相关论文: CoNO: Complex Neural Operator for Continuous Dynam…

Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both to accelerate…

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…

We introduce the Z-Domain Neural Operator (ZNO), a causal neural operator whose layers are stable low-rank multiple-input multiple-output (MIMO) rational filters parameterized directly in the $z$-plane. ZNO addresses a limitation of…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…

Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can…

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…

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…

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent…

Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead of full-field…

Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly learning maps between infinite-dimensional function spaces that…

Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial…

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage the advanced search algorithms for multiobjective optimization in DeepHyper, a scalable hyperparameter…

Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of the Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals…

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…