相关论文: A new reduction strategy for special negative sect…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
By introducing a new mechanism based on purely imaginary conjugate metamaterials (PICMs), we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PICMs, which is a breakthrough to the…
As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…
In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is…
In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics…
An improved PV-reduction method for one-loop integrals with auxiliary vector $R$ has been proposed in \cite{Feng:2021enk,Hu:2021nia}. It has also been shown that the new method is a self-completed method in \cite{Feng:2022uqp}. Analytic…
This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the…
The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set…
Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
Second-order methods have shown state-of-the-art performance for optimizing deep neural networks. Nonetheless, their large memory requirement and high computational complexity, compared to first-order methods, hinder their versatility in a…