Related papers: U-NO: U-shaped Neural Operators
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
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…
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…
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…
Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…
In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value…
Fast and accurate predictions of turbulent flows are of great importance in the science and engineering field. In this paper, we investigate the implicit U-Net enhanced Fourier neural operator (IUFNO) in the stable prediction of long-time…
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,…
Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In…
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…
Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…
Ensemble simulations of high-dimensional flow models (e.g., Navier Stokes type PDEs) are computationally prohibitive for real time applications. Neural operators enable fast inference but are limited by costly data requirements and poor…
Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…
Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…
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 paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…
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…
Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…
Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled…
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of…