Related papers: Deep neural operators can predict the real-time re…
Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods,…
This study presents an enhanced multi-fidelity Deep Operator Network (DeepONet) framework for efficient spatio-temporal flow field prediction when high-fidelity data is scarce. Key innovations include: a merge network replacing traditional…
Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling…
High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…
Critical evaluation and understanding of ship responses in the ocean is important for not only the design and engineering of future platforms but also the operation and safety of those that are currently deployed. Simulations or experiments…
Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as seismic imaging and inversion. High-contrast settings, such as…
This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…
In this paper, we propose a novel data-driven operator learning framework referred to as the \textit{Randomized Prior Wavelet Neural Operator} (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator,…
Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator…
Uncertainty and delayed reactions in human driving behavior lead to stop-and-go traffic congestion on freeways. The freeway traffic dynamics are governed by the Aw-Rascle-Zhang (ARZ) traffic Partial Differential Equation (PDE) models with…
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…
Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and…
Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…
This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…
The goal of this work is to investigate the capability of a neural operator (DeepONet) to accurately capture the complex deformation of a platelet's membrane under shear flow. The surrogate model approximated by the neural operator predicts…
Numerical simulations are essential tools to evaluate the solution of the wave equation in complex settings, such as three-dimensional (3D) domains with heterogeneous properties. However, their application is limited by high computational…
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…
Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and…
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,…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…