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Register a new userPhysics-Informed Neural Network Super Resolution for Advection-Diffusion Models
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Physics-informed neural networks (NN) are an emerging technique to improve spatial resolution and enforce physical consistency of data from physics models or satellite observations. A super-resolution (SR) technique is explored to reconstruct high-resolution images ($4times$) from lower resolution images in an advection-diffusion model of atmospheric pollution plumes. SR performance is generally increased when the advection-diffusion equation constrains the NN in addition to conventional pixel-based constraints. The ability of SR techniques to also reconstruct missing data is investigated by randomly removing image pixels from the simulations and allowing the system to learn the content of missing data. Improvements in S/N of $11%$ are demonstrated when physics equations are included in SR with $40%$ pixel loss. Physics-informed NNs accurately reconstruct corrupted images and generate better results compared to the standard SR approaches.
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We propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled advection-dispersion and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward advection-dispersion equations (ADEs), where its performance for various P{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1% and outperforms some conventional discretization-based methods for $Pe$ larger than 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50% in the considered cases) the accuracy of the PINN solution of the backward ADE.
With the development of the super-resolution convolutional neural network (SRCNN), deep learning technique has been widely applied in the field of image super-resolution. Previous works mainly focus on optimizing the structure of SRCNN, which have been achieved well performance in speed and restoration quality for image super-resolution. However, most of these approaches only consider a specific scale image during the training process, while ignoring the relationship between different scales of images. Motivated by this concern, in this paper, we propose a cascaded convolution neural network for image super-resolution (CSRCNN), which includes three cascaded Fast SRCNNs and each Fast SRCNN can process a specific scale image. Images of different scales can be trained simultaneously and the learned network can make full use of the information resided in different scales of images. Extensive experiments show that our network can achieve well performance for image SR.
Most video super-resolution methods focus on restoring high-resolution video frames from low-resolution videos without taking into account compression. However, most videos on the web or mobile devices are compressed, and the compression can be severe when the bandwidth is limited. In this paper, we propose a new compression-informed video super-resolution model to restore high-resolution content without introducing artifacts caused by compression. The proposed model consists of three modules for video super-resolution: bi-directional recurrent warping, detail-preserving flow estimation, and Laplacian enhancement. All these three modules are used to deal with compression properties such as the location of the intra-frames in the input and smoothness in the output frames. For thorough performance evaluation, we conducted extensive experiments on standard datasets with a wide range of compression rates, covering many real video use cases. We showed that our method not only recovers high-resolution content on uncompressed frames from the widely-used benchmark datasets, but also achieves state-of-the-art performance in super-resolving compressed videos based on numerous quantitative metrics. We also evaluated the proposed method by simulating streaming from YouTube to demonstrate its effectiveness and robustness.
Single image super-resolution (SISR) aims to reconstruct high-resolution (HR) images from the given low-resolution (LR) ones, which is an ill-posed problem because one LR image corresponds to multiple HR images. Recently, learning-based SISR methods have greatly outperformed traditional ones, while suffering from over-smoothing, mode collapse or large model footprint issues for PSNR-oriented, GAN-driven and flow-based methods respectively. To solve these problems, we propose a novel single image super-resolution diffusion probabilistic model (SRDiff), which is the first diffusion-based model for SISR. SRDiff is optimized with a variant of the variational bound on the data likelihood and can provide diverse and realistic SR predictions by gradually transforming the Gaussian noise into a super-resolution (SR) image conditioned on an LR input through a Markov chain. In addition, we introduce residual prediction to the whole framework to speed up convergence. Our extensive experiments on facial and general benchmarks (CelebA and DIV2K datasets) show that 1) SRDiff can generate diverse SR results in rich details with state-of-the-art performance, given only one LR input; 2) SRDiff is easy to train with a small footprint; and 3) SRDiff can perform flexible image manipulation including latent space interpolation and content fusion.
Physics Informed Neural Network (PINN) is a scientific computing framework used to solve both forward and inverse problems modeled by Partial Differential Equations (PDEs). This paper introduces IDRLnet, a Python toolbox for modeling and solving problems through PINN systematically. IDRLnet constructs the framework for a wide range of PINN algorithms and applications. It provides a structured way to incorporate geometric objects, data sources, artificial neural networks, loss metrics, and optimizers within Python. Furthermore, it provides functionality to solve noisy inverse problems, variational minimization, and integral differential equations. New PINN variants can be integrated into the framework easily. Source code, tutorials, and documentation are available at url{https://github.com/idrl-lab/idrlnet}.
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