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Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
Achieving high-quality High Dynamic Range (HDR) imaging on resource-constrained edge devices is a critical challenge in computer vision, as its performance directly impacts downstream tasks such as intelligent surveillance and autonomous…
Transformer-based methods have achieved impressive results in time series forecasting. However, existing Transformers still exhibit limitations in sequence modeling as they tend to overemphasize temporal dependencies. This incurs additional…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
We address the channel estimation (CE) problem in reconfigurable intelligent surface (RIS) aided orthogonal frequency-division multiplexing (OFDM) systems by proposing a dual-structure and multi-dimensional transformations (DS-MDT)…
Parameter-efficient fine-tuning (PEFT) has emerged as an effective method for adapting pre-trained language models to various tasks efficiently. Recently, there has been a growing interest in transferring knowledge from one or multiple…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
Multimodal machine translation (MMT) aims to improve translation quality by incorporating information from other modalities, such as vision. Previous MMT systems mainly focus on better access and use of visual information and tend to…
Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge. Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while…
In recent years, multimodal learning has become essential in robotic vision and information fusion, especially for understanding human behavior in complex environments. However, current methods struggle to fully leverage the textual…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…