Related papers: An Operator Learning Framework for Spatiotemporal …

Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise. Numerical simulations present an…

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…

Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…

Although remarkable progress has been made on single image super-resolution due to the revival of deep convolutional neural networks, deep learning methods are confronted with the challenges of computation and memory consumption in…

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Semi-supervised semantic segmentation aims to learn from a small amount of labeled data and plenty of unlabeled ones for the segmentation task. The most common approach is to generate pseudo-labels for unlabeled images to augment the…

While depth sensors are becoming increasingly popular, their spatial resolution often remains limited. Depth super-resolution therefore emerged as a solution to this problem. Despite much progress, state-of-the-art techniques suffer from…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…

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…

Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to…

Convolutional neural networks (CNNs) depend on deep network architectures to extract accurate information for image super-resolution. However, obtained information of these CNNs cannot completely express predicted high-quality images for…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…