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Hybrid deep learning and isogeometric analysis for bearing capacity assessment of sand over clay

Journal of Rock Mechanics and Geotechnical engineering 2024年

作者： Toan Nguyen-Minh Tram Bui-Ngoc Jim Shiau Tan Nguyen Trung Nguyen-Thoi Faculty of Civil Engineering Ton Duc Thang University Ho Chi Minh City 700000 Vietnam Laboratory for Computational Mechanics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City 700000 Vietnam Faculty of Mechanical - Electrical and Computer Engineering School of Technology Van Lang University Ho Chi Minh City 700000 Vietnam School of Engineering University of Southern Queensland Toowoomba QLD 4350 Australia Smart Computing in Civil Engineering Research Group Ton Duc Thang University Ho Chi Minh City 700000 Vietnam Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City 700000 Vietnam

In this paper, Isogeometric analysis (IGA) is effectively integrated with machine learning (ML) to investigate the bearing capacity of strip footings in layered soil profiles, with a focus on a sand-over-clay configuration. The study begins with the generation of a comprehensive dataset of 10,000 samples from IGA upper bound (UB) limit analyses, facilitating an in-depth examination of various material and geometric conditions. A hybrid deep neural network, specifically the Whale Optimization Algorithm-Deep Neural Network (WOA-DNN), is then employed to utilize these 10,000 outputs for precise bearing capacity predictions. Notably, the WOA-DNN model outperforms conventional ML techniques, offering a robust and accurate prediction tool. This innovative approach explores a broad range of design parameters, including sand layer depth, load-to-soil unit weight ratio, internal friction angle, cohesion, and footing roughness. A detailed analysis of the dataset reveals the significant influence of these parameters on bearing capacity, providing valuable insights for practical foundation design. This research demonstrates the usefulness of data-driven techniques in optimizing the design of shallow foundations within layered soil profiles, marking a significant stride in geotechnical engineering advancements.

关键词： UB limit analysis Isogeometric analysis (IGA) hybrid deep neural network Whale optimization algorithm

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High order asymptotic preserving discontinuous galerkin methods for gray radiative transfer equations

arXiv

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arXiv 2020年

作者： Xiong, Tao Sun, Wenjun Shi, Yi Song, Peng School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University XiamenFujian361005 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

In this paper, we will develop a class of high order asymptotic preserving (AP) discontinuous Galerkin (DG) methods for nonlinear time-dependent gray radiative transfer equations (GRTEs). Inspired by the work [34], in which stability enhanced high order AP DG methods are proposed for linear transport equations, we propose to pernalize the nonlinear GRTEs under the micro-macro decomposition framework by adding a weighted linear diffusive term. In the diffusive limit, a hyperbolic, namely ∆t = O(h) where ∆t and h are the time step and mesh size respectively, instead of parabolic ∆t = O(h2) time step restriction is obtained, which is also free from the photon mean free path. The main new ingredient is that we further employ a Picard iteration with a predictor-corrector procedure, to decouple the resulting global nonlinear system to a linear system with local nonlinear algebraic equations from an outer iterative loop. Our scheme is shown to be asymptotic preserving and asymptotically accurate. Numerical tests for one and two spatial dimensional problems are performed to demonstrate that our scheme is of high order, effective and efficient. © 2020, CC-BY.

关键词： Radiative transfer

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The role of slow manifolds in parameter estimation for a multiscale stochastic system with α-stable Lévy noise

arXiv

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arXiv 2020年

作者： Chao, Ying Wei, Pingyuan Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory for Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian α-stable Lévy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for this estimation is quantified by p-moment with p ∈ (1, α), with the help of a reduced system through random slow manifold approximation. This method provides an advantage in computational complexity and cost, due to the dimension reduction in stochastic systems. To numerically illustrate this method, and to corroborate that the parameter estimator based on the reduced slow system is a good approximation for the true parameter value of the original system, a prototypical example is present. Copyright © 2020, The Authors. All rights reserved.

关键词： Parameter estimation

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A framework for evaluating statistical models in physics education research

arXiv

引用

arXiv 2021年

作者： Aiken, John M. de Bin, Riccardo Lewandowski, H.J. Caballero, Marcos D. Center for Computing in Science Education Department of Physics University of Oslo OsloN-0316 Norway Department of Mathematics University of Oslo OsloN-0316 Norway Department of Physics University of Colorado Boulder BoulderCO80309 United States JILA National Institute of Standards and Technology The University of Colorado BoulderCO80309 United States Department of Physics and Astronomy Department of Computational Mathematics Sciences and Engineering CREATE for STEM Institute Michigan State University East LansingMI48824 United States

Across the field of education research there has been an increased focus on the development, critique, and evaluation of statistical methods and data usage due to recently created, very large data sets and machine learning techniques. In physics education research (PER), this increased focus has recently been shown through the 2019 Physical Review PER Focused Collection examining quantitative methods in PER. Quantitative PER has provided strong arguments for reforming courses by including interactive engagement, demonstrated that students often move away from scientist-like views due to science education, and has injected robust assessment into the physics classroom via concept inventories. The work presented here examines the impact that machine learning may have on physics education research, presents a framework for the entire process including data management, model evaluation, and results communication, and demonstrates the utility of this framework through the analysis of two types of survey data. © 2021, CC BY.

关键词： Information management

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A computational model for investigating the evolution of colonic crypts during Lynch syndrome carcinogenesis

Computational and Systems Oncology

引用

computational and Systems Oncology 2021年第2期1卷

作者： Haupt, Saskia Gleim, Nils Ahadova, Aysel Bläker, Hendrik von Knebel Doeberitz, Magnus Kloor, Matthias Heuveline, Vincent Engineering Mathematics and Computing Lab (EMCL) Interdisciplinary Center for Scientific Computing (IWR) Heidelberg University Heidelberg Germany Data Mining and Uncertainty Quantification (DMQ) Heidelberg Institute for Theoretical Studies (HITS) Heidelberg Germany Department of Applied Tumor Biology (ATB) Institute of Pathology University Hospital Heidelberg Heidelberg Germany Clinical Cooperation Unit Applied Tumor Biology German Cancer Research Center Heidelberg Germany Institute of Pathology University Hospital Leipzig Leipzig Germany

Lynch syndrome (LS), the most common inherited colorectal cancer (CRC) syndrome, increases the cancer risk in affected individuals. LS is caused by pathogenic germline variants in one of the DNA mismatch repair (MMR) genes, complete inactivation of which causes numerous mutations in affected cells. As CRC is believed to originate in colonic crypts, understanding the intra-crypt dynamics caused by mutational processes is essential for a complete picture of LS CRC and may have significant implications for cancer prevention. We propose a computational model describing the evolution of colonic crypts during LS carcinogenesis. Extending existing modeling approaches for the non-Lynch scenario, we incorporated MMR deficiency and implemented recent experimental data demonstrating that somatic CTNNB1 mutations are common drivers of LS-associated CRCs, if affecting both alleles of the gene. Further, we simulated the effect of different mutations on the entire crypt, distinguishing non-transforming and transforming mutations. As an example, we analyzed the spread of mutations in the genes APC and CTNNB1, which are frequently mutated in LS tumors, as well as of MMR deficiency itself. We quantified each mutation's potential for monoclonal conversion and investigated the influence of the cell location and of stem cell dynamics on mutation spread. The in silico experiments underline the importance of stem cell dynamics for the overall crypt evolution. Further, simulating different mutational processes is essential in LS since mutations without survival advantages (the MMR deficiency-inducing second hit) play a key role. The effect of other mutations can be simulated with the proposed model. Our results provide first mathematical clues towards more effective surveillance protocols for LS carriers. © 2021 The Authors. computational and Systems Oncology published by Wiley Periodicals LLC.

关键词： Carcinogenesis Colonic Crypts Colorectal Cancer computational Modeling Lynch Syndrome Monoclonal Conversion Voronoi Tessellation Model

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Impact of subdominant modes on the interpretation of gravitational-wave signals from heavy binary black hole systems

引用

Physical Review D 2020年第12期101卷 124054-124054页

作者： Feroz H. Shaik Jacob Lange Scott E. Field Richard O’Shaughnessy Vijay Varma Lawrence E. Kidder Harald P. Pfeiffer Daniel Wysocki Department of Physics Department of Mathematics and the Center for Scientific Computing & Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Center for Computational Relativity and Gravitation Rochester Institute of Technology Rochester New York 14623 USA Department of Mathematics and the Center for Scientific Computing & Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Theoretical Astrophysics California Institute of Technology Pasadena California 91125 USA Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 14476 Potsdam Germany

Over the past year, a handful of new gravitational wave models have been developed to include multiple harmonic modes thereby enabling for the first time fully Bayesian inference studies including higher modes to be performed. Using one recently developed numerical relativity surrogate model, NRHybSur3dq8, we investigate the importance of higher modes on parameter inference of coalescing massive binary black holes. We focus on examples relevant to the current three-detector network of observatories, with a detector-frame mass set to 120 M⊙ and with signal amplitude values that are consistent with plausible candidates for the next few observing runs. We show that for such systems the higher mode content will be important for interpreting coalescing binary black holes, reducing systematic bias, and computing properties of the remnant object. Even for comparable-mass binaries and at low signal amplitude, the omission of higher modes can influence posterior probability distributions. We discuss the impact of our results on source population inference and self-consistency tests of general relativity. Our work can be used to better understand asymmetric binary black hole merger events, such as GW190412. Higher modes are critical for such systems, and their omission usually produces substantial parameter biases.

关键词： Gravitational waves

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Effective Combined Method for Calculation of Excitation Dielectric Sphere with a Thin Coating

Effective Combined Method for Calculation of Excitation Diel...

引用

2019 Radiation and Scattering of Electromagnetic Waves, RSEMW 2019

作者： Kisel, N.N. Panychev, A.I. Alpatova, A.V. Kisel, D.V. Department of Antennas and Radio Transmitting Devices Southern Federal University Institute of Radio Engineering Systems and Management Taganrog Russia Scientific Researched Institute of Communication Taganrog Russia Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russia

ISBN: (纸本)9781728106892

The method of calculation for thin coatings of dielectric sphere is proposed in this paper and the boundaries of applicability of the algorithm are estimated. Approximate boundary conditions for electric and magnetic fields are used to solve the problem of exciting a sphere covered with a thin coating (shell), the dielectric sphere is described by the exact method of eigenfunctions. This approach greatly simplifies the solution algorithm and practically does not reduce the accuracy and allows you to obtain a solution in an analytical form. © 2019 IEEE.

关键词： Eigenvalues and eigenfunctions

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A real neural network state for quantum chemistry

arXiv

引用

arXiv 2023年

作者： Wu, Yangjun Xu, Xiansong Poletti, Dario Fan, Yi Guo, Chu Shang, Honghui Institute of Computing Technology Chinese Academy of Sciences Beijing China Science Mathematics and Technology Cluster Singapore University of Technology and Design 8 Somapah Road 487372 Singapore College of Physics and Electronic Engineering Center for Computational Sciences Sichuan Normal University Chengdu610068 China EPD Pillar Singapore University of Technology and Design 8 Somapah Road 487372 Singapore University of Science and Technology of China Hefei China Henan Key Laboratory of Quantum Information and Cryptography Henan Zhengzhou450000 China Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education Department of Physics Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha410081 China

The restricted Boltzmann machine (RBM) has been successfully applied to solve the many-electron Schrödinger equation. In this work we propose a single-layer fully connected neural network adapted from RBM and apply it to study ab initio quantum chemistry problems. Our contribution is two-fold: 1) our neural network only uses real numbers to represent the real electronic wave function, while we obtain comparable precision to RBM for various prototypical molecules;2) we show that the knowledge of the Hartree-Fock reference state can be used to systematically accelerate the convergence of the variational Monte Carlo algorithm as well as to increase the precision of the final energy. © 2023, CC BY.

关键词： Wave functions

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An a posteriori error estimator for the spectral fractional power of the Laplacian

arXiv

引用

arXiv 2022年

作者： Bulle, Raphaël Barrera, Olga Bordas, Stéphane P.A. Chouly, Franz Hale, Jack S. Institute of Computational Engineering University of Luxembourg 6 Avenue de la Fonte Esch-sur-Alzette4362 Luxembourg Université Bourgogne Franche-Comté Institut de Mathématiques de Bourgogne Dijon21078 France Center for Mathematical Modeling Department of Mathematical Engineering University of Chile IRL 2807 - CNRS Santiago Chile School of Engineering Computing and Mathematics Oxford Brookes University Oxford United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Department of Medical Research China Medical University Hospital China Medical University Taichung Taiwan Departamento de Ingenería Matématica CI2MA Universidad de Concepción Casilla 160-C Concepción Chile

We develop a novel a posteriori error estimator for the L2 error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization scheme using rational approximations which allow to reformulate the fractional problem into a family of non-fractional parametric problems. The estimator involves applying the implicit Bank-Weiser error estimation strategy to each parametric non-fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. In addition we propose an algorithm to adapt both the finite element mesh and the rational scheme in order to balance the discretization errors. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement *** Codes 65N15, 65N30 © 2022, CC BY-NC-ND.

关键词： Finite element method

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Analysis and approximations of dirichlet boundary control of stokes flows in the energy space

arXiv

引用

arXiv 2020年

作者： Gong, Wei Mateos, Mariano Singler, John R. Zhang, Yangwen State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Dpto. de Matemáticas Universidad de Oviedo Campus de Gijón Spain Department of Mathematics and Statistics Missouri University of Science and Technology RollaMO United States Department of Mathematical Science University of Delaware NewarkDE United States

We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the L2 norm and an energy space seminorm. We prove well-posedness and regularity results for both problems, develop finite element discretizations for both problems, and prove finite element error estimates for the latter problem. The motivation to study the energy space problem follows from our analysis: we prove that the choice of the control space L2(Γ) can lead to an optimal control with discontinuities at the corners, even when the domain is convex. We observe this phenomenon in numerical experiments. This behavior does not occur in Dirichlet boundary control problems for the Poisson equation on convex polygonal domains, and may not be desirable in real applications. For the energy space problem, we derive the first order optimality conditions, and show that the solution of the control problem is more regular than the solution of the problem with the L2(Γ) regularization. We also prove a priori error estimates for the control in the energy norm, and present several numerical experiments for both control problems on convex and nonconvex domains. © 2020, CC0.

关键词： Poisson equation

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