Abstract : Topics of this mini-symposium include, but not limited to, data-driven methods; incorporation of machine learning techniques; uncertainty quantification, and inverse problems in structures, structural dynamics and materials. Special emphasis is on the fields of structures, structural dynamics and materials with large-scale industry-relevant problems. Potential topics also include integrated modeling and design optimization, multiscale/multi-physics simulation based on the relevant data-driven process. The mini-symposium will bring together researchers working on both fundamental and applied aspects of data-driven computational mechanics to provide a forum for discussion, interaction, and assessment of techniques.
[03299] Investigation on the hyper-reduction approach for the contact-impact simulation
Format : Talk at Waseda University
Author(s) :
SANGJOON SHIN (Seoul National University)
Seung-Hoon Kang (Seoul National University)
Minho Hwang (Seoul National University)
Yongse Kim (Republic of Korea Air Force)
Haeseong Cho (Jeonbuk National University)
Abstract : In the multi-body finite element analysis, the contact algorithm usually requires huge computational cost to capture the temporal/spatial discontinuity on the contact surface. This presentation will investigate the projection-based reduced-order model for the contact-impact simulation. Discrete empirical interpolation method (DEIM) will be employed among the hyper-reduction approaches for computation acceleration. Treatment on each nonlinear component, internal and contact force vectors, will be examined for the generation of DEIM basis and sparse sampling.
[05003] Manifold-Augmented Deep learning-based Approach for Prediction of Airfoil Aerodynamic Performance at Low Reynolds Number
Format : Talk at Waseda University
Author(s) :
Seongwoo Cheon (Jeonbuk National University)
Hyejin Kim (Jeonbuk National University)
Seokhui Ryu (Gyeongsang National University)
Haeseong Cho (Jeonbuk National University)
Hakjin Lee (Gyeongsang National University)
Abstract : Computational fluid dynamics (CFD) analysis usually gives an accurate performance, better reliability, but it requires intensive computational time and cost. In this study, the deep learning-based MOR framework is proposed to predict the aerodynamic performance of airfoils. For this purpose, the proper orthogonal decompostion (POD), autoencoder (AE), and variational autoencoder (VAE) is carried out to gather the latent vectors from full-order snapshot matrix. Moreover, a novel generative model using projection-based manifold learning is proposed to overcome the lack of data due to the computational cost of CFD analysis and augment the training data.
[05436] High-dimensional regression using partition of unity networks (POU-Net)
Format : Online Talk on Zoom
Author(s) :
Eric Felix Darve (Stanford University)
Tiffany Fan (Stanford University)
Nathaniel Trask (Sandia National Laboratories)
Marta D'Elia (Stanford University)
Abstract : High-dimensional regression problems present challenges in scientific and engineering applications. Conventional approaches like polynomial interpolation become computationally expensive as the dimensionality increases exponentially. Sparse grids and radial basis function regression have been developed as alternatives, but they suffer from high computational costs, low accuracy, and instability in some cases. Deep Neural Networks (DNNs) have proven to be a reliable regression method for high-dimensional problems. However, designing an optimal DNN structure, weight initialization, and achieving high accuracy with the optimizer pose difficulties, making error control challenging in engineering and scientific applications. Additionally, reproducibility is often problematic. To address these issues, we introduce POU-Net and its variants. POU-Net takes advantage of DNNs’ dimensionality reduction and regression capabilities. Additionally, it utilizes the reliability, accuracy, and computational efficiency of polynomial interpolation within the reduced dimension. Our approach enables robust and accurate regression across a wide range of input dimensions. We evaluate the proposed method using various benchmarks and applications, comparing its performance to state-of-the-art techniques.
[03424] Model Order Reduction for Fluid-Structure Interaction Analysis via the Data-driven Machine Learning
Format : Talk at Waseda University
Author(s) :
SiHun Lee (Seoul National University)
Sangmin Lee (Seoul National University)
Haeseong Cho (Jeonbuk National University)
SANGJOON SHIN (Seoul National University)
Abstract : Analysis on the multi-disciplinary analysis such as a fluid-structure interaction usually requires huge computational time due to nonlinearity and interpolation. In this research, a completely data-driven model order reduction method is considered that is capable of the parametric estimation regarding fluid-structure interaction analysis. The proposed method first constructs a snapshot matrix that contains various parametric result and then, singular value decomposition (SVD) is conducted. By SVD, proper orthogonal decomposition (POD) modes and coefficients will be gathered, which is interpolated by the machine learning technique.
[05031] Data-driven Model Reduction Approach for Multiscale Homogenization of Microstructure
Format : Talk at Waseda University
Author(s) :
Hyejin Kim (Jeonbuk National University)
Dahan Song (Jeonbuk National University)
Seongwoo Cheon (Jeonbuk National University)
Haeseong Cho (Jeonbuk National University)
Abstract : Given the heterogeneous nature of composite materials at the microscopic level, computational multiscale homogenization can be employed to obtain effective macroscopic material properties. However, it requires significant computational resources for recursive procedures. In this study, an efficient data-driven homogenization method is proposed. Herein, a clustering-based data-driven model reduction and autoencoder are utilized to alleviate high-dimensional data, followed by the application of a recurrent network model to predict the stress field of microstructure from loading conditions.
[05220] An efficient neural network approximation of entropy solutions
Format : Talk at Waseda University
Author(s) :
Donsub Rim (Washington University in St. Louis)
Gerrit Welper (University of Central Florida)
Randall J LeVeque (University of Washington)
Abstract : We show that a family of neural networks with fixed number of layers and degrees of freedom, can approximate any entropy solution to scalar conservation laws and furthermore, the embedded dynamics in the free parameters is linear regardless of the complexity of the solution.
[03428] Machine learning-based methods for the nonlinear structural analysis
Format : Talk at Waseda University
Author(s) :
Sangmin Lee (Seoul National University)
SiHun Lee (Seoul National University)
Haeseong Cho (Jeonbuk National University)
SANGJOON SHIN (Seoul National University)
Abstract : Nonlinear structural analysis plays an important role in many fields of engineering, but it requires substantial computational resources to conduct repetitive high-fidelity simulation. In this study, a machine learning based non-intrusive model order reduction (MOR) is proposed for the parameterized structural analysis in which the geometric nonlinearities are involved. For this purpose, the proper orthogonal decomposition (POD) is carried out to gather the reduced bases from the full-order snapshot matrix. Then, the modified nouveau variational autoencoder (mNVAE) is conducted to interpolate such POD coefficients.
Youngsoo Choi (Lawrence Livermore National Laboratory)
Guangting Yu (Arizona State University)
Abstract : In this work, we propose a hypernetwork-based reduced order modeling approach for solving parameterized partial differential equations. The hypernetwork is trained to produce model parameters of latent dynamics models, which governs the evolution of reduced states in a low-dimensional manifold. We parameterize the latent dynamics as neural ordinary differential equations (NODEs). To improve the hypernetwork’s inference capability, we develop a variant of NODEs, low-rank NODEs, where the model parameters are approximated in low-rank.
[05408] An augmented Lagrangian method to accelerate constrained optimization using hyperreduction
Format : Online Talk on Zoom
Author(s) :
Tianshu Wen (University of Notre Dame)
Matthew Zahr (University of Notre Dame)
Abstract : We present a numerical method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems of equations using an augmented Lagrangian framework. A globally convergent, hyperreduced trust-region framework is embedded in the proposed framework to accelerate the optimization process in each major iteration. The trust-region framework constructs a hyperreduction model via empirical quadrature procedure on-the-fly, which completely avoids an offline training phase.
