Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels (2011.02364v1)

Abstract: High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. How to enhance spatial resolution and decrease the noise level of flow data is essential and practically useful. Deep learning (DL) techniques have been demonstrated to be effective for super-resolution (SR) tasks, which, however, primarily rely on sufficient HR labels for training. In this work, we present a novel physics-informed DL-based SR solution using convolutional neural networks (CNN), which is able to produce HR flow fields from low-resolution (LR) inputs in high-dimensional parameter space. By leveraging the conservation laws and boundary conditions of fluid flows, the CNN-SR model is trained without any HR labels. Moreover, the proposed CNN-SR solution unifies the forward SR and inverse data assimilation for the scenarios where the physics is partially known, e.g., unknown boundary conditions. Several flow SR problems relevant to cardiovascular applications have been studied to demonstrate the proposed method's effectiveness and merit. Both Gaussian and non-Gaussian MRI noises are investigated to illustrate the denoising capability.

Physics-Informed Deep Learning for Fluid Flow Super-Resolution

The research paper presents a novel approach to the problem of super-resolution and denoising of fluid flow data using Convolutional Neural Networks (CNNs) integrated with physics-informed learning. In various engineering fields, high-resolution (HR) data is crucial for accurate quantitative analyses of fluid systems, but obtaining such data is often constrained by computational or experimental limits. Fluid data are generally sparse, incomplete, and subjected to noise, necessitating effective methods to enhance spatial resolution and reduce noise levels.

Key Contributions

The paper introduces a method for super-resolving low-resolution (LR) flow data without relying on HR labels, leveraging the inherent physical laws and boundary conditions of fluid flows. The proposed physics-informed CNN model can generate HR flow fields from LR inputs in high-dimensional parameter spaces. The approach is groundbreaking in its ability to unify forward super-resolution and inverse data assimilation, which is particularly valuable when dealing with scenarios involving unknown boundary conditions.

Numerical and Denoising Performance

Several cardiovascular application scenarios are explored to demonstrate the methodology's effectiveness. The CNN successfully addresses both Gaussian and non-Gaussian MRI noise problems, revealing its practical utility in biomedical imaging where HR data is hard to obtain due to resolution limits of current measurement techniques. For instance, LR data with 100% Gaussian noise reduced the error significantly when processed through the CNN, ensuring physical fidelity compared to conventional bicubic interpolation methods. Moreover, applications to parametric problems showed the robustness of the CNN-SR model across a range of conditions defined by varying boundary parameters.

Theoretical Implications

The integration of physical constraints within the deep learning framework offers an advancement in how fluid dynamics problems are approached computationally. The physics-informed method circumvents the dependency on HR data, which is often unavailable, and provides a mechanism to assimilate sparse observations effectively. Additionally, the parameterized surrogate modeling capability of the CNN highlights its potential for cost-effective, massive query applications like optimization and uncertainty quantification in high-dimensional spaces.

Future Directions

This paper has laid a foundation for further developments in AI-driven fluid dynamics simulations. Future work could extend the framework to cover both spatial and temporal super-resolution in three-dimensional complex geometries, making it a comprehensive tool for unsteady fluid flow analysis. Additionally, real-world implementation, especially in medical imaging and aerospace engineering, could be explored, leveraging the demonstrated computational efficiency over traditional numerical simulations.

In conclusion, the paper presents notable results that encourage the exploration of physics-informed neural networks as a reliable and efficient alternative for enhancing fluid flow data resolution and quality, underscoring the synergy between AI and traditional fluid dynamics modeling.