相关论文: SIMR-NO: A Spectrally-Informed Multi-Resolution Ne…

Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation…

Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…

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…

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…

Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We…

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here we develop a two-stage super-resolution method using spectral filtering to restore the high-wavenumber…

Structured illumination microscopy (SIM) reconstructs a super-resolved image from multiple raw images captured with different illumination patterns; hence, acquisition speed is limited, making it unsuitable for dynamic scenes. We propose a…

Structured illumination microscopy (SIM) has become an important technique for optical super-resolution imaging because it allows a doubling of image resolution at speeds compatible for live-cell imaging. However, the reconstruction of SIM…

We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machine-learning models are developed; namely the convolutional neural…

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

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…

We present a new turbulent data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening, which can recover high-resolution turbulent flows from grossly coarse flow data in space and…

Super-resolution is an innovative technique that upscales the resolution of an image or a video and thus enables us to reconstruct high-fidelity images from low-resolution data. This study performs super-resolution analysis on turbulent…

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…

Structured illumination microscopy (SIM) is a wide-field super-resolution technique normally limited to roughly twice the diffraction-limited resolution ($\approx 100$--$200$~nm). Surpassing this bound is a classic ill-posed inverse…

Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only…

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we…

Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, the Fourier-based neural operator framework inherently truncates high-frequency…

Flexible and accurate interpolation schemes using machine learning could be of great benefit for many use-cases in numerical simulations and post-processing, such as temporal upsampling or storage reduction. In this work, we adapt the…