相关论文: A Prefixed Patch Time Series Transformer for Two-P…

Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…

In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of…

This work presents a robust Model Predictive Controller (MPC) to solve the problem of spacecraft rendezvous in the context of the restricted three-body problem (R3BP) as will be required to dock with space stations in cislunar space. The…

This article presents an alternative approach to finite elements for modeling and analyzing 3D static mooring lines using string theory and the shooting method (SM) to solve two-point boundary value problems (TPBVPs) for 3D nonlinear static…

This contribution focuses on the design of low-energy transfers between planetary moons and presents an efficient technique to compute trajectories characterized by desirable behaviors in the vicinities of the departure and destination…

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have…

In this paper, a new block preconditioner is proposed for the saddle point problem arising from the Neumann boundary control problem. In order to deal with the singularity of the stiffness matrix, the saddle point problem is first extended…

Medical image segmentation is a vital healthcare endeavor requiring precise and efficient models for appropriate diagnosis and treatment. Vision transformer (ViT)-based segmentation models have shown great performance in accomplishing this…

A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial…

In the context of increasing demands for long-term multi-energy load forecasting in real-world applications, this paper introduces Patchformer, a novel model that integrates patch embedding with encoder-decoder Transformer-based…

Transformer models have redefined sequence learning, yet dot-product self-attention introduces a quadratic token-mixing bottleneck for long-context time-series. We introduce the \textbf{Phasor Transformer} block, a phase-native alternative…

In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order…

This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems common in nonlinear partial differential equations (PDEs).…

Irregularly sampled time series data with missing values is observed in many fields like healthcare, astronomy, and climate science. Interpolation of these types of time series is crucial for tasks such as root cause analysis and medical…

In this study, we present a simulation-based numerical method for solving a class of singularly perturbed second-order differential equations that come from a simplified biologically motivated model of human gait. Important physical factors…

Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…

Although the Transformer has been the dominant architecture for time series forecasting tasks in recent years, a fundamental challenge remains: the permutation-invariant self-attention mechanism within Transformers leads to a loss of…

The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…