Martin Zlatić, Felipe Rocha, Laurent Stainier, Marko Čanađija
We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The second is a neural network (NN) based approach, where a neural network is used as a constitutive model. It is trained on data to learn the underlying material behaviour and is implemented in the same way as conventional models. The DDCM approach has been extended to include strategies for recovering isotropic behaviour and local smoothing of data. These have proven to be critical in certain cases and increase accuracy in most cases. The NN approach contains certain elements to enforce principles such as material symmetry, thermodynamic consistency, and convexity. In order to provide a fair comparison between the approaches, they use the same data and solve the same numerical problems with a selection of problems highlighting the advantages and disadvantages of each approach. Both the DDCM and the NNs have shown acceptable performance. The DDCM performed better when applied to cases similar to those from which the data is gathered from, albeit at the expense of generality, whereas NN models were more advantageous when applied to wider range of applications.
我们对利用数据模拟超弹性材料行为的两种方法进行了比较。第一种方法是一种基于数据驱动计算力学（DDCM）的新方法，它完全绕过了材料模型的定义，只使用模拟或实际实验的数据进行计算。第二种是基于神经网络（NN）的方法，即使用神经网络作为构成模型。神经网络通过数据训练来学习基本的材料行为，其实现方式与传统模型相同。DDCM 方法已扩展到包括恢复各向同性行为和局部平滑数据的策略。NN 方法包含某些执行原则的元素，如材料对称性、热力学一致性和凸性。为了对这两种方法进行公平比较，它们使用相同的数据，解决相同的数值问题，并选择一些问题来突出每种方法的优缺点。DDCM 和 NN 的性能都可以接受。DDCM 在应用于与收集数据的情况相似的情况时表现更好，尽管牺牲了一般性；而 NN 模型在应用于更广泛的情况时更具优势。
{"title":"Data-driven methods for computational mechanics: A fair comparison between neural networks based and model-free approaches","authors":"Martin Zlatić, Felipe Rocha, Laurent Stainier, Marko Čanađija","doi":"arxiv-2409.06727","DOIUrl":"https://doi.org/arxiv-2409.06727","url":null,"abstract":"We present a comparison between two approaches to modelling hyperelastic\u0000material behaviour using data. The first approach is a novel approach based on\u0000Data-driven Computational Mechanics (DDCM) that completely bypasses the\u0000definition of a material model by using only data from simulations or real-life\u0000experiments to perform computations. The second is a neural network (NN) based\u0000approach, where a neural network is used as a constitutive model. It is trained\u0000on data to learn the underlying material behaviour and is implemented in the\u0000same way as conventional models. The DDCM approach has been extended to include\u0000strategies for recovering isotropic behaviour and local smoothing of data.\u0000These have proven to be critical in certain cases and increase accuracy in most\u0000cases. The NN approach contains certain elements to enforce principles such as\u0000material symmetry, thermodynamic consistency, and convexity. In order to\u0000provide a fair comparison between the approaches, they use the same data and\u0000solve the same numerical problems with a selection of problems highlighting the\u0000advantages and disadvantages of each approach. Both the DDCM and the NNs have\u0000shown acceptable performance. The DDCM performed better when applied to cases\u0000similar to those from which the data is gathered from, albeit at the expense of\u0000generality, whereas NN models were more advantageous when applied to wider\u0000range of applications.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sergio Consoli, Peter Markov, Nikolaos I. Stilianakis, Lorenzo Bertolini, Antonio Puertas Gallardo, Mario Ceresa
This paper presents a novel approach to epidemic surveillance, leveraging the power of Artificial Intelligence and Large Language Models (LLMs) for effective interpretation of unstructured big data sources, like the popular ProMED and WHO Disease Outbreak News. We explore several LLMs, evaluating their capabilities in extracting valuable epidemic information. We further enhance the capabilities of the LLMs using in-context learning, and test the performance of an ensemble model incorporating multiple open-source LLMs. The findings indicate that LLMs can significantly enhance the accuracy and timeliness of epidemic modelling and forecasting, offering a promising tool for managing future pandemic events.
{"title":"Epidemic Information Extraction for Event-Based Surveillance using Large Language Models","authors":"Sergio Consoli, Peter Markov, Nikolaos I. Stilianakis, Lorenzo Bertolini, Antonio Puertas Gallardo, Mario Ceresa","doi":"arxiv-2408.14277","DOIUrl":"https://doi.org/arxiv-2408.14277","url":null,"abstract":"This paper presents a novel approach to epidemic surveillance, leveraging the\u0000power of Artificial Intelligence and Large Language Models (LLMs) for effective\u0000interpretation of unstructured big data sources, like the popular ProMED and\u0000WHO Disease Outbreak News. We explore several LLMs, evaluating their\u0000capabilities in extracting valuable epidemic information. We further enhance\u0000the capabilities of the LLMs using in-context learning, and test the\u0000performance of an ensemble model incorporating multiple open-source LLMs. The\u0000findings indicate that LLMs can significantly enhance the accuracy and\u0000timeliness of epidemic modelling and forecasting, offering a promising tool for\u0000managing future pandemic events.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This manuscript proposes an optimization framework to find the tailor-made functionally graded material (FGM) profiles for thermoelastic applications. This optimization framework consists of (1) a random profile generation scheme, (2) deep learning (DL) based surrogate models for the prediction of thermal and structural quantities, and (3) a genetic algorithm (GA). From the proposed random profile generation scheme, we strive for a generic design space that does not contain impractical designs, i.e., profiles with sharp gradations. We also show that the power law is a strict subset of the proposed design space. We use a dense neural network-based surrogate model for the prediction of maximum stress, while the deep neural operator DeepONet is used for the prediction of the thermal field. The point-wise effective prediction of the thermal field enables us to implement the constraint that the metallic content of the FGM remains within a specified limit. The integration of the profile generation scheme and DL-based surrogate models with GA provides us with an efficient optimization scheme. The efficacy of the proposed framework is demonstrated through various numerical examples.
该优化框架包括：（1）随机剖面生成方案；（2）基于深度学习（DL）的代用模型，用于预测热量和结构量；（3）遗传算法（GA）。根据所提出的随机轮廓生成方案，我们努力寻求一个通用的设计空间，该空间不包含不切实际的设计，即具有尖锐梯度的轮廓。我们使用基于密集神经网络的代用模型预测最大应力，同时使用深度神经算子 DeepONet 预测热场。通过对热场进行有效的点预测，我们可以实现 FGM 金属含量保持在指定范围内的约束。轮廓生成方案和基于 DL 的代用模型与 GA 的集成为我们提供了一个高效的优化方案。我们通过各种数值示例证明了所提出框架的有效性。
{"title":"Efficient FGM optimization with a novel design space and DeepONet","authors":"Piyush Agrawal, Ihina Mahajan, Shivam Choubey, Manish Agrawal","doi":"arxiv-2408.14203","DOIUrl":"https://doi.org/arxiv-2408.14203","url":null,"abstract":"This manuscript proposes an optimization framework to find the tailor-made\u0000functionally graded material (FGM) profiles for thermoelastic applications.\u0000This optimization framework consists of (1) a random profile generation scheme,\u0000(2) deep learning (DL) based surrogate models for the prediction of thermal and\u0000structural quantities, and (3) a genetic algorithm (GA). From the proposed\u0000random profile generation scheme, we strive for a generic design space that\u0000does not contain impractical designs, i.e., profiles with sharp gradations. We\u0000also show that the power law is a strict subset of the proposed design space.\u0000We use a dense neural network-based surrogate model for the prediction of\u0000maximum stress, while the deep neural operator DeepONet is used for the\u0000prediction of the thermal field. The point-wise effective prediction of the\u0000thermal field enables us to implement the constraint that the metallic content\u0000of the FGM remains within a specified limit. The integration of the profile\u0000generation scheme and DL-based surrogate models with GA provides us with an\u0000efficient optimization scheme. The efficacy of the proposed framework is\u0000demonstrated through various numerical examples.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical relationships were derived through experimentation and curve fitting. Recently, to automate the constitutive modeling process, data-driven approaches based on neural networks have been explored. While initial naive approaches violated established mechanical principles, recent efforts concentrate on designing neural network architectures that incorporate physics and mechanistic assumptions into machine-learning-based constitutive models. For history-dependent materials, these models have so far predominantly been restricted to small-strain formulations. In this work, we develop a finite strain plasticity formulation based on thermodynamic potentials to model mixed isotropic and kinematic hardening. We then leverage physics-augmented neural networks to automate the discovery of thermodynamically consistent constitutive models of finite strain elastoplasticity from uniaxial experiments. We apply the framework to both synthetic and experimental data, demonstrating its ability to capture complex material behavior under cyclic uniaxial loading. Furthermore, we show that the neural network enhanced model trains easier than traditional phenomenological models as it is less sensitive to varying initial seeds. our model's ability to generalize beyond the training set underscores its robustness and predictive power. By automating the discovery of hardening models, our approach eliminates user bias and ensures that the resulting constitutive model complies with thermodynamic principles, thus offering a more systematic and physics-informed framework.
{"title":"Automated model discovery of finite strain elastoplasticity from uniaxial experiments","authors":"Asghar A. Jadoon, Knut A. Meyer, Jan N. Fuhg","doi":"arxiv-2408.14615","DOIUrl":"https://doi.org/arxiv-2408.14615","url":null,"abstract":"Constitutive modeling lies at the core of mechanics, allowing us to map\u0000strains onto stresses for a material in a given mechanical setting.\u0000Historically, researchers relied on phenomenological modeling where simple\u0000mathematical relationships were derived through experimentation and curve\u0000fitting. Recently, to automate the constitutive modeling process, data-driven\u0000approaches based on neural networks have been explored. While initial naive\u0000approaches violated established mechanical principles, recent efforts\u0000concentrate on designing neural network architectures that incorporate physics\u0000and mechanistic assumptions into machine-learning-based constitutive models.\u0000For history-dependent materials, these models have so far predominantly been\u0000restricted to small-strain formulations. In this work, we develop a finite\u0000strain plasticity formulation based on thermodynamic potentials to model mixed\u0000isotropic and kinematic hardening. We then leverage physics-augmented neural\u0000networks to automate the discovery of thermodynamically consistent constitutive\u0000models of finite strain elastoplasticity from uniaxial experiments. We apply\u0000the framework to both synthetic and experimental data, demonstrating its\u0000ability to capture complex material behavior under cyclic uniaxial loading.\u0000Furthermore, we show that the neural network enhanced model trains easier than\u0000traditional phenomenological models as it is less sensitive to varying initial\u0000seeds. our model's ability to generalize beyond the training set underscores\u0000its robustness and predictive power. By automating the discovery of hardening\u0000models, our approach eliminates user bias and ensures that the resulting\u0000constitutive model complies with thermodynamic principles, thus offering a more\u0000systematic and physics-informed framework.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problem has been hindered by the computational costs of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROM). To demonstrate the potential of this combination, in this paper we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. The main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. We present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, iteration counts, and timings.
{"title":"An optimization-based coupling of reduced order models with efficient reduced adjoint basis generation approach","authors":"Elizabeth Hawkins, Paul Kuberry, Pavel Bochev","doi":"arxiv-2408.14450","DOIUrl":"https://doi.org/arxiv-2408.14450","url":null,"abstract":"Optimization-based coupling (OBC) is an attractive alternative to traditional\u0000Lagrange multiplier approaches in multiple modeling and simulation contexts.\u0000However, application of OBC to time-dependent problem has been hindered by the\u0000computational costs of finding the stationary points of the associated\u0000Lagrangian, which requires primal and adjoint solves. This issue can be\u0000mitigated by using OBC in conjunction with computationally efficient reduced\u0000order models (ROM). To demonstrate the potential of this combination, in this\u0000paper we develop an optimization-based ROM-ROM coupling for a transient\u0000advection-diffusion transmission problem. The main challenge in this\u0000formulation is the generation of adjoint snapshots and reduced bases for the\u0000adjoint systems required by the optimizer. One of the main contributions of the\u0000paper is a new technique for efficient adjoint snapshot collection for\u0000gradient-based optimizers in the context of optimization-based ROM-ROM\u0000couplings. We present numerical studies demonstrating the accuracy of the\u0000approach along with comparison between various approaches for selecting a\u0000reduced order basis for the adjoint systems, including decay of snapshot\u0000energy, iteration counts, and timings.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hooman Danesh, Daniele Di Lorenzo, Francisco Chinesta, Stefanie Reese, Tim Brepols
Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying structural geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The unit cells feature orthogonal voids in four distinct shapes, including rectangular, diamond, oval, and peanut-shaped voids, each characterized by specific void diameters. The generated surrogate models accept geometric parameters and the elastic properties of the base material as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing the surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters.
{"title":"FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design","authors":"Hooman Danesh, Daniele Di Lorenzo, Francisco Chinesta, Stefanie Reese, Tim Brepols","doi":"arxiv-2408.13532","DOIUrl":"https://doi.org/arxiv-2408.13532","url":null,"abstract":"Auxetic structures, known for their negative Poisson's ratio, exhibit\u0000effective elastic properties heavily influenced by their underlying structural\u0000geometry and base material properties. While periodic homogenization of auxetic\u0000unit cells can be used to investigate these properties, it is computationally\u0000expensive and limits design space exploration and inverse analysis. In this\u0000paper, surrogate models are developed for the real-time prediction of the\u0000effective elastic properties of auxetic unit cells with orthogonal voids of\u0000different shapes. The unit cells feature orthogonal voids in four distinct\u0000shapes, including rectangular, diamond, oval, and peanut-shaped voids, each\u0000characterized by specific void diameters. The generated surrogate models accept\u0000geometric parameters and the elastic properties of the base material as inputs\u0000to predict the effective elastic constants in real-time. This rapid evaluation\u0000enables a practical inverse analysis framework for obtaining the optimal design\u0000parameters that yield the desired effective response. The fast Fourier\u0000transform (FFT)-based homogenization approach is adopted to efficiently\u0000generate data for developing the surrogate models, bypassing concerns about\u0000periodic mesh generation and boundary conditions typically associated with the\u0000finite element method (FEM). The performance of the generated surrogate models\u0000is rigorously examined through a train/test split methodology, a parametric\u0000study, and an inverse problem. Finally, a graphical user interface (GUI) is\u0000developed, offering real-time prediction of the effective tangent stiffness and\u0000performing inverse analysis to determine optimal geometric parameters.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce STAResNet, a ResNet architecture in Spacetime Algebra (STA) to solve Maxwell's partial differential equations (PDEs). Recently, networks in Geometric Algebra (GA) have been demonstrated to be an asset for truly geometric machine learning. In cite{brandstetter2022clifford}, GA networks have been employed for the first time to solve partial differential equations (PDEs), demonstrating an increased accuracy over real-valued networks. In this work we solve Maxwell's PDEs both in GA and STA employing the same ResNet architecture and dataset, to discuss the impact that the choice of the right algebra has on the accuracy of GA networks. Our study on STAResNet shows how the correct geometric embedding in Clifford Networks gives a mean square error (MSE), between ground truth and estimated fields, up to 2.6 times lower than than obtained with a standard Clifford ResNet with 6 times fewer trainable parameters. STAREsNet demonstrates consistently lower MSE and higher correlation regardless of scenario. The scenarios tested are: sampling period of the dataset; presence of obstacles with either seen or unseen configurations; the number of channels in the ResNet architecture; the number of rollout steps; whether the field is in 2D or 3D space. This demonstrates how choosing the right algebra in Clifford networks is a crucial factor for more compact, accurate, descriptive and better generalising pipelines.
我们介绍了 STAResNet，这是时空代数（STA）中的一种 ResNet 架构，用于求解麦克斯韦偏微分方程（PDE）。最近，几何代数（GA）中的网络已被证明是真正几何机器学习的资产。在《cite{brandstetter2022clifford}》一书中，GA网络首次被用于求解偏微分方程（PDEs），与实值网络相比，其准确性得到了提高。在这项研究中，我们采用相同的 ResNet 架构和数据集，在 GA 和 STA 中求解了麦克斯韦 PDE，并讨论了右代数的选择对 GA 网络准确性的影响。我们对 STAResNet 的研究表明，在克利福德网络中进行正确的几何嵌入后，地面实况与估计场之间的均方误差（MSE）比可训练参数少 6 倍的标准克利福德 ResNet 低 2.6 倍。STAREsNet 在任何情况下都表现出较低的 MSE 和较高的相关性。测试的场景包括：数据集的采样周期；存在可见或不可见配置的障碍物；ResNet 架构中的通道数量；滚动步骤的数量；场地是在二维空间还是三维空间。这说明了在克利福德网络中选择正确的代数是如何成为更紧凑、更准确、更有描述性和更有概括性的管道的关键因素。
{"title":"STAResNet: a Network in Spacetime Algebra to solve Maxwell's PDEs","authors":"Alberto Pepe, Sven Buchholz, Joan Lasenby","doi":"arxiv-2408.13619","DOIUrl":"https://doi.org/arxiv-2408.13619","url":null,"abstract":"We introduce STAResNet, a ResNet architecture in Spacetime Algebra (STA) to\u0000solve Maxwell's partial differential equations (PDEs). Recently, networks in\u0000Geometric Algebra (GA) have been demonstrated to be an asset for truly\u0000geometric machine learning. In cite{brandstetter2022clifford}, GA networks\u0000have been employed for the first time to solve partial differential equations\u0000(PDEs), demonstrating an increased accuracy over real-valued networks. In this\u0000work we solve Maxwell's PDEs both in GA and STA employing the same ResNet\u0000architecture and dataset, to discuss the impact that the choice of the right\u0000algebra has on the accuracy of GA networks. Our study on STAResNet shows how\u0000the correct geometric embedding in Clifford Networks gives a mean square error\u0000(MSE), between ground truth and estimated fields, up to 2.6 times lower than\u0000than obtained with a standard Clifford ResNet with 6 times fewer trainable\u0000parameters. STAREsNet demonstrates consistently lower MSE and higher\u0000correlation regardless of scenario. The scenarios tested are: sampling period\u0000of the dataset; presence of obstacles with either seen or unseen\u0000configurations; the number of channels in the ResNet architecture; the number\u0000of rollout steps; whether the field is in 2D or 3D space. This demonstrates how\u0000choosing the right algebra in Clifford networks is a crucial factor for more\u0000compact, accurate, descriptive and better generalising pipelines.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christoffer Fyllgraf Christensen, Jonas Engqvist, Fengwen Wang, Ole Sigmund, Mathias Wallin
Preemptive identification of potential failure under loading of engineering structures is a critical challenge. Our study presents an innovative approach to built-in pre-failure indicators within multiscale structural designs utilizing the design freedom of topology optimization. The indicators are engineered to visibly signal load conditions approaching the global critical buckling load. By showing non-critical local buckling when activated, the indicators provide early warning without compromising the overall structural integrity of the design. This proactive safety feature enhances design reliability. With multiscale analysis, macroscale stresses are related to microscale buckling stability. This relationship is applied through tailored stress constraints to prevent local buckling in general while deliberately triggering it at predefined locations under specific load conditions. Experimental testing of 3D-printed designs confirms a strong correlation with numerical simulations. This not only demonstrates the feasibility of creating structures that can signal the need for load reduction or maintenance but also significantly narrows the gap between theoretical optimization models and their practical application. This research contributes to the design of safer structures by introducing built-in early-warning failure systems.
{"title":"Extremal Structures with Embedded Pre-Failure Indicators","authors":"Christoffer Fyllgraf Christensen, Jonas Engqvist, Fengwen Wang, Ole Sigmund, Mathias Wallin","doi":"arxiv-2408.13113","DOIUrl":"https://doi.org/arxiv-2408.13113","url":null,"abstract":"Preemptive identification of potential failure under loading of engineering\u0000structures is a critical challenge. Our study presents an innovative approach\u0000to built-in pre-failure indicators within multiscale structural designs\u0000utilizing the design freedom of topology optimization. The indicators are\u0000engineered to visibly signal load conditions approaching the global critical\u0000buckling load. By showing non-critical local buckling when activated, the\u0000indicators provide early warning without compromising the overall structural\u0000integrity of the design. This proactive safety feature enhances design\u0000reliability. With multiscale analysis, macroscale stresses are related to\u0000microscale buckling stability. This relationship is applied through tailored\u0000stress constraints to prevent local buckling in general while deliberately\u0000triggering it at predefined locations under specific load conditions.\u0000Experimental testing of 3D-printed designs confirms a strong correlation with\u0000numerical simulations. This not only demonstrates the feasibility of creating\u0000structures that can signal the need for load reduction or maintenance but also\u0000significantly narrows the gap between theoretical optimization models and their\u0000practical application. This research contributes to the design of safer\u0000structures by introducing built-in early-warning failure systems.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a parameterised quasi-static solid-mechanical problem. The local basis method by Amsallem et al. [1] addresses this deficiency by introducing a locally, rather than globally, linear approximation of the solution manifold. However, this generally successful approach comes with some limitations, especially in the data-poor setting. In this proof-of-concept investigation, we instead propose a graph-based manifold learning approach to nonlinear projection-based MOR which uses a global, continuously nonlinear approximation of the solution manifold. Approximations of local tangents to the solution manifold, which are necessary for a Galerkin scheme, are computed in the online phase. As an example application for the resulting nonlinear MOR algorithms, we consider simple representative volume element computations. On this example, the manifold learning approach Pareto-dominates the POD and local basis method in terms of the error and runtime achieved using a range of model dimensionalities.
适当正交分解法（POD）是一种流行的基于投影的模型阶次缩减法（MOR），它可能需要大量的模型维数才能成功捕捉由参数化准静态固体力学问题产生的非线性解流形。Amsallem 等人[1]提出的局部基础法通过引入解流形的局部线性近似而非全局线性近似解决了这一不足。然而，这种普遍成功的方法也有一些局限性，尤其是在数据贫乏的情况下。在本概念验证研究中，我们提出了一种基于图的流形学习方法来实现基于非线性投影的 MOR，该方法使用解流形的全局连续非线性近似。作为非线性 MOR 算法的一个应用实例，我们考虑了简单的代表性体积元素计算。在这个例子中，流形学习方法在一系列模型维度下的误差和运行时间方面，帕累托优势明显优于 POD 和局部基础方法。
{"title":"A manifold learning approach to nonlinear model order reduction of quasi-static problems in solid mechanics","authors":"Lisa Scheunemann, Erik Faust","doi":"arxiv-2408.12415","DOIUrl":"https://doi.org/arxiv-2408.12415","url":null,"abstract":"The proper orthogonal decomposition (POD) -- a popular projection-based model\u0000order reduction (MOR) method -- may require significant model dimensionalities\u0000to successfully capture a nonlinear solution manifold resulting from a\u0000parameterised quasi-static solid-mechanical problem. The local basis method by\u0000Amsallem et al. [1] addresses this deficiency by introducing a locally, rather\u0000than globally, linear approximation of the solution manifold. However, this\u0000generally successful approach comes with some limitations, especially in the\u0000data-poor setting. In this proof-of-concept investigation, we instead propose a\u0000graph-based manifold learning approach to nonlinear projection-based MOR which\u0000uses a global, continuously nonlinear approximation of the solution manifold.\u0000Approximations of local tangents to the solution manifold, which are necessary\u0000for a Galerkin scheme, are computed in the online phase. As an example\u0000application for the resulting nonlinear MOR algorithms, we consider simple\u0000representative volume element computations. On this example, the manifold\u0000learning approach Pareto-dominates the POD and local basis method in terms of\u0000the error and runtime achieved using a range of model dimensionalities.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The comprehensive strength of a country varies from strong to weak, divided into three condition: descending, periodicity destruction or rapidly rising, Exploring the differences can solve the development crisis. the most important things for a country are interests, weapons and creature, corresponding to money, technology and people. The ship industry has two attribute of financial benefits and technological weapons. Commercial ships can transport massive commodity and warships carry updating of massive technological weapons; But a new core: equity incentives have emerged, and it has helped the rapid development of the computer industry. This article uses comparative analysis and comparative historical analysis to observe the changes in the United States and China after the mutual circulation of two elements and the double circulation of three elements in history, such as the growth rates of GDP and patent applications. Then, it summarizes the changes brought by the core of civilization to the country.Through this article, it can be concluded that the core of civilization consists of ships and equity incentives; Through the circulation of new elements, a country can transform into civilizations with three cycles, achieving mutual circulation among the three and enhancing endogenous power; The core of civilization can enhance the stability of economic development, prevent economic crises, and achieve a more balanced civilization.
{"title":"The continuous accumulation of civilization core in the cycle of elements-creature, benefits and weapons","authors":"Hongfa Zi, Zhen Liu","doi":"arxiv-2408.11317","DOIUrl":"https://doi.org/arxiv-2408.11317","url":null,"abstract":"The comprehensive strength of a country varies from strong to weak, divided\u0000into three condition: descending, periodicity destruction or rapidly rising,\u0000Exploring the differences can solve the development crisis. the most important\u0000things for a country are interests, weapons and creature, corresponding to\u0000money, technology and people. The ship industry has two attribute of financial\u0000benefits and technological weapons. Commercial ships can transport massive\u0000commodity and warships carry updating of massive technological weapons; But a\u0000new core: equity incentives have emerged, and it has helped the rapid\u0000development of the computer industry. This article uses comparative analysis\u0000and comparative historical analysis to observe the changes in the United States\u0000and China after the mutual circulation of two elements and the double\u0000circulation of three elements in history, such as the growth rates of GDP and\u0000patent applications. Then, it summarizes the changes brought by the core of\u0000civilization to the country.Through this article, it can be concluded that the\u0000core of civilization consists of ships and equity incentives; Through the\u0000circulation of new elements, a country can transform into civilizations with\u0000three cycles, achieving mutual circulation among the three and enhancing\u0000endogenous power; The core of civilization can enhance the stability of\u0000economic development, prevent economic crises, and achieve a more balanced\u0000civilization.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：