相关论文: ARC-STAR: Auditable Post-Hoc Correction for PDE Fo…

We present a novel methodology for designing output-feedback backstepping boundary controllers for an unstable 1-D diffusion-reaction partial differential equation with spatially-varying reaction. Using "folding" transforms the parabolic…

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…

Generating calibrated and sharp neural network predictive distributions for regression problems is essential for optimal decision-making in many real-world applications. To address the miscalibration issue of neural networks, various…

Adverse weather removal (AWR) in real-world images remains challenging due to heterogeneous and unseen degradations, while distortion-driven training often yields overly smooth results. We propose PVRF, a unified framework that integrates…

This paper introduces a novel framework for physics-aware sparse signal recovery in measurement systems governed by partial differential equations (PDEs). Unlike conventional compressed sensing approaches that treat measurement systems as…

The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties,…

Attention-based models have revolutionized AI, but the quadratic cost of self-attention incurs severe computational and memory overhead. Sparse attention methods alleviate this by skipping low-relevance token pairs. However, current…

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…

We consider a smoothed online convex optimization (SOCO) problem with predictions, where the learner has access to a finite lookahead window of time-varying stage costs, but suffers a switching cost for changing its actions at each stage.…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

We consider a linear elliptic partial differential equation (PDE) with a generic uniformly bounded parametric coefficient. The solution to this PDE problem is approximated in the framework of stochastic Galerkin finite element methods. We…

Large language models frequently commit unrecoverable reasoning errors mid-generation: once a wrong step is taken, subsequent tokens compound the mistake rather than correct it. We introduce $\textbf{Latent Phase-Shift Rollback}$ (LPSR): at…

Due to the difficulty in obtaining real samples and ground truth, the generalization performance and domain adaptation performance are critical for the feasibility of stereo matching methods in practical applications. However, there are…

Fluid-Structure Interaction (FSI) is a crucial problem in ocean engineering. The smoothed particle hydrodynamics (SPH) method has been employed recently for FSI problems in light of its Lagrangian nature and its advantage in handling…

In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…

Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a…

Satellite radar altimetry is one of the most powerful techniques for measuring sea surface height variations, with applications ranging from operational oceanography to climate research. Over open oceans, altimeter return waveforms…

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

Diffusion models have achieved remarkable success in generative tasks but suffer from high computational costs due to their iterative sampling process and quadratic attention costs. Existing training-free acceleration strategies that reduce…

There is often a trade-off between performance and latency in streaming automatic speech recognition (ASR). Traditional methods such as look-ahead and chunk-based methods, usually require information from future frames to advance…