Although geometric reconstruction of general objects from images has made remarkable progress in recent years, slender structures remain largely underexplored, despite their critical importance in engineering, biomedical, and agricultural applications. To bridge this gap, we propose a dedicated 2DGS-based geometric reconstruction framework tailored for slender structures, achieving accurate and faithful geometry recovery. Our method first addresses the challenge that most slender objects are texture-less, which hinders reliable feature matching and pose estimation in traditional SfM pipelines. By leveraging the curve-like nature of slender structures, we perform a curve-guided SfM process that provides robust camera poses and accurate 3D curve initialization for Gaussian primitives. To ensure SfM reliability, we introduce a high-precision mask extraction strategy that integrates geometric priors with a segmentation network, effectively handling self-occlusion and thin geometry. Furthermore, to enhance fine geometric recovery, we incorporate a differentiable Poisson reconstruction module to extract an initial mesh during training, which is then refined via image-space iterative optimization using differentiable mesh rasterization. In contrast to conventional approaches that rely on differentiable Gaussian rasterization followed by TSDF-based mesh extraction, our method avoids the additional geometric errors and artifacts introduced during the intermediate TSDF conversion, thereby improving the overall reconstruction quality. Comprehensive experiments on both synthetic and real-world datasets validate that our method achieves superior reconstruction quality compared to state-of-the-art approaches.

The existing constrained multiobjective evolutionary algorithms (CMOEAs) still have great room for improvement in balancing populations convergence, diversity and feasibility on complex constrained multiobjective optimization problems (CMOPs). Besides, their effectiveness deteriorates dramatically when facing the CMOPs with scaling-up objective space or search space. We are thus motivated to design a learning-aided CMOEA with promising problem-solving ability and scalability for various CMOPs. In the proposed solver, two learning models are respectively trained online on constrained-ignored task and feasibility-first task, which are then used to learn the two improvement-based vectors for enhancing the search by differential evolution. In addition, the union population of parent and child solutions is divided into multiple subsets with a hierarchical clustering based on cosine similarity. A comprehensive indicator, considering objective-based performance and constraint violation degree of a solution, is developed to select the representative solution from each cluster. The effectiveness of the proposed optimizer is verified by solving the CMOPs with various irregular Pareto fronts, the number of objectives ranging from 2 to 15, and the dimensionality of search space scaling up to 1000.

Replicability, the ability to replicate scientific findings, is a prerequisite for scientific discovery and clinical utility. Troublingly, we are in the midst of a replicability crisis. A key to replicability is that multiple measurements of the same item (e.g., experimental sample or clinical participant) under fixed experimental constraints are relatively similar to one another. Thus, statistics that quantify the relative contributions of accidental deviations-such as measurement error-as compared to systematic deviations-such as individual differences-are critical. We demonstrate that existing replicability statistics, such as intra-class correlation coefficient and fingerprinting, fail to adequately differentiate between accidental and systematic deviations in very simple settings. We therefore propose a novel statistic, discriminability, which quantifies the degree to which an individual's samples are relatively similar to one another, without restricting the data to be univariate, Gaussian, or even Euclidean. Using this statistic, we introduce the possibility of optimizing experimental design via increasing discriminability and prove that optimizing discriminability improves performance bounds in subsequent inference tasks. In extensive simulated and real datasets (focusing on brain imaging and demonstrating on genomics), only optimizing data discriminability improves performance on all subsequent inference tasks for each dataset. We therefore suggest that designing experiments and analyses to optimize discriminability may be a crucial step in solving the replicability crisis, and more generally, mitigating accidental measurement error.

In this paper, we describe the algorithms implemented in MBEM, a program for wideband impedance extraction of complicated 3-D structures. MBEM is based on a mixed boundary element method (BEM), which reduces the number of unknowns from about 7N in FastImp to 4N, for MQS analysis. Efficient techniques are proposed to handle the extra matrix multiplication, form post-process matrices, and solve the final linear equation system. The inaccuracy of calculation using FastImp at low frequency is also analyzed, which shows the mixed BEM eliminates it completely. Experiments on several typical 3-D structures validate the advantage of MBEM over FastImp, on both accuracy and efficiency.

An efficient method is proposed to consider the process variations with spatial correlation, for chip-level capacitance extraction based on the window technique. In each window, an efficient technique of Hermite polynomial collocation (HPC) is presented to extract the statistical capacitance. The capacitance covariances between windows are then calculated to reflect the spatial correlation. The proposed method is practical for chip-level extraction task, and the experiments on full-path extraction exhibit its high accuracy and efficiency.

An efficient method based on a direct boundary element method is proposed for extracting frequency-dependent substrate coupling parameters. A frequency-independent real-valued linear equation system is first solved. Then, the solution is transformed into frequency-dependent parameters at a specified frequency with the Sherman-Morrison-Woodbury formula. The first step is performed only once for a given structure, and the method is very efficient for extraction with multiple frequencies. The proposed method is compared with the Green's function-based method and the approach in our earlier paper for typical substrate structures. Numerical results demonstrate its accuracy, efficiency, and versatility.

The couplings via realistic lossy substrates can be modeled as frequency-dependent coupling parameters. The fast extraction at multiple frequencies can be accomplished in two sequent steps. The first is to extract the coupling resistance using a direct boundary element method (DBEM). The second is to revise the resistance into the parameter at the frequency in an exact and rapid way. The first step is time-consuming, while it runs only one time; the second repeats at each frequency, but is much easier. For more frequency calculation, this method is more advanced. Numerical experiments illustrate that this method has high accuracy, and it can be hundreds of times faster than an advanced Green's function based method. Substrates with arbitrary doping profiles can also be easily handled, which is partly verified by experiment.

It is important to model substrate couplings for SoC/mixed-signal circuit designs. After introducing the continuation equation of full current in lossy substrates, we present a new direct boundary element method (DBEM), which can handle the substrates with arbitrary doping profiles. Three techniques can speed up the DBEM remarkably, which include reusing coefficient matrices for multiple-frequency calculation, condensing the linear system, and sparsifying coefficient matrix. Numerical experiments illustrate that DBEM has high accuracy and high efficiency, and is versatile for arbitrary doping profiles.

A complete multiple reciprocity method (CMRM), usually for the eigenvalue analysis of Helmholtz equation, is introduced to the BEM for frequency-dependent inductance extraction. Several approaches are proposed to resolve the problem of "ill-conditioned" series encountered when applying the CMRM practically. Using the BEM combined with CMRM, the major operations of calculating the numerical integrals for a frequency point become reusable, so that inductance extraction for a frequency range is greatly accelerated. Numerical results verify the accuracy and efficiency of the proposed method

As shown in literatures, partial reluctance based circuit analysis is efficient in capturing on-chip inductance effect, because the partial reluctance exhibits much better locality than partial inductance. However, most previous works on reluctance extraction did not take high frequency effect into account and were not efficient enough for 3D complex structure. In this paper, a new reluctance extraction algorithm is proposed considering the high frequency effect. Numerical experiments demonstrate that our algorithm can handle complex 3D interconnect structures while exhibiting high accuracy and a speed-up ratio of several tens to hundreds over FastHenry.

It is important to model the substrate coupling for mixed-signal or RF circuit designs. In this paper, a direct boundary element method (DBEM) and related efficient techniques are presented to calculate the coupling resistances for three-dimensional substrate structure. First, a nonuniform meshing scheme is presented to reduce boundary elements while preserving accuracy. Then, the unknowns on top medium surface are removed from the discretized linear system of DBEM with a matrix reduction technique. The third technique is applying the quasi-multiple medium idea (W. Yu, Z. Wang, and J. Gu, "Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM," IEEE Trans. Microwave Theory Tech., vol. 51, no. 1, pp. 109-199, Jan. 2003), which greatly reduces the expense of matrix reduction and makes the final coefficient matrix much sparser. With these proposed techniques, the linear equation system is largely condensed and sparsified and then solved with a preconditioned generalized minimum residual solver for multiple right-hand sides to get the whole resistance matrix. Numerical experiments on typical substrates with various doping profiles show the high accuracy of the DBEM-based method. The authors also compared the DBEM method with the Green's function methods accelerated by discrete cosine transform or eigendecomposition techniques. The results show that the DBEM-based method is several times or tens of times faster than the other two. At the same time, the DBEM method has no difficulty in handling substrates with more complex than stratified doping profiles, which is a large advantage over the existing methods

Inserting dummy (area fill) metals is necessary to reduce the pattern-dependent variation of dielectric thickness in the chemical-mechanical polishing (CMP) process. Such floating dummy metals affect interconnect capacitance and, therefore, signal delay and crosstalk significantly. To take the floating dummies into account, an efficient method for three-dimensional (3-D) capacitance extraction based on boundary element method is proposed. By introducing a floating condition into the direct boundary integral equation (BIE) and adopting an efficient preconditioning technique, and the quasi-multiple medium (QMM) acceleration, the method achieves very high computational speed. For some typical structures of area fill, the presented algorithm has shown over 1000/spl times/ speedup over the industry-standard Raphael while preserving high accuracy. Compared with the recently proposed PASCAL in the work of Park et al. (2000), the proposed method also has about ten times speedup. Since the dummies are not regarded as normal electrodes in capacitance extraction, the proposed method is much more efficient than the conventional method, especially in cases with a large number of floating dummies.

It is important to model the substrate coupling for mixed-signal circuit designs today. This paper presents the direct boundary element method (BEM) for substrate resistance calculation, where only the boundary of substrate region is discretized. Firstly, an efficient scheme for non-uniform element partition is proposed. Secondly, a new technique is presented which can reduce the scale of produced linear system and then accelerate the equation solving, especially for the multiple right-hand sides problem like substrate resistance extraction. Experiments show that the proposed method has shown high efficiency compared with existing methods while preserving high accuracy.

It is important to model the substrate coupling for mixed-signal circuit designs today. This paper presents an improved direct boundary element method (DBEM) for substrate resistance calculation, where only the boundary of substrate volumes is discretized and only the free-space Green function is used. At first, we discard some inessential unknowns to compress the linear system without accuracy loss. Then we make the coefficient matrix sparser. In this way, solving the linear system is greatly accelerated. Experiments on various substrates validate that DBEM is several to tens of times faster than DCT-accelerated Green's function methods and the eigendecomposition method, while preserving high accuracy. Besides, another experiment shows that this method is versatile for irregular substrates.

Fast and accurate interconnect parasitic parameter extraction has become increasingly critical for verification and analysis in VLSI today. In this paper, a fast hierarchical extraction approach based on Boundary Element Method (BEM) is presented for 3-D parasitic capacitance computation. Hierarchical partition of the 3-D field creates many parts which are called 3-D BEM blocks. After combining all the 3-D BEM blocks, the capacitance matrix for a given set of nets can be computed by applying the boundary conditions. Numerical results shows that this method performs many times faster than the 3-D field solver, with equal accuracy.

The computational time and memory of three-dimensional (3-D) capacitance extraction have been greatly reduced by using a quasimultiple medium (QMM) technology, because it enlarges the matrix sparsity produced by the direct boundary element method (BEM). An approach to automatically determining the QMM cutting pair number and a preconditioning technique are proposed to enhance the QMM-based capacitance extraction. With these two enhancements, the capacitance extraction can achieve much higher speed and adaptability. Experimental results show over 10X speed-up and memory saving over the multipole approach with comparable accuracy.

The high frequency resistance and inductance of the 3-D complex interconnect structures can be calculated by solving an eddy current electromagnetic problem. In this paper, a model for charactering such a 3-D eddy current problem is proposed, in which the electromagnetic fields in both the conducting and non-conducting regions are described in terms of the magnetic vector potential, and a set of the indirect boundary integral equations (IBIE) is obtained. The IBIEs can be solved by boundary element method, so this method avoids discretizing the domain of the conductors. As an indirect boundary element method, it is of minimum order. It does not restrict the direction of the current in conductors, and hence it can consider the mutual impedance between two perpendicular conductors. The numerical results can well meet the analytical solution of a 2-D problem. The mutual impedance of two perpendicular conductors is also shown under the different gaps between conductors and different frequencies.

A virtual 3-D extractor of the single dielectric is presented in this paper. In the indirect boundary integral equations, the plane charge distribution on the surface of conductors is replaced with mesh charge distribution, and we use the multipole-accelerated algorithm to further depress the computational complexity. Numerical results show that its computational complexity is about O(n), where n is the number of the discrete variables. Within the comparable accuracy, it runs several times faster than the Fastcap, which is a very advanced multipole-accelerated parasitic capacitance extractor now.

In this paper, the quasi-multiple medium (QMM) method based on the direct boundary element method (BEM) is used to extract the capacitance of three-dimensional (3-D) VLSI interconnects with multiple dielectrics. Each dielectric in 3-D VLSI parasitic capacitor is cut into several fictitious mediums, so it produces much fewer non-zero entries to the total coefficients matrix. As a result, the QMM algorithm can greatly reduce the CPU time and memory space used in the capacitance extraction. To characterize the efficiency of QMM algorithm, we discuss accuracy, storage and timing statistics in comparison with the analogous information from non-QMM algorithm.

Abstract This paper describes a simplified hybrid method to calculate the frequency-dependent inductances of transmission lines, which combines cross-section coupled circuit method with boundary element method (BEM) just solving Laplace’s equation. The coupled circuit method is used to calculate inductance in low frequency range; The BEM builds the capacitance matrix, then we invert this matrix (omit the row and column relate to ground plane), we can obtain inductance relating to the high frequency at which the current only distributes on surfaces of conductor. A cubic spline interpolation between inductance at low and very high frequency gives a good result over entire frequency range. Comparing this method with previous hybrid method [3], it avoids solving Helmholtz’s equation and obtains the capacitance matrix at the same time, greatly reducing the total burden of calculation. Numerical tests show it is applicable and efficient. I.

%&''&()**& +,$ %&''&() -'$ ., /012"" " "

In deep submicron VLSI circuits, the interconnect parasitic capacitance is a very important factor determining circuit performances such as power and time-delay. The Boundary Element Method (BEM) is an effective tool for solving Laplacian's equation applied in the parasitic capacitance extraction. In this paper, a hierarchical h-adaptive BEM is presented. It constructs a 3-D linear hierarchical shape function based on a constant boundary element and uses previous computations and solutions. Hence, it reduces computation significantly in the adaptive procedure. Besides, a combination of a residual-type estimator and reduced Z-Z error estimator for more reliable and efficient estimation of error is presented. Some numerical results show that this method is effective.

Because of the widespread application of deep sub-micron and multilayer routing techniques, the interconnection parasitic influence has more and more effect on the performance of VLSI circuits. Parallel direct boundary element calculation of three-dimensional (3-D) resistance and capacitance is an important method for fast extraction. In this paper, a parallel algorithm to implement linear boundary element calculation using PVM (Parallel Virtual Machine, distributed calculating software) is introduced. The hierarchical calculation scheme of the setup and solution processes of linear equations is discussed. At the end, the performance and workload balance of the algorithm are analyzed.

This paper gives an improved single-layer potential formula for extracting the parasitic capacitance of multiple conductors, embedded in the infinite or finite dielectrics, based on the MultiPole Accelerated (MPA) method. In fact, many capacitors should be considered to be bounded by a finite region. This indicates that the improvement is necessary to raise extraction accuracy. The nonuniform cube subdivision is used in the simulator. The reason for this is that it is an important base of further implementing the real adaptive calculation, for example h-version of the MPA. Also, it can save a lot of memory for ignoring most empty cubes. Only two lists of the cubes are used, thus simplifying the classification of five cube types. The simplified cell classification scheme eases book keeping in the parallel implementation. In developing a parallel MPA algorithm on the transputer network, a parallel machine of the MIMD type, we pay great attention to balancing workload and reducing communication for general nonuniform distribution of the particles. The results show that the total balance can be well achieved by balancing workload in every level of cubes. The pipeline communication mode shows higher efficiency if the processor number P used can well match problem size.

A resistance simulator for extraction of the parasitic parameters from VLSI layout is presented. The calculation of the resistor network is based on the boundary element method (BEM). The computational results indicate that the BEM has an advantage over the finite difference method (FDM) and the finite element method (FEM). Since only discretized equations on the boundary of solved domain need to be solved, the grid number on the boundary is much smaller and mesh generation is greatly simplified. Hence the execution CPU time is reduced drastically. In order to treat the corners on the boundary, the concept of multiple normal derivatives at a corner is proposed. The concept is used in both continuous and partially discontinuous linear elements to increase the accuracy and reduce the number of unknowns. It is shown that a nonuniform mesh scheme is useful for problems with some stronger singularities.>