English
Related papers

Related papers: A Unified Multiscale Auxiliary PINN Framework for …

200 papers

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Computational Engineering, Finance, and Science · Computer Science 2022-01-26 Han Gao , Matthew J. Zahr , Jian-Xun Wang

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Numerical Analysis · Mathematics 2024-11-28 Marco Berardi , Fabio Difonzo , Matteo Icardi

Advances in nanotechnology have facilitated the exploration of submicron thermal transport. At this scale, Fourier's law is no longer applicable, and the governing equation for thermal transport is the phonon Boltzmann transport equation…

Mesoscale and Nanoscale Physics · Physics 2023-06-27 Yue Hu , Ru Jia , Jiaxuan Xu , Yufei Sheng , Minhua Wen , James Lin , Yongxing Shen , Hua Bao

In this study, we propose a novel approach, termed boundary integrated neural networks (BINNs), for analyzing in-plane crack problems within the framework of linear elastic fracture mechanics. The proposed approach integrates artificial…

Computational Engineering, Finance, and Science · Computer Science 2025-03-03 Peijun Zhang , Yan Gu , Okyay Altay , Chuanzeng Zhang

Physics-Informed Neural Networks (PINNs) have gained popularity in solving nonlinear partial differential equations (PDEs) via integrating physical laws into the training of neural networks, making them superior in many scientific and…

Machine Learning · Computer Science 2023-08-15 Milad Ramezankhani , Abbas S. Milani

Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport…

Mesoscale and Nanoscale Physics · Physics 2015-06-23 Jesse Maassen , Mark Lundstrom

We develop a computational framework, based on the Boltzmann transport equation, with the ability to compute the thermal transport in nanostructured materials of any geometry using as the only input the bulk thermal conductivity…

Mesoscale and Nanoscale Physics · Physics 2014-10-20 Giuseppe Romano , Jeffrey C. Grossman

Physics-Informed Neural Networks (PINNs) have emerged as an influential technology, merging the swift and automated capabilities of machine learning with the precision and dependability of simulations grounded in theoretical physics. PINNs…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Machine Learning · Computer Science 2024-01-17 Abdul Hannan Mustajab , Hao Lyu , Zarghaam Rizvi , Frank Wuttke

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

Computational Engineering, Finance, and Science · Computer Science 2023-11-06 Chen Xu , Ba Trung Cao , Yong Yuan , Günther Meschke

Efficient cooling is vital for the performance and reliability of modern systems such as electronics, nuclear reactors, and industrial equipment. Jet impingement cooling is widely used for its high local heat transfer rates. Accurate…

Fluid Dynamics · Physics 2025-07-15 Arijit Hazra , Prahar Sarkar , Sourav Sarkar

Physics-informed neural networks (PINNs) have recently been used to solve various computational problems which are governed by partial differential equations (PDEs). In this paper, we propose a multi-output physics-informed neural network…

Computational Engineering, Finance, and Science · Computer Science 2022-12-07 Mingyuan Yang , John T. Foster

Accurate characterization of temperature-dependent thermoelectric properties (TEPs), such as thermal conductivity and the Seebeck coefficient, is essential for reliable modeling and efficient design of thermoelectric devices. However, their…

Materials Science · Physics 2025-06-11 Hyeonbin Moon , Songho Lee , Wabi Demeke , Byungki Ryu , Seunghwa Ryu

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…

Machine Learning · Computer Science 2024-08-28 Sen Wang , Peizhi Zhao , Qinglong Ma , Tao Song

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…

Numerical Analysis · Mathematics 2024-03-05 Hongyan Li , Song Jiang , Wenjun Sun , Liwei Xu , Guanyu Zhou

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…

Numerical Analysis · Mathematics 2025-07-11 Jaemin Oh , Seung Yeon Cho , Seok-Bae Yun , Eunbyung Park , Youngjoon Hong

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…

Machine Learning · Computer Science 2023-07-13 Junjun Yan , Xinhai Chen , Zhichao Wang , Enqiang Zhou , Jie Liu

Phonon Boltzmann transport equation (BTE) is an important tool for studying the nanoscale thermal transport. Because phonons have a large spread in their properties, the non-gray (i.e. considering different phonon bands) phonon BTE is…

Computational Physics · Physics 2021-09-29 Yue Hu , Yongxing Shen , Hua Bao

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Optimization and Control · Mathematics 2024-09-06 Michael Hintermüller , Denis Korolev