Related papers: Efficient Compilation of a Class of Variational Fo…

The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…

Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected…

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$. This algorithm reduces the computational complexity of state-of-the-art tensor…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…

Laminated composite materials are widely used in most fields of engineering. Wave propagation analysis plays an essential role in understanding the short-duration transient response of composite structures. The forward physics-based models…

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…

Finite element methods require the composition of the global stiffness matrix from local finite element contributions. The composition process combines the computation of element stiffness matrices and their assembly into the global…

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…

The concept of effective resistance, originally introduced in electrical circuit theory, has been extended to the setting of graphs by interpreting each edge as a resistor. In this context, the effective resistance between two vertices…

As deep learning inference is increasingly deployed in shared and cloud-based settings, a growing concern is input repurposing, in which data submitted for one task is reused by unauthorized models for another. Existing privacy defenses…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

Recurrent neural networks have a strong inductive bias towards learning temporally compressed representations, as the entire history of a sequence is represented by a single vector. By contrast, Transformers have little inductive bias…

We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least $2$ associated with representations whose kernel is a congruence…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Learning representations for graph-structured data is essential for graph analytical tasks. While remarkable progress has been made on static graphs, researches on temporal graphs are still in its beginning stage. The bottleneck of the…

Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a…

Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to…