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Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…

The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline SAV method can keep a modified energy dissipation law but…

In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…

This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for solving a general problem, which involves a large body of nonconvex sparse and structured sparse related problems. Comparing with previous iterative solvers for…

We have introduced the generalized alternating direction implicit iteration (GADI) method for solving large sparse complex symmetric linear systems and proved its convergence properties. Additionally, some numerical results have…

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms…

Motivation: Modern biobanks, with unprecedented sample sizes and phenotypic diversity, have become foundational resources for genomic studies, enabling powerful cross-phenotype and population-scale analyses. As studies grow in complexity,…

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for…

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein…

Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration.…

Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…

We introduce Pawsterior, a variational flow-matching framework for improved and extended simulation-based inference (SBI). Many SBI problems involve posteriors constrained by structured domains, such as bounded physical parameters or hybrid…

Elliptic variational inequalities (EVIs) present significant challenges in numerical computation due to their inherent non-smoothness, nonlinearity, and inequality formulations. Traditional mesh-based methods often struggle with complex…

The scalar auxiliary variable (SAV) approach is a highly efficient method widely used for solving gradient flow systems. This approach offers several advantages, including linearity, unconditional energy stability, and ease of…

Safety performance evaluation is critical for developing and deploying connected and automated vehicles (CAVs). One prevailing way is to design testing scenarios using prior knowledge of CAVs, test CAVs in these scenarios, and then evaluate…

Two common methods for solving absolute value equations (AVE) are SOR-like iteration method and fixed point iteration (FPI) method. In this paper, novel convergence analysis, which result wider convergence range, of the SOR-like iteration…

Jackknife instrumental variable estimation (JIVE) is a classic method to leverage many weak instrumental variables (IVs) to estimate linear structural models, overcoming the bias of standard methods like two-stage least squares. In this…

In this paper, we consider the monotone generalized variational inequality (MGVI) where the monotone operator is Lipschitz continuous. Inspired by the extragradient method and the projection contraction algorithms for monotone variational…

We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…