Haojie Lian¹, Jiaqi Wang¹, Leilei Chen^2,*, Shengze Li³, Ruochen Cao⁴, Qingyuan Hu⁵, Peiyun Zhao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.1, pp. 1143-1163, 2024, DOI:10.32604/cmes.2024.048549

Abstract This paper presents a novel framework aimed at quantifying uncertainties associated with the 3D reconstruction of smoke from 2D images. This approach reconstructs color and density fields from 2D images using Neural Radiance Field (NeRF) and improves image quality using frequency regularization. The NeRF model is obtained via joint training of multiple artificial neural networks, whereby the expectation and standard deviation of density fields and RGB values can be evaluated for each pixel. In addition, customized physics-informed neural network (PINN) with residual blocks and two-layer activation functions are utilized to input the density fields of the NeRF into Navier-Stokes equations… More >

Jiepeng Yao^1,2, Zhanjia Peng^1,2, Jingjing Liu^1,2, Chengxiao Fan^1,2, Zhongyi Wang^1,2,3, Lan Huang^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2243-2265, 2023, DOI:10.32604/cmes.2023.028101

Abstract In the establishment of differential equations, the determination of time-varying parameters is a difficult problem, especially for equations related to life activities. Thus, we propose a new framework named BioE-PINN based on a physical information neural network that successfully obtains the time-varying parameters of differential equations. In the proposed framework, the learnable factors and scale parameters are used to implement adaptive activation functions, and hard constraints and loss function weights are skillfully added to the neural network output to speed up the training convergence and improve the accuracy of physical information neural networks. In this paper, taking the electrophysiological differential… More >

Loc Vu-Quoc^1,*, Alexander Humer²

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1069-1343, 2023, DOI:10.32604/cmes.2023.028130

Abstract Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional… More >