This paper considers the reconstruction of a defect in a two-dimensional waveguide during non-destructive ultrasonic inspection using a derivative-based optimization approach. The propagation of the mechanical waves is simulated by the Scaled Boundary Finite Element Method (SBFEM) that builds on a semi-analytical approach. The simulated data is then fitted to a given set of data describing the reflection of a defect to be reconstructed. For this purpose, we apply an iteratively regularized Gauss-Newton method in combination with algorithmic differentiation to provide the required derivative information accurately and efficiently. We present numerical results for three different kinds of defects, namely a crack, a delamination, and a corrosion. These examples show that the parameterization of the defect can be reconstructed efficiently and robustly in the presence of noise.
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Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin and stochastic collocations methods. This work is concerned with a non-intrusive generalization of the adaptive Galerkin FEM with residual based error estimation. It combines the non-intrusive character of a randomized least-squares method with the a posteriori error analysis of stochastic Galerkin methods. The proposed approach uses the Variational Monte Carlo method to obtain a quasi-optimal low-rank approximation of the Galerkin projection in a highly efficient hierarchical tensor format. We derive an adaptive refinement algorithm which is steered by a reliable error estimator. Opposite to stochastic Galerkin methods, the approach is easily applicable to a wide range of problems, enabling a fully automated adjustment of all discretization parameters. Benchmark examples with affine and (unbounded) lognormal coefficient fields illustrate the performance of the non-intrusive adaptive algorithm, showing best-in-class performance.
To create heterogeneous, multiscale structures with unprecedented functionalities, recent topology optimization approaches design either fully aperiodic systems or functionally graded structures, which compete in terms of design freedom and efficiency. We propose to inherit the advantages of both through a data-driven framework for multiclass functionally graded structures that mixes several families, i.e., classes, of microstructure topologies to create spatially-varying designs with guaranteed feasibility. The key is a new multiclass shape blending scheme that generates smoothly graded microstructures without requiring compatible classes or connectivity and feasibility constraints. Moreover, it transforms the microscale problem into an efficient, low-dimensional one without confining the design to predefined shapes. Compliance and shape matching examples using common truss geometries and diversity-based freeform topologies demonstrate the versatility of our framework, while studies on the effect of the number and diversity of classes illustrate the effectiveness. The generality of the proposed methods supports future extensions beyond the linear applications presented.
Parameter identification for marine ecosystem models is important for the assessment and validation of marine ecosystem models against observational data. The surrogate-based optimization (SBO) is a computationally efficient method to optimize complex models. SBO replaces the computationally expensive (high-fidelity) model by a surrogate constructed from a less accurate but computationally cheaper (low-fidelity) model in combination with an appropriate correction approach, which improves the accuracy of the low-fidelity model. To construct a computationally cheap low-fidelity model, we tested three different approaches to compute an approximation of the annual periodic solution (i.e., a steady annual cycle) of a marine ecosystem model: firstly, a reduced number of spin-up iterations (several decades instead of millennia), secondly, an artificial neural network (ANN) approximating the steady annual cycle and, finally, a combination of both approaches. Except for the low-fidelity model using only the ANN, the SBO yielded a solution close to the target and reduced the computational effort significantly. If an ANN approximating appropriately a marine ecosystem model is available, the SBO using this ANN as low-fidelity model presents a promising and computational efficient method for the validation.
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful to devise an automated method which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions. We solve these equations through associated recursions of the expansion coefficient of the multivalued formal Taylor series. The expansion coefficients can be determined using either the package {\tt Sigma} in the case of linear difference equations or by applying heuristic methods in the case of partial linear difference equations. In the present context a new type of sums occurs, the Hurwitz harmonic sums, and generalized versions of them. The code {\tt HypSeries} transforming classes of differential equations into analytic series expansions is described. Also partial difference equations having rational solutions and rational function solutions of Pochhammer symbols are considered, for which the code {\tt solvePartialLDE} is designed. Generalized hypergeometric functions, Appell-,~Kamp\'e de F\'eriet-, Horn-, Lauricella-Saran-, Srivasta-, and Exton--type functions are considered. We illustrate the algorithms by examples.
Obtaining high-quality 3D reconstructions of room-scale scenes is of paramount importance for upcoming applications in AR or VR. These range from mixed reality applications for teleconferencing, virtual measuring, virtual room planing, to robotic applications. While current volume-based view synthesis methods that use neural radiance fields (NeRFs) show promising results in reproducing the appearance of an object or scene, they do not reconstruct an actual surface. The volumetric representation of the surface based on densities leads to artifacts when a surface is extracted using Marching Cubes, since during optimization, densities are accumulated along the ray and are not used at a single sample point in isolation. Instead of this volumetric representation of the surface, we propose to represent the surface using an implicit function (truncated signed distance function). We show how to incorporate this representation in the NeRF framework, and extend it to use depth measurements from a commodity RGB-D sensor, such as a Kinect. In addition, we propose a pose and camera refinement technique which improves the overall reconstruction quality. In contrast to concurrent work on integrating depth priors in NeRF which concentrates on novel view synthesis, our approach is able to reconstruct high-quality, metrical 3D reconstructions.
Magnetic Resonance Imaging (MRI) is an important medical imaging modality, while it requires a long acquisition time. To reduce the acquisition time, various methods have been proposed. However, these methods failed to reconstruct images with a clear structure for two main reasons. Firstly, similar patches widely exist in MR images, while most previous deep learning-based methods ignore this property and only adopt CNN to learn local information. Secondly, the existing methods only use clear images to constrain the upper bound of the solution space, while the lower bound is not constrained, so that a better parameter of the network cannot be obtained. To address these problems, we propose a Contrastive Learning for Local and Global Learning MRI Reconstruction Network (CLGNet). Specifically, according to the Fourier theory, each value in the Fourier domain is calculated from all the values in Spatial domain. Therefore, we propose a Spatial and Fourier Layer (SFL) to simultaneously learn the local and global information in Spatial and Fourier domains. Moreover, compared with self-attention and transformer, the SFL has a stronger learning ability and can achieve better performance in less time. Based on the SFL, we design a Spatial and Fourier Residual block as the main component of our model. Meanwhile, to constrain the lower bound and upper bound of the solution space, we introduce contrastive learning, which can pull the result closer to the clear image and push the result further away from the undersampled image. Extensive experimental results on different datasets and acceleration rates demonstrate that the proposed CLGNet achieves new state-of-the-art results.
This paper describes the design and control of a support and recovery system for use with planar legged robots. The system operates in three modes. First, it can be operated in a fully transparent mode where no forces are applied to the robot. In this mode, the system follows the robot closely to be able to quickly catch the robot if needed. Second, it can provide a vertical supportive force to assist a robot during operation. Third, it can catch the robot and pull it away from the ground after a failure to avoid falls and the associated damages. In this mode, the system automatically resets the robot after a trial allowing for multiple consecutive trials to be run without manual intervention. The supportive forces are applied to the robot through an actuated cable and pulley system that uses series elastic actuation with a unidirectional spring to enable truly transparent operation. The nonlinear nature of this system necessitates careful design of controllers to ensure predictable, safe behaviors. In this paper we introduce the mechatronic design of the recovery system, develop suitable controllers, and evaluate the system's performance on the bipedal robot RAMone.
With the advent of deep neural networks, learning-based approaches for 3D reconstruction have gained popularity. However, unlike for images, in 3D there is no canonical representation which is both computationally and memory efficient yet allows for representing high-resolution geometry of arbitrary topology. Many of the state-of-the-art learning-based 3D reconstruction approaches can hence only represent very coarse 3D geometry or are limited to a restricted domain. In this paper, we propose occupancy networks, a new representation for learning-based 3D reconstruction methods. Occupancy networks implicitly represent the 3D surface as the continuous decision boundary of a deep neural network classifier. In contrast to existing approaches, our representation encodes a description of the 3D output at infinite resolution without excessive memory footprint. We validate that our representation can efficiently encode 3D structure and can be inferred from various kinds of input. Our experiments demonstrate competitive results, both qualitatively and quantitatively, for the challenging tasks of 3D reconstruction from single images, noisy point clouds and coarse discrete voxel grids. We believe that occupancy networks will become a useful tool in a wide variety of learning-based 3D tasks.
The Normalized Cut (NCut) objective function, widely used in data clustering and image segmentation, quantifies the cost of graph partitioning in a way that biases clusters or segments that are balanced towards having lower values than unbalanced partitionings. However, this bias is so strong that it avoids any singleton partitions, even when vertices are very weakly connected to the rest of the graph. Motivated by the B\"uhler-Hein family of balanced cut costs, we propose the family of Compassionately Conservative Balanced (CCB) Cut costs, which are indexed by a parameter that can be used to strike a compromise between the desire to avoid too many singleton partitions and the notion that all partitions should be balanced. We show that CCB-Cut minimization can be relaxed into an orthogonally constrained $\ell_{\tau}$-minimization problem that coincides with the problem of computing Piecewise Flat Embeddings (PFE) for one particular index value, and we present an algorithm for solving the relaxed problem by iteratively minimizing a sequence of reweighted Rayleigh quotients (IRRQ). Using images from the BSDS500 database, we show that image segmentation based on CCB-Cut minimization provides better accuracy with respect to ground truth and greater variability in region size than NCut-based image segmentation.
Limited capture range, and the requirement to provide high quality initialization for optimization-based 2D/3D image registration methods, can significantly degrade the performance of 3D image reconstruction and motion compensation pipelines. Challenging clinical imaging scenarios, which contain significant subject motion such as fetal in-utero imaging, complicate the 3D image and volume reconstruction process. In this paper we present a learning based image registration method capable of predicting 3D rigid transformations of arbitrarily oriented 2D image slices, with respect to a learned canonical atlas co-ordinate system. Only image slice intensity information is used to perform registration and canonical alignment, no spatial transform initialization is required. To find image transformations we utilize a Convolutional Neural Network (CNN) architecture to learn the regression function capable of mapping 2D image slices to a 3D canonical atlas space. We extensively evaluate the effectiveness of our approach quantitatively on simulated Magnetic Resonance Imaging (MRI), fetal brain imagery with synthetic motion and further demonstrate qualitative results on real fetal MRI data where our method is integrated into a full reconstruction and motion compensation pipeline. Our learning based registration achieves an average spatial prediction error of 7 mm on simulated data and produces qualitatively improved reconstructions for heavily moving fetuses with gestational ages of approximately 20 weeks. Our model provides a general and computationally efficient solution to the 2D/3D registration initialization problem and is suitable for real-time scenarios.
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