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Neural operators learn to map initial conditions to the terminal solution of partial differential equations (PDEs), providing a surrogate for the full operator mapping. This enables rapid prediction across different input configurations.…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation guarantees for DONs…
We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) architecture. For broad classes of Lipschitz multiple operator…
Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…
This work studies machine learning for electron density prediction, which is fundamental for understanding chemical systems and density functional theory (DFT) simulations. To this end, we introduce the Gaussian plane-wave neural operator…
This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…
Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…
Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…
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…
Density functional theory (DFT) is one of the primary approaches to get a solution to the many-body Schrodinger equation. The essential part of the DFT theory is the exchange-correlation (XC) functional, which can not be obtained in…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any…
Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…
Deep operator networks (DeepONets) are powerful architectures for fast and accurate emulation of complex dynamics. As their remarkable generalization capabilities are primarily enabled by their projection-based attribute, we investigate…
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…
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…