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Related papers: ARC-STAR: Auditable Post-Hoc Correction for PDE Fo…

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We present the Spatial Adapter, a parameter-efficient post-hoc layer that equips any frozen first-stage predictor with a structured spatial representation of its residual field and an induced closed-form spatial covariance. The adapter…

Machine Learning · Statistics 2026-05-13 Wen-Ting Wang , Wei-Ying Wu , Hao-Yun Huang , Xuan-Chun Wang

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…

Numerical Analysis · Mathematics 2022-10-14 Dmitrii Chaikovskii , Aleksei Liubavin , Ye Zhang

We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…

Numerical Analysis · Mathematics 2025-03-31 T. Chaumont-Frelet

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation…

Optimization and Control · Mathematics 2025-09-29 Kaijing Lyu , Junmin Wang , Yihuai Zhang , Huan Yu

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…

Machine Learning · Computer Science 2026-03-03 Siming Shan , Min Zhu , Youzuo Lin , Lu Lu

Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the inherent complexity and diversity, such as long…

Machine Learning · Computer Science 2024-05-08 Zhongkai Hao , Chang Su , Songming Liu , Julius Berner , Chengyang Ying , Hang Su , Anima Anandkumar , Jian Song , Jun Zhu

Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…

Machine Learning · Computer Science 2025-09-29 Juan Diego Toscano , Daniel T. Chen , Vivek Oommen , Jérôme Darbon , George Em Karniadakis

Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.…

Machine Learning · Computer Science 2025-12-23 Rajyasri Roy , Dibyajyoti Nayak , Somdatta Goswami

In this paper, we present a dynamically reconfigurable hardware accelerator called FADES (Fused Architecture for DEnse and Sparse matrices). The FADES design offers multiple configuration options that trade off parallelism and complexity…

Hardware Architecture · Computer Science 2023-04-18 Jose Nunez-Yanez , Andres Otero , Eduardo de la Torre

Remote sensing image (RSI) denoising is an important topic in the field of remote sensing. Despite the impressive denoising performance of RSI denoising methods, most current deep learning-based approaches function as black boxes and lack…

Computer Vision and Pattern Recognition · Computer Science 2025-06-02 Jingjing Liu , Jiashun Jin , Xianchao Xiu , Jianhua Zhang , Wanquan Liu

In this paper, Decentralized Periodic Approach for Adaptive Fault Diagnosis (DP-AFD) algorithm is proposed for fault diagnosis in distributed systems with arbitrary topology. Faulty nodes may be either unresponsive, may have either software…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-12-20 Latika Sarna , Sumedha Shenolikar , Poorva Kulkarni , Varsha Deshpande , Supriya Kelkar

Evaluating policies using off-policy data is crucial for applying reinforcement learning to real-world problems such as healthcare and autonomous driving. Previous methods for off-policy evaluation (OPE) generally suffer from high variance…

Machine Learning · Computer Science 2024-10-04 Shreyas Chaudhari , Ameet Deshpande , Bruno Castro da Silva , Philip S. Thomas

Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long…

Computational Engineering, Finance, and Science · Computer Science 2026-04-14 Mario Lino , Nils Thuerey

Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced order model (ROM) that is comparable to the cost of the original full order model (FOM). To address this,…

Numerical Analysis · Mathematics 2024-12-04 Lijie Ji , Zhichao Peng , Yanlai Chen

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

Machine Learning · Statistics 2026-05-26 Xifeng Zhang , Jin Zhao

We propose an unsupervised adaptation framework, Self-TAught Recognizer (STAR), which leverages unlabeled data to enhance the robustness of automatic speech recognition (ASR) systems in diverse target domains, such as noise and accents.…

Computation and Language · Computer Science 2024-05-24 Yuchen Hu , Chen Chen , Chao-Han Huck Yang , Chengwei Qin , Pin-Yu Chen , Eng Siong Chng , Chao Zhang

Sparse recovery Space-time Adaptive Processing (STAP) can reduce the requirements of clutter samples, and suppress clutter effectively using limited training samples for airborne radar. The whole angle-Doppler plane is discretized into…

Signal Processing · Electrical Eng. & Systems 2020-04-10 Tao Zhang , Hai Li , Yongsheng Hu , Ran Lai , Juncheng Guo

We investigate geometric regularization strategies for learned latent representations in encoder--decoder reduced-order models. In a fixed experimental setting for the advection--diffusion--reaction (ADR) equation, we model latent dynamics…

Machine Learning · Computer Science 2026-03-04 Mikhail Osipov

This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…

Numerical Analysis · Mathematics 2025-11-14 Yuwen Li