Related papers: Equivariant U-Shaped Neural Operators for the Cahn…

Neural operators for time-dependent PDEs face a structural tension: spectral architectures (FNO and descendants) inherit exponential rollout-error growth from their one-step Lipschitz constant, while hierarchical U-Net operators trade…

This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…

We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of…

Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…

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…

Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous…

Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…

Neural network force fields have significantly advanced ab initio atomistic simulations across diverse fields. However, their application in the realm of magnetic materials is still in its early stage due to challenges posed by the subtle…

Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…

Automated medical image segmentation plays a key role in quantitative research and diagnostics. Convolutional neural networks based on the U-Net architecture are the state-of-the-art. A key disadvantage is the hard-coding of the receptive…

Machine Learning with deep neural networks has transformed computational approaches to scientific and engineering problems. Central to many of these advancements are precisely tuned neural architectures that are tailored to the domains in…

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…

Medical image segmentation plays a crucial role in advancing healthcare systems for disease diagnosis and treatment planning. The u-shaped architecture, popularly known as U-Net, has proven highly successful for various medical image…

Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-resolution training data. In this paper, we break this…

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…

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…

The ability of convolutional neural networks (CNNs) to recognize objects regardless of their position in the image is due to the translation-equivariance of the convolutional operation. Group-equivariant CNNs transfer this equivariance to…

Predicting the evolution of complex systems governed by partial differential equations (PDEs) remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier Neural Operators (kFNO) and…