Related papers: A Resolution Independent Neural Operator

With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being…

In this paper, we consider the use of deep neural networks in the context of Multiple-Input-Multiple-Output (MIMO) detection. We give a brief introduction to deep learning and propose a modern neural network architecture suitable for this…

Despite the recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling complex physical systems remains under-explored. Learning…

Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire…

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

Particle-in-Cell (PIC) simulations are widely used for modeling plasma kinetics by tracking discrete particle dynamics. However, their computational cost remains prohibitively high, due to the need to simulate large numbers of particles to…

The use of Implicit Neural Representation (INR) through a hash-table has demonstrated impressive effectiveness and efficiency in characterizing intricate signals. However, current state-of-the-art methods exhibit insufficient…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

Recently, deep feedforward neural networks have achieved considerable success in modeling biological sensory processing, in terms of reproducing the input-output map of sensory neurons. However, such models raise profound questions about…

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

This paper introduces an incremental training framework for compressing popular Deep Neural Network (DNN) based unfolded multiple-input-multiple-output (MIMO) detection algorithms like DetNet. The idea of incremental training is explored to…

Purpose: Recently, several attempts were conducted to transfer deep learning to medical image reconstruction. An increasingly number of publications follow the concept of embedding the CT reconstruction as a known operator into a neural…

Spectral super-resolution (SSR) aims to reconstruct hyperspectral images (HSIs) from multispectral observations, with broad applications in computer vision and remote sensing. Deep learning-based methods have been widely used, but they…

FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…

Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different…

Adaptive inference is an effective mechanism to achieve a dynamic tradeoff between accuracy and computational cost in deep networks. Existing works mainly exploit architecture redundancy in network depth or width. In this paper, we focus on…