Related papers: SineNet: Learning Temporal Dynamics in Time-Depend…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Deep learning has made significant progress in computer vision, specifically in image classification, object detection, and semantic segmentation. The skip connection has played an essential role in the architecture of deep neural…
In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…
Skip connections are increasingly utilized by deep neural networks to improve accuracy and cost-efficiency. In particular, the recent DenseNet is efficient in computation and parameters, and achieves state-of-the-art predictions by directly…
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…
Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…
This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…
Improving the quality of underwater images is essential for advancing marine research and technology. This work introduces a sparsity-driven interpretable neural network (SINET) for the underwater image enhancement (UIE) task. Unlike pure…
Deep neural networks (DNNs) provide high image classification accuracy, but experience significant performance degradation when perturbation from various sources are present in the input. The lack of resilience to input perturbations makes…
Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…
The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…
DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…
In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…
Recent years have seen a surge in research on dynamic graph representation learning, which aims to model temporal graphs that are dynamic and evolving constantly over time. However, current work typically models graph dynamics with…
The objective of this paper is 3D shape understanding from single and multiple images. To this end, we introduce a new deep-learning architecture and loss function, SilNet, that can handle multiple views in an order-agnostic manner. The…
U-Net has been providing state-of-the-art performance in many medical image segmentation problems. Many modifications have been proposed for U-Net, such as attention U-Net, recurrent residual convolutional U-Net (R2-UNet), and U-Net with…
Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical…
The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…
In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…
High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…