scholarly journals Inverse Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks

2021 ◽  
Author(s):  
Suryanarayana Maddu Maddu ◽  
Dominik Sturm ◽  
Christian L. Müller ◽  
Ivo F. Sbalzarini
Keyword(s):  
Neural Networks ◽  
Scale Model ◽  
Seamless Integration ◽  
Multi Scale ◽  
Physical Equation ◽  
Active Turbulence ◽  
Data Fidelity ◽  
Catastrophic Interference ◽  
Sequential Training ◽  
Magnitude Improvement

Abstract We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically ε-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.

AC Loss Prediction Model of a 150 kJ HTS SMES Based on Multi-Scale Model and Artificial Neural Networks

2018 ◽  
Vol 54 (11) ◽  
pp. 1-5 ◽  
Author(s):  
Zhongping Zhang ◽  
Li Ren ◽  
Ying Xu ◽  
Zuoshuai Wang ◽  
Yajun Xia ◽  
...  
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Prediction Model ◽  
Ac Loss ◽  
Scale Model ◽  
Multi Scale ◽  
Loss Prediction ◽  
Artificial Neural ◽  
Hts Smes

Three-dimensional Reconstruction of Microscopic Image Based on Multi-ST Algorithm

2020 ◽  
Vol 64 (2) ◽  
pp. 20506-1-20506-7
Author(s):  
Min Zhu ◽  
Rongfu Zhang ◽  
Pei Ma ◽  
Xuedian Zhang ◽  
Qi Guo
Keyword(s):  
3D Reconstruction ◽  
Three Dimensional ◽  
Scale Model ◽  
Microscopic Image ◽  
Multi Scale ◽  
Gaussian Pyramid ◽  
Cost Aggregation ◽  
Dimensional Reconstruction ◽  
Image Pairs ◽  
Accurate Matching

Abstract Three-dimensional (3D) reconstruction is extensively used in microscopic applications. Reducing excessive error points and achieving accurate matching of weak texture regions have been the classical challenges for 3D microscopic vision. A Multi-ST algorithm was proposed to improve matching accuracy. The process is performed in two main stages: scaled microscopic images and regularized cost aggregation. First, microscopic image pairs with different scales were extracted according to the Gaussian pyramid criterion. Second, a novel cost aggregation approach based on the regularized multi-scale model was implemented into all scales to obtain the final cost. To evaluate the performances of the proposed Multi-ST algorithm and compare different algorithms, seven groups of images from the Middlebury dataset and four groups of experimental images obtained by a binocular microscopic system were analyzed. Disparity maps and reconstruction maps generated by the proposed approach contained more information and fewer outliers or artifacts. Furthermore, 3D reconstruction of the plug gauges using the Multi-ST algorithm showed that the error was less than 0.025 mm.

Effects of parametric uncertainty on multi-scale model predictions of shock response of a pressed energetic material

2019 ◽  
Vol 125 (23) ◽  
pp. 235104 ◽  
Author(s):  
Sangyup Lee ◽  
Oishik Sen ◽  
Nirmal Kumar Rai ◽  
Nicholas J. Gaul ◽  
K. K. Choi ◽  
...  
Keyword(s):  
Energetic Material ◽  
Parametric Uncertainty ◽  
Scale Model ◽  
Multi Scale ◽  
Model Predictions ◽  
Shock Response

scholarly journals The Winter Habitat Selection of Red Deer (Cervus elaphus) Based on a Multi-Scale Model

Animals ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2454
Author(s):  
Yue Sun ◽  
Yanze Yu ◽  
Jinhao Guo ◽  
Minghai Zhang
Keyword(s):  
Habitat Selection ◽  
Environmental Factors ◽  
Cervus Elaphus ◽  
Red Deer ◽  
Scale Model ◽  
Winter Habitat ◽  
Multi Scale ◽  
Optimal Scale ◽  
Scale Models ◽  
Selection Of

Single-scale frameworks are often used to analyze the habitat selections of species. Research on habitat selection can be significantly improved using multi-scale models that enable greater in-depth analyses of the scale dependence between species and specific environmental factors. In this study, the winter habitat selection of red deer in the Gogostaihanwula Nature Reserve, Inner Mongolia, was studied using a multi-scale model. Each selected covariate was included in multi-scale models at their “characteristic scale”, and we used an all subsets approach and model selection framework to assess habitat selection. The results showed that: (1) Univariate logistic regression analysis showed that the response scale of red deer to environmental factors was different among different covariate. The optimal scale of the single covariate was 800–3200 m, slope (SLP), altitude (ELE), and ratio of deciduous broad-leaved forests were 800 m in large scale, except that the farmland ratio was 200 m in fine scale. The optimal scale of road density and grassland ratio is both 1600 m, and the optimal scale of net forest production capacity is 3200 m; (2) distance to forest edges, distance to cement roads, distance to villages, altitude, distance to all road, and slope of the region were the most important factors affecting winter habitat selection. The outcomes of this study indicate that future studies on the effectiveness of habitat selections will benefit from multi-scale models. In addition to increasing interpretive and predictive capabilities, multi-scale habitat selection models enhance our understanding of how species respond to their environments and contribute to the formulation of effective conservation and management strategies for ungulata.

Multi-Scale Anti-Occlusion Correlation Filters Object Tracking Method Based on Complementary Features

2020 ◽  
pp. 2155002
Author(s):  
Xiuhua Hu ◽  
Yuan Chen ◽  
Yan Hui ◽  
Yingyu Liang ◽  
Guiping Li ◽  
...  
Keyword(s):  
Object Tracking ◽  
Scale Model ◽  
Correlation Filters ◽  
Motion Feature ◽  
Tracking Method ◽  
Object State ◽  
Multi Scale ◽  
Tracking Process ◽  
Object Appearance ◽  
Response Peak

Aiming to tackle the problem of tracking drift easily caused by complex factors during the tracking process, this paper proposes an improved object tracking method under the framework of kernel correlation filter. To achieve discriminative information that is not sensitive to object appearance change, it combines dimensionality-reduced Histogram of Oriented Gradients features and Lab color features, which can be used to exploit the complementary characteristics robustly. Based on the idea of multi-resolution pyramid theory, a multi-scale model of the object is constructed, and the optimal scale for tracking the object is found according to the confidence maps’ response peaks of different sizes. For the case that tracking failure can easily occur when there exists inappropriate updating in the model, it detects occlusion based on whether the occlusion rate of the response peak corresponding to the best object state is less than a set threshold. At the same time, Kalman filter is used to record the motion feature information of the object before occlusion, and predict the state of the object disturbed by occlusion, which can achieve robust tracking of the object affected by occlusion influence. Experimental results show the effectiveness of the proposed method in handling various internal and external interferences under challenging environments.

scholarly journals A parametric prediction of the Young’s modulus of polymers enhanced with ΜWCNTs

2018 ◽  
Vol 233 ◽  
pp. 00025
Author(s):  
P.V. Polydoropoulou ◽  
K.I. Tserpes ◽  
Sp.G. Pantelakis ◽  
Ch.V. Katsiropoulos
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Experimental Results ◽  
Scale Model ◽  
Fe Model ◽  
Multi Scale ◽  
Unit Cells ◽  
Random Dispersion

In this work a multi-scale model simulating the effect of the dispersion, the waviness as well as the agglomerations of MWCNTs on the Young’s modulus of a polymer enhanced with 0.4% MWCNTs (v/v) has been developed. Representative Unit Cells (RUCs) have been employed for the determination of the homogenized elastic properties of the MWCNT/polymer. The elastic properties computed by the RUCs were assigned to the Finite Element (FE) model of a tension specimen which was used to predict the Young’s modulus of the enhanced material. Furthermore, a comparison with experimental results obtained by tensile testing according to ASTM 638 has been made. The results show a remarkable decrease of the Young’s modulus for the polymer enhanced with aligned MWCNTs due to the increase of the CNT agglomerations. On the other hand, slight differences on the Young’s modulus have been observed for the material enhanced with randomly-oriented MWCNTs by the increase of the MWCNTs agglomerations, which might be attributed to the low concentration of the MWCNTs into the polymer. Moreover, the increase of the MWCNTs waviness led to a significant decrease of the Young’s modulus of the polymer enhanced with aligned MWCNTs. The experimental results in terms of the Young’s modulus are predicted well by assuming a random dispersion of MWCNTs into the polymer.

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