相关论文: A DeepONet joint Neural Tangent Kernel Hybrid Fram…

BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs). Traditional PINNs, which typically…

DeepONet enables retraining-free inference across varying initial conditions or source terms at the cost of high computational requirements. This paper proposes a hybrid quantum operator network (Quantum AS-DeepOnet) suitable for solving 2D…

Despite their immense promise in performing a variety of learning tasks, a theoretical understanding of the limitations of Deep Neural Networks (DNNs) has so far eluded practitioners. This is partly due to the inability to determine the…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Image downscaling is a fundamental operation in image processing, crucial for adapting high-resolution content to various display and storage constraints. While classic methods often introduce blurring or aliasing, recent learning-based…

How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its width --- namely, number of channels in convolutional layers, and number of nodes in fully-connected internal…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Large machine learning models based on Convolutional Neural Networks (CNNs) with rapidly increasing number of parameters, trained with massive amounts of data, are being deployed in a wide array of computer vision tasks from self-driving…

Object detection in aerial images is a fundamental research topic in the geoscience and remote sensing domain. However, the advanced approaches on this topic mainly focus on designing the elaborate backbones or head networks but ignore neck…

Deep Learning (DL) has shown remarkable results in solving inverse problems in various domains. In particular, the Tikhonet approach is very powerful to deconvolve optical astronomical images (Sureau et al. 2020). Yet, this approach only…

This work bridges two important concepts: the Neural Tangent Kernel (NTK), which captures the evolution of deep neural networks (DNNs) during training, and the Neural Collapse (NC) phenomenon, which refers to the emergence of symmetry and…

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

We propose a novel decoding approach for neural machine translation (NMT) based on continuous optimisation. We convert decoding - basically a discrete optimization problem - into a continuous optimization problem. The resulting constrained…

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…

Current Deep Learning approaches have been very successful using convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers. Three limitations of this approach are: 1) they are based on a simple…

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…

This paper addresses the limitations of Physics-Informed Neural Networks for time-dependent problems by introducing a tangent bundle learning framework. Instead of directly approximating the solution, we parameterize its temporal derivative…

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Little is known about the training dynamics of equivariant neural networks, in particular how it compares to data augmented training of their non-equivariant counterparts. Recently, neural tangent kernels (NTKs) have emerged as a powerful…

Downward continuation is a critical task in potential field processing, including gravity and magnetic fields, which aims to transfer data from one observation surface to another that is closer to the source of the field. Its effectiveness…