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

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…

We introduce the Equilibrated Averaging Residual Method (EARM), a unified equilibrated flux-recovery framework for elliptic interface problems that applies to a broad class of finite element discretizations. The method is applicable in both…

In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…

We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…

The emergence of foundation models has substantially advanced zero-shot generalization in monocular depth estimation (MDE), as exemplified by the Depth Anything series. However, given access to some data from downstream tasks, a natural…

The semiparametric accelerated failure time (AFT) model offers a direct and interpretable alternative to the Cox proportional hazards model, yet practical diagnostic tools for this framework remain limited. We introduce afttest, an R…

This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations within a fully differentiable Machine Learning framework. The proposed formulation provides a unified and user-friendly…

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…

Clinical 12-lead ECG classification remains difficult because of diverse recording conditions, overlapping pathologies, and pronounced label imbalance hinder generalization, while unconstrained augmentations risk distorting diagnostically…

The partial domain adaptation (PDA) challenge is a prevalent issue in industrial fault diagnosis. Drawing inspiration from traditional classification settings where such partial challenge is not a concern, we propose a novel PDA framework…

We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where…

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

This work proposes a robust Partial Domain Adaptation (PDA) framework that mitigates the negative transfer problem by incorporating a robust target-supervision strategy. It leverages ensemble learning and includes diverse, complementary…

Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…

I provide a pedagogic review of adaptive mesh refinement (AMR) radiation hydrodynamics (RHD) methods and codes used in simulations of star formation, at a level suitable for researchers who are not computational experts. I begin with a…

We develop reinforcement learning (RL) boundary controllers to mitigate stop-and-go traffic congestion on a freeway segment. The traffic dynamics of the freeway segment are governed by a macroscopic Aw-Rascle-Zhang (ARZ) model, consisting…

Restoration in power distribution systems (PDSs) is well studied, however, most existing research focuses on network partition and microgrid formation, where load transfer is limited to adjacent feeders. This focus is not practical, as when…

We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed…

We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…