINUOUS GALERKIN SOLUTIONS TO ELLIPTIC PROBLEMS VIA SMALL LINEAR CONVOLUTIONAL NEURAL NETWORKS

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arXiv 2025年

作者： Celaya, Adrian Wang, Yimo Fuentes, David Riviere, Beatrice Dept. of Computational Applied Mathematics and Operations Research Rice University United States Dept. of Imaging Physics The University of Texas MD Anderson Cancer Center United States Ken Kennedy Institute Dept. of Computational Applied Mathematics and Operations Research Rice University United States

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such as physics-informed neural networks, depend on automatic differentiation and the sampling of collocation points, which can result in a lack of interpretability and lower accuracy compared to traditional numerical methods. To address this issue, we propose two approaches for learning discontinuous Galerkin solutions to PDEs using small linear convolutional neural networks. Our first approach is supervised and depends on labeled data, while our second approach is unsupervised and does not rely on any training data. In both cases, our methods use substantially fewer parameters than similar numerics-based neural networks while also demonstrating comparable accuracy to the true and DG solutions for elliptic problems. © 2025, CC BY.

关键词： Convolutional neural networks

The OpenLAM Challenges

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arXiv 2025年

作者： Peng, Anyang Liu, Xinzijian Guo, Ming-Yu Zhang, Linfeng Wang, Han AI for Science Institute Beijing100080 China DP Technology Beijing100080 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China School of Chemistry Sun Yat-sen University Guangzhou510006 China

Inspired by the success of Large Language Models (LLMs), the development of Large Atom Models (LAMs) has gained significant momentum in scientific computation. Since 2022, the Deep Potential team has been actively pretraining LAMs and launched the OpenLAM Initiative to develop an open-source foundation model spanning the periodic table. A core objective is establishing comprehensive benchmarks for reliable LAM evaluation, addressing limitations in existing datasets. As a first step, the LAM Crystal Philately competition has collected over 19.8 million valid structures, including 1 million on the OpenLAM convex hull, driving advancements in generative modeling and materials science applications. Copyright © 2025, The Authors. All rights reserved.

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Simulation of Electromagnetic Pulse Coupling Effect with a Parallel Time-Domain FEM Solver

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Simulation of Electromagnetic Pulse Coupling Effect with a P...

International applied computational Electromagnetics Society Symposium (ACES)

作者： Yan-Nan Liu Wei-Jie Wang Zhen-Guo Zhao CAEP Software Center for High Performance Numerical Simulation Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

The electromagnetic pulse (EMP) coupling effect is an important research area in electromagnetic compatibility and electromagnetic interference. Numerical simulation plays an important role in the study of the pulse coupling effect. To achieve an efficient and effective simulation, a parallel solver based on time-domain finite element method (TD-FEM) is proposed, which is developed based on JAUMIN framework. This parallel TD-FEM solver is employed to simulate the effects of an EMP coupling to a printed circuit board at work.

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High-Order Adaptive Multi-Resolution Method on Curvilinear Girds I: Finite Difference Framework

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SSRN

SSRN 2023年

作者： Ma, Wenhua Luo, Dongmi Li, Shiyi Qiu, Jianxian Ni, Guoxi Chen, Yibing Institute of Applied Physics and Computational Mathematics Beijing100191 China School of Mathematical Sciences Xiamen University Xiamen361005 China

In this paper, we present a high-order adaptive multi-resolution method on curvilinear grids for solving the hyperbolic conservation laws. The method has three primary components. Firstly, the governing equations and physical variables on curvilinear grids are transformed into Cartesian grids, which thus contain the geometric metrics. Secondly, the highorder geometric conservation laws (GCLs) preserving WENO-ZQ finite difference scheme is constructed to solve the transformed governing equations. Thus, the new scheme can achieve the designed high-order accuracy on curvilinear grids. Finally, to further improve the resolution near the discontinuities, the adaptive multi-resolution method, which has been well developed on Cartesian grids, is also extended to curvilinear grids. Coupled with the GCLs-preserving WENO-ZQ scheme and the adaptive multi-resolution method, the new high-order adaptive multi-resolution method on curvilinear grids is obtained. The advantage of this work is that by handling the geometric metrics with care, it avoids the complexity of constructing a high-order adaptive method directly on curvilinear grids. The high-order accuracy, high resolution, and efficiency of the developed method are demonstrated with several benchmark tests in one and two dimensions. © 2023, The Authors. All rights reserved.

关键词： Finite difference method

Total Ionizing Dose Effects of A 180 nm Bulk CMOS

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Total Ionizing Dose Effects of A 180 nm Bulk CMOS

International applied computational Electromagnetics Society Symposium (ACES)

作者： Wenbin Wu Haijing Zhou Qianhong Zhou Hantian Zhang Yang Liu Qiang Liu Zhenguo Zhao Institute of Applied Physics and Computational Mathematics Beijing China CAEP Software Center for High Performance Numerical Simulation Beijing China

CMOS devices are widely used in modern integrated circuits. However, like any semiconductor device, CMOS devices are susceptible to total ionizing dose (TID) effects when exposed to ionizing radiation environments. In this work, a TCAD model of a 180 nm bulk COMS is developed to investigate the impact of TID effects. Simulated results show that the TID effects can cause a negative shift in the voltage characteristics curve and an increase in leakage current of CMOS devices.

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Quantum dynamics of Gaudin magnets

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Communications in Theoretical physics 2022年第9期74卷 39-48页

作者： Wen-Bin He Stefano Chesi Hai-Qing Lin Xi-Wen Guan Beijing Computational Science Research Center Beijing 100193China State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics Wuhan Institute of Physics and MathematicsAPMChinese Academy of SciencesWuhan 430071China The Abdus Salam International Center for Theoretical Physics Strada Costiera 11I-34151 TriesteItaly Department of Physics Beijing Normal UniversityBeijing 100875China NSFC-SPTP Peng Huanwu Center for Fundamental Theory Xi’an 710127China Department of Theoretical Physics Research School of Physics and EngineeringAustralian National UniversityCanberra ACT 0200Australia

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and *** question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains *** this paper,using the Bethe ansatz wave function,we study the quantum dynamics of an inhomogeneous Gaudin *** derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins,such as:the spin distribution function,the spin-spin correlation function,and the Loschmidt *** also numerically study the relaxation behavior of these dynamic properties,gaining considerable insight into coherence and entanglement between the central spin and the *** particular,we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling,whereas the Loschmidt echo shows an exponential relaxation to its steady *** results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.

关键词： Gaudin magnets central spin model Bethe ansatz spin polarization spin-spin correlation Loschmidt echo

The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution

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arXiv 2024年

作者： Zakradze, Mamuli Tabagari, Zaza Koblishvili, Nana Davitashvili, Tinatin Criado-Aldeanueva, Francisco Department of Computational Methods Muskhelishvili Institute of Computational Mathematics Georgian Technical University Georgia Iv.Javakhishvili Tbilisi State University FENS Georgia Department of Applied Physics II Polytechnic School Malaga University Spain

In the present paper an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given. Under a generalized problem is meant the problem when a boundary function has a finite number of curves with the first kind of discontinuity. The algorithm consists of the following main stages: 1) transition from an infinite domain to a finite domain by an inversion;2) consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin’s theorem for the obtained finite domain;3) application of the MPS for the numerical solution a new problem which in turn is based on a computer simulation of the Wiener process;4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration numerical examples are considered and results are *** Codes 35J05, 35J25, 65C30, 65N75 © 2024, CC BY-NC-ND.

关键词： Spheres

Response of NMOS to Combined Ionization and EMP Environments

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Response of NMOS to Combined Ionization and EMP Environments

International applied computational Electromagnetics Society Symposium (ACES)

Electronic systems in space or nuclear devices are exposed to both ionizing radiation and electromagnetic radiation environments. Experimental results have indicated that the semiconductor devices may suffer severe damage in the combined environment of ionizing radiation and electromagnetic radiation. In this work, a total ionizing dose (TID) effects and electromagnetic pulses (EMP) combined effect model of NMOS device is established. Simulation results show that the NMOS will exhibit more severe leakage current increase and sub-threshold characteristics degradation in the combined environments.

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An asymptotic-preserving IMEX PN method for the gray model of the radiative transfer equation

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arXiv 2024年

作者： Fu, Jinxue Cheng, Juan Li, Weiming Xiong, Tao Wang, Yanli Institute of Applied Physics and Computational Mathematics Beijing100088 China Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China School of Mathematical Sciences University of Science and Technology of China Anhui Hefei230026 China Beijing Computational Science Research Center Beijing100193 China

An asymptotic-preserving (AP) implicit-explicit PN numerical scheme is proposed for the gray model of the radiative transfer equation, where the first- and second-order numerical schemes are discussed for both the linear and nonlinear models. The AP property of this numerical scheme is proved theoretically and numerically, while the numerical stability of the linear model is verified by Fourier analysis. Several classical benchmark examples are studied to validate the efficiency of this numerical scheme. © 2024, CC BY-NC-ND.

关键词： Radiative transfer