Pub Date : 2024-06-06DOI: 10.1007/s00366-024-02005-y
Yuhui Zhang, Ji Lin, S. Reutskiy, Timon Rabczuk, Jun-an Lu
{"title":"A novel local meshless collocation method with partial upwind scheme for solving convection-dominated diffusion problems","authors":"Yuhui Zhang, Ji Lin, S. Reutskiy, Timon Rabczuk, Jun-an Lu","doi":"10.1007/s00366-024-02005-y","DOIUrl":"https://doi.org/10.1007/s00366-024-02005-y","url":null,"abstract":"","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141379566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.1007/s00366-024-02001-2
Jing Zhang, Marco Enea, A. Pagani, E. Carrera, E. Madenci, Xia Liu, Qingsheng Yang
{"title":"A computational approach to integrate three-dimensional peridynamics and two-dimensional higher-order classical elasticity theory for fracture analysis","authors":"Jing Zhang, Marco Enea, A. Pagani, E. Carrera, E. Madenci, Xia Liu, Qingsheng Yang","doi":"10.1007/s00366-024-02001-2","DOIUrl":"https://doi.org/10.1007/s00366-024-02001-2","url":null,"abstract":"","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141385522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-01DOI: 10.1007/s00366-024-02006-x
Haoxuan Zhang, Haisheng Li, Xiaoqun Wu, Nan Li
Mesh quality directly affects the accuracy and efficiency of numerical simulation. Mesh quality evaluation aims to evaluate the suitability of the mesh generated in CAE pre-processing for numerical simulation. Recent work has introduced deep neural networks for mesh quality evaluation. However, these methods treat the mesh quality evaluation task as a multi-classification problem, resulting in serious correlations among different quality categories, which makes it difficult to learn the boundaries of different categories. In this paper, we propose a topology-guided graph neural network, MTGNet, which treats the mesh quality evaluation task as a multi-label task. Specifically, we first decomposed the categories in traditional multi-classification problems and obtained three completely orthogonal mesh quality labels, namely orthogonality, smoothness and, distribution. Then, MTGNet introduces a topology-guided feature representation for structured mesh data, which can generate multiple blocks of element-based graphs through the mesh topology. In order to better fuse features in different blocks, MTGNet also introduces an attention-based block graph pooling (ABGPool) method. Experimental results on the NACA-Market dataset demonstrate MTGNet shows superior or at least comparable performance to the state-of-the-art (SOTA) approaches.
{"title":"MTGNet: multi-label mesh quality evaluation using topology-guided graph neural network","authors":"Haoxuan Zhang, Haisheng Li, Xiaoqun Wu, Nan Li","doi":"10.1007/s00366-024-02006-x","DOIUrl":"https://doi.org/10.1007/s00366-024-02006-x","url":null,"abstract":"<p>Mesh quality directly affects the accuracy and efficiency of numerical simulation. Mesh quality evaluation aims to evaluate the suitability of the mesh generated in CAE pre-processing for numerical simulation. Recent work has introduced deep neural networks for mesh quality evaluation. However, these methods treat the mesh quality evaluation task as a multi-classification problem, resulting in serious correlations among different quality categories, which makes it difficult to learn the boundaries of different categories. In this paper, we propose a topology-guided graph neural network, MTGNet, which treats the mesh quality evaluation task as a multi-label task. Specifically, we first decomposed the categories in traditional multi-classification problems and obtained three completely orthogonal mesh quality labels, namely orthogonality, smoothness and, distribution. Then, MTGNet introduces a topology-guided feature representation for structured mesh data, which can generate multiple blocks of element-based graphs through the mesh topology. In order to better fuse features in different blocks, MTGNet also introduces an attention-based block graph pooling (ABGPool) method. Experimental results on the NACA-Market dataset demonstrate MTGNet shows superior or at least comparable performance to the state-of-the-art (SOTA) approaches.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-31DOI: 10.1007/s00366-024-01989-x
Jiarui Wang, Yuri Bazilevs
A thin shell formulation is developed for the approximation by a meshfree Reproducing Kernel Particle Method (RKPM). The formulation is derived from a degenerated shell approach where the structure is treated as a 3D solid subjected to kinematic constraints of the Kirchhoff–Love (KL) shell theory. To address the challenge of surface geometry representation in a meshfree method, a local parameterization using principal component analysis (PCA) is employed. Taylor-series expansion adapted to the shell formulation is developed to address the accuracy and stability issues of nodal quadrature. Several approaches that address membrane locking are also considered. The effectiveness of the proposed RKPM KL shell formulation is demonstrated using an extensive set of linear-elastic and finite-deformation inelastic test cases.
{"title":"A general-purpose meshfree Kirchhoff–Love shell formulation","authors":"Jiarui Wang, Yuri Bazilevs","doi":"10.1007/s00366-024-01989-x","DOIUrl":"https://doi.org/10.1007/s00366-024-01989-x","url":null,"abstract":"<p>A thin shell formulation is developed for the approximation by a meshfree Reproducing Kernel Particle Method (RKPM). The formulation is derived from a degenerated shell approach where the structure is treated as a 3D solid subjected to kinematic constraints of the Kirchhoff–Love (KL) shell theory. To address the challenge of surface geometry representation in a meshfree method, a local parameterization using principal component analysis (PCA) is employed. Taylor-series expansion adapted to the shell formulation is developed to address the accuracy and stability issues of nodal quadrature. Several approaches that address membrane locking are also considered. The effectiveness of the proposed RKPM KL shell formulation is demonstrated using an extensive set of linear-elastic and finite-deformation inelastic test cases.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-30DOI: 10.1007/s00366-024-01990-4
Toru Takahashi
This study proposes a shape optimisation framework for unsteady electromagnetic scattering problems on the basis of the time-domain boundary integral equation method, focusing on the perfectly electric conductors (PECs). The boundary-only formulation is ideal for treating a shape optimisation problem in an exterior domain. However, the electromagnetic shape optimisation in concern has been unrealised with the boundary integral approach regardless of the fact that the boundary-type shape derivative has been known in the literature. The first contribution of the present study is to derive a novel expression of the shape derivative in terms of the surface current densities of the primary and adjoint problems, by considering that the surface current density is handled by usual integral equations methods. The second contribution is to clarify the integral representations and equations of the adjoint electromagnetic fields in terms of the reversal time. These theoretical achievements possess a high affinity with the standard spatial discretising approach (i.e. RWG basis) whenever the temporal basis is sufficiently smooth. The numerical experiments confirmed the reliability of the proposed shape optimisation methodology and indicated the capability to deal with scientific and engineering applications.
{"title":"An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations","authors":"Toru Takahashi","doi":"10.1007/s00366-024-01990-4","DOIUrl":"https://doi.org/10.1007/s00366-024-01990-4","url":null,"abstract":"<p>This study proposes a shape optimisation framework for unsteady electromagnetic scattering problems on the basis of the time-domain boundary integral equation method, focusing on the perfectly electric conductors (PECs). The boundary-only formulation is ideal for treating a shape optimisation problem in an exterior domain. However, the electromagnetic shape optimisation in concern has been unrealised with the boundary integral approach regardless of the fact that the boundary-type shape derivative has been known in the literature. The first contribution of the present study is to derive a novel expression of the shape derivative in terms of the surface current densities of the primary and adjoint problems, by considering that the surface current density is handled by usual integral equations methods. The second contribution is to clarify the integral representations and equations of the adjoint electromagnetic fields in terms of the reversal time. These theoretical achievements possess a high affinity with the standard spatial discretising approach (i.e. RWG basis) whenever the temporal basis is sufficiently smooth. The numerical experiments confirmed the reliability of the proposed shape optimisation methodology and indicated the capability to deal with scientific and engineering applications.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-28DOI: 10.1007/s00366-024-02000-3
Xiliang Liu, Liang Gao, Mi Xiao
It is vital to control the vibration of cellular composites under harmonic excitation in engineering. Due to numerous design variables and expensive frequency domain integration operation, the majority of multiscale topology optimization methods for frequency response minimization of cellular composites tend to be conservative, where a small number of types of microstructures are considered. This paper proposes an efficient multiscale topology optimization method to minimize the frequency response of cellular composites over specified frequency intervals. This method utilizes multiclass graded lattice unit cells (LUCs) as design candidates, offering great design space to improve the dynamic performance of cellular composites. At microscale, the proposed method leverages Kriging metamodels to replace the the homogenization method in each iteration step, thus accelerating the performance estimation of multiclass graded LUCs. At macroscale, the second-order Krylov subspace with moment-matching Gram-Schmidt orthonormalization (SOMMG) method is introduced to expedite the frequency response analysis of cellular composites. Two types of design variables are employed to construct the Kriging metamodel assisted Uniform Multiphase Materials Interpolation (KUMMI) model, facilitating the concurrent updating of LUCs’ classes and relative densities. Several numerical examples are presented to validate the effectiveness and efficiency of the proposed method in minimizing the frequency response of cellular composites.
{"title":"An efficient multiscale topology optimization method for frequency response minimization of cellular composites","authors":"Xiliang Liu, Liang Gao, Mi Xiao","doi":"10.1007/s00366-024-02000-3","DOIUrl":"https://doi.org/10.1007/s00366-024-02000-3","url":null,"abstract":"<p>It is vital to control the vibration of cellular composites under harmonic excitation in engineering. Due to numerous design variables and expensive frequency domain integration operation, the majority of multiscale topology optimization methods for frequency response minimization of cellular composites tend to be conservative, where a small number of types of microstructures are considered. This paper proposes an efficient multiscale topology optimization method to minimize the frequency response of cellular composites over specified frequency intervals. This method utilizes multiclass graded lattice unit cells (LUCs) as design candidates, offering great design space to improve the dynamic performance of cellular composites. At microscale, the proposed method leverages Kriging metamodels to replace the the homogenization method in each iteration step, thus accelerating the performance estimation of multiclass graded LUCs. At macroscale, the second-order Krylov subspace with moment-matching Gram-Schmidt orthonormalization (SOMMG) method is introduced to expedite the frequency response analysis of cellular composites. Two types of design variables are employed to construct the Kriging metamodel assisted Uniform Multiphase Materials Interpolation (KUMMI) model, facilitating the concurrent updating of LUCs’ classes and relative densities. Several numerical examples are presented to validate the effectiveness and efficiency of the proposed method in minimizing the frequency response of cellular composites.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-25DOI: 10.1007/s00366-024-01994-0
Christos Tsolakis, Nikos Chrisochoides
Efficient and robust anisotropic mesh adaptation is crucial for Computational Fluid Dynamics (CFD) simulations. The CFD Vision 2030 Study highlights the pressing need for this technology, particularly for simulations targeting supercomputers. This work applies a fine-grained speculative approach to anisotropic mesh operations. Our implementation exhibits more than 90% parallel efficiency on a multi-core node. Additionally, we evaluate our method within an adaptive pipeline for a spectrum of publicly available test-cases that includes both analytically derived and error-based fields. For all test-cases, our results are in accordance with published results in the literature. Support for CAD-based data is introduced, and its effectiveness is demonstrated on one of NASA’s High-Lift prediction workshop cases.
高效稳健的各向异性网格适应对于计算流体动力学(CFD)模拟至关重要。CFD 2030 愿景研究》强调了对这项技术的迫切需求,尤其是针对超级计算机的模拟。这项工作将细粒度投机方法应用于各向异性网格操作。我们的实现在多核节点上显示出 90% 以上的并行效率。此外,我们还在自适应流水线中对我们的方法进行了评估,该方法适用于一系列公开的测试案例,其中包括分析得出的场和基于误差的场。对于所有测试案例,我们的结果与文献中公布的结果一致。我们还介绍了对基于 CAD 的数据的支持,并在 NASA 的一个高升力预测研讨会案例中演示了其有效性。
{"title":"Speculative anisotropic mesh adaptation on shared memory for CFD applications","authors":"Christos Tsolakis, Nikos Chrisochoides","doi":"10.1007/s00366-024-01994-0","DOIUrl":"https://doi.org/10.1007/s00366-024-01994-0","url":null,"abstract":"<p>Efficient and robust anisotropic mesh adaptation is crucial for Computational Fluid Dynamics (CFD) simulations. The CFD Vision 2030 Study highlights the pressing need for this technology, particularly for simulations targeting supercomputers. This work applies a fine-grained speculative approach to anisotropic mesh operations. Our implementation exhibits more than 90% parallel efficiency on a multi-core node. Additionally, we evaluate our method within an adaptive pipeline for a spectrum of publicly available test-cases that includes both analytically derived and error-based fields. For all test-cases, our results are in accordance with published results in the literature. Support for CAD-based data is introduced, and its effectiveness is demonstrated on one of NASA’s High-Lift prediction workshop cases.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-21DOI: 10.1007/s00366-024-01999-9
Pradiktio Putrayudanto, J. Lai, Pei-Pu Song, Yao-Chen Tsai, Chia-Hsiang Hsu
{"title":"Automatic decomposition of protrusion volumes on thin-shell models for hexahedral mesh generation","authors":"Pradiktio Putrayudanto, J. Lai, Pei-Pu Song, Yao-Chen Tsai, Chia-Hsiang Hsu","doi":"10.1007/s00366-024-01999-9","DOIUrl":"https://doi.org/10.1007/s00366-024-01999-9","url":null,"abstract":"","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141117776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Machine learning is employed for solving physical systems governed by general nonlinear partial differential equations (PDEs). However, complex multi-physics systems such as acoustic-structure coupling are often described by a series of PDEs that incorporate variable physical quantities, which are referred to as parametric systems. There are lack of strategies for solving parametric systems governed by PDEs that involve explicit and implicit quantities. In this paper, a deep learning-based Multi Physics-Informed PointNet (MPIPN) is proposed for solving parametric acoustic-structure systems. First, the MPIPN introduces an enhanced point-cloud architecture that encompasses explicit physical quantities and geometric features of computational domains. Then, the MPIPN extracts local and global features of the reconstructed point-cloud as parts of solving criteria of parametric systems, respectively. Besides, implicit physical quantities are embedded by encoding techniques as another part of solving criteria. Finally, all solving criteria that characterize parametric systems are amalgamated to form distinctive sequences as the input of the MPIPN, whose outputs are solutions of systems. The proposed framework is trained by adaptive physics-informed loss functions for corresponding computational domains. The framework is generalized to deal with new parametric conditions of systems. The effectiveness of the MPIPN is validated by applying it to solve steady parametric acoustic-structure coupling systems governed by the Helmholtz equations. An ablation experiment has been implemented to demonstrate the efficacy of physics-informed impact with a minority of supervised data. The proposed method yields reasonable precision across all computational domains under constant parametric conditions and changeable combinations of parametric conditions for acoustic-structure systems.
{"title":"MPIPN: a multi physics-informed PointNet for solving parametric acoustic-structure systems","authors":"Chu Wang, Jinhong Wu, Yanzhi Wang, Zhijian Zha, Qi Zhou","doi":"10.1007/s00366-024-01998-w","DOIUrl":"https://doi.org/10.1007/s00366-024-01998-w","url":null,"abstract":"<p>Machine learning is employed for solving physical systems governed by general nonlinear partial differential equations (PDEs). However, complex multi-physics systems such as acoustic-structure coupling are often described by a series of PDEs that incorporate variable physical quantities, which are referred to as parametric systems. There are lack of strategies for solving parametric systems governed by PDEs that involve explicit and implicit quantities. In this paper, a deep learning-based Multi Physics-Informed PointNet (MPIPN) is proposed for solving parametric acoustic-structure systems. First, the MPIPN introduces an enhanced point-cloud architecture that encompasses explicit physical quantities and geometric features of computational domains. Then, the MPIPN extracts local and global features of the reconstructed point-cloud as parts of solving criteria of parametric systems, respectively. Besides, implicit physical quantities are embedded by encoding techniques as another part of solving criteria. Finally, all solving criteria that characterize parametric systems are amalgamated to form distinctive sequences as the input of the MPIPN, whose outputs are solutions of systems. The proposed framework is trained by adaptive physics-informed loss functions for corresponding computational domains. The framework is generalized to deal with new parametric conditions of systems. The effectiveness of the MPIPN is validated by applying it to solve steady parametric acoustic-structure coupling systems governed by the Helmholtz equations. An ablation experiment has been implemented to demonstrate the efficacy of physics-informed impact with a minority of supervised data. The proposed method yields reasonable precision across all computational domains under constant parametric conditions and changeable combinations of parametric conditions for acoustic-structure systems.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-18DOI: 10.1007/s00366-024-01984-2
Vahidullah Taç, Manuel K. Rausch, Ilias Bilionis, Francisco Sahli Costabal, Adrian Buganza Tepole
Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that—by construction—create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity.
{"title":"Generative hyperelasticity with physics-informed probabilistic diffusion fields","authors":"Vahidullah Taç, Manuel K. Rausch, Ilias Bilionis, Francisco Sahli Costabal, Adrian Buganza Tepole","doi":"10.1007/s00366-024-01984-2","DOIUrl":"https://doi.org/10.1007/s00366-024-01984-2","url":null,"abstract":"<p>Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that—by construction—create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}