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1. Fusion of physically-based registration and deformation modeling for nonrigid motion analysis

   https://doi.org/10.1109/83.967394  

   Tsap, L.V.; Goldgof, D.B.; Sarkar, S. (November 2001, IEEE Transactions on Image Processing)

   In our previous work, we used finite element models to determine nonrigid motion parameters and recover unknown local properties of objects given correspondence data recovered with snakes or other tracking models. In this paper, we present a novel multiscale approach to recovery of nonrigid motion from sequences of registered intensity and range images. The main idea of our approach is that a finite element (FEM) model incorporating material properties of the object can naturally handle both registration and deformation modeling using a single model-driving strategy. The method includes a multiscale iterative algorithm based on analysis of the undirected Hausdorff distance to recover correspondences. The method is evaluated with respect to speed and accuracy. Noise sensitivity issues are addressed. Advantages of the proposed approach are demonstrated using man-made elastic materials and human skin motion. Experiments with regular grid features are used for performance comparison with a conventional approach (separate snakes and FEM models). It is shown, however, that the new method does not require a sampling/correspondence template and can adapt the model to available object features. Usefulness of the method is presented not only in the context of tracking and motion analysis, but also for a burn scar detection application. 

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2. Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

   https://doi.org/10.3390/math8060904  

   Spiridonov, Denis; Vasilyeva, Maria; Chung, Eric T.; Efendiev, Yalchin; Jana, Raghavendra (June 2020, Mathematics)

   In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features. The mathematical model is based on the Richards’ equation with three different types of boundary conditions on the surface: Dirichlet, Neumann, and Robin boundary conditions. For coarse-grid discretization, the Generalized Multiscale Finite Element Method (GMsFEM) is used. Multiscale basis functions that incorporate small scale heterogeneities into the basis functions are constructed. To treat rough boundaries, we construct additional basis functions to take into account the influence of boundary conditions on rough surfaces. We present numerical results for two-dimensional and three-dimensional model problems. To verify the obtained results, we calculate relative errors between the multiscale and reference (fine-grid) solutions for different numbers of multiscale basis functions. We obtain a good agreement between fine-grid and coarse-grid solutions. 

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3. Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains

   https://doi.org/10.3390/computation8020058  

   Alekseev, Valentin; Tang, Qili; Vasilyeva, Maria; Chung, Eric T.; Efendiev, Yalchin (June 2020, Computation)

   In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional approximation. For the solution on the fine grid, we construct approximation using the mixed finite element method. To reduce the size of the fine grid system, we will develop a Mixed Generalized Multiscale Finite Element Method (Mixed GMsFEM). The method differs from existing approaches and requires some modifications to represent the flow and magnetic fields. Numerical results are presented for a two-dimensional model problem in perforated domains. This model problem is a special case for the general 3D problem. We study the influence of the number of multiscale basis functions on the accuracy of the method and show that the proposed method provides a good accuracy with few basis functions. 

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4. Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations

   https://doi.org/10.3390/math8050720  

   Zhang, Zecheng; Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat (May 2020, Mathematics)

   In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the generalized multiscale finite element method (GMsFEM). In order to obtain a small dimensional representation of the solution in each coarse block, the uncertainty space needs to be partitioned (coarsened). This coarsenining collects realizations that provide similar multiscale features as outlined in GMsFEM (or other method of choice). This step is known to be computationally demanding as it requires many local solves and clustering based on them. In this work, we take a different approach and learn coarsening the uncertainty space. Our methods use deep learning techniques in identifying clusters (coarsening) in the uncertainty space. We use convolutional neural networks combined with some techniques in adversary neural networks. We define appropriate loss functions in the proposed neural networks, where the loss function is composed of several parts that includes terms related to clusters and reconstruction of basis functions. We present numerical results for channelized permeability fields in the examples of flows in porous media. 

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5. A Physics‐Aware Deep Learning Model for Energy Localization in Multiscale Shock‐To‐Detonation Simulations of Heterogeneous Energetic Materials

   https://doi.org/10.1002/prep.202200268  

   Nguyen, Phong C. H.; Nguyen, Yen‐Thi; Seshadri, Pradeep K.; Choi, Joseph B.; Udaykumar, H. S.; Baek, Stephen (March 2023, Propellants, Explosives, Pyrotechnics)

   Abstract Predictive simulations of the shock‐to‐detonation transition (SDT) in heterogeneous energetic materials (EM) are vital to the design and control of their energy release and sensitivity. Due to the complexity of the thermo‐mechanics of EM during the SDT, both macro‐scale response and sub‐grid mesoscale energy localization must be captured accurately. This work proposes an efficient and accurate multiscale framework for SDT simulations of EM. We introduce a new approach for SDT simulation by using deep learning to model the mesoscale energy localization of shock‐initiated EM microstructures. The proposed multiscale modeling framework is divided into two stages. First, a physics‐aware recurrent convolutional neural network (PARC) is used to model the mesoscale energy localization of shock‐initiated heterogeneous EM microstructures. PARC is trained using direct numerical simulations (DNS) of hotspot ignition and growth within microstructures of pressed HMX material subjected to different input shock strengths. After training, PARC is employed to supply hotspot ignition and growth rates for macroscale SDT simulations. We show that PARC can play the role of a surrogate model in a multiscale simulation framework, while drastically reducing the computation cost and providing improved representations of the sub‐grid physics. The proposed multiscale modeling approach will provide a new tool for material scientists in designing high‐performance and safer energetic materials. 

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