相关论文: Efficient and generalizable nested Fourier-DeepONe…
The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…
High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…
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…
Geological Carbon Sequestration (GCS) has emerged as a promising strategy for mitigating global warming, yet its effectiveness heavily depends on accurately characterizing subsurface flow dynamics. The inherent geological uncertainty,…
We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO…
Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations.…
Data assimilation (DA) is crucial for enhancing solutions to partial differential equations (PDEs), such as those in numerical weather prediction, by optimizing initial conditions using observational data. Variational DA methods are widely…
We formulate mold filling in metal casting as a 2D neural operator learning problem that maps geometry and boundary data on an unstructured mesh to time resolved flow quantities, replacing expensive transient CFD. In the proposed method, a…
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…
Reservoir simulations are computationally expensive in the well control and well placement optimization. Generally, numerous simulation runs (realizations) are needed in order to achieve the optimal well locations. In this paper, we propose…
Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…
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…
Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows…
Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically…
Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in…
Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…
Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…