Physics-informed deep-learning applications to experimental fluid mechanics

TL;DR

This work shows how physics-informed neural networks (PINNs) can reconstruct high-fidelity, continuous flow fields from sparse, noisy experimental data without requiring high-resolution targets. By embedding governing PDEs into the training loss, PINNs enforce physical consistency via residuals computed with automatic differentiation, enabling robust super-resolution in both time and space. The authors validate the approach across Burgers’ equation, 2D cylinder wake, and a minimal turbulent channel, and extend it to real hot-wire measurements for resolution enhancement and de-noising, highlighting improved fidelity, especially for large-scale features and near-wall regions. The study demonstrates PINNs as a practical data-augmentation tool for experimental fluid mechanics, capable of delivering physically plausible reconstructions with limited and imperfect data.

Abstract

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete and noisy. Deep-learning approaches have been shown suitable for such super-resolution tasks. However, a high number of high-resolution examples is needed, which may not be available for many cases. Moreover, the obtained predictions may lack in complying with the physical principles, e.g. mass and momentum conservation. Physics-informed deep learning provides frameworks for integrating data and physical laws for learning. In this study, we apply physics-informed neural networks (PINNs) for super-resolution of flow-field data both in time and space from a limited set of noisy measurements without having any high-resolution reference data. Our objective is to obtain a continuous solution of the problem, providing a physically-consistent prediction at any point in the solution domain. We demonstrate the applicability of PINNs for the super-resolution of flow-field data in time and space through three canonical cases: Burgers' equation, two-dimensional vortex shedding behind a circular cylinder and the minimal turbulent channel flow. The robustness of the models is also investigated by adding synthetic Gaussian noise. Furthermore, we show the capabilities of PINNs to improve the resolution and reduce the noise in a real experimental dataset consisting of hot-wire-anemometry measurements. Our results show the adequate capabilities of PINNs in the context of data augmentation for experiments in fluid mechanics.

Figures (15)

• Figure 1: Schematic representation of proposed PINNs architecture. Note the use of the index notation.
• Figure 2: Super-resolution in time using PINNs for the one-dimensional Burger's equation: (a) comparison of the solution obtained from PINNs with the reference data; continuous solution of the shock-formation process (top) and the absolute error $\varepsilon = \left| u - \tilde{u} \right|$, where $u$ denotes the reference data and $\tilde{u}$ represents the PINN predictions (bottom). The red vertical lines indicate the data used for supervised learning. (b) Supervised and unsupervised losses, $L_s$ and $L_e$ respectively, during the training process. The green dashed line indicates $L_s$ and the blue line represents $L_e$.
• Figure 3: A schematic view of the resolution of the training data used for the supervised learning for the two-dimensional vortex shedding behind a circular cylinder. Colors depict the streamwise velocity. The blue line shows the first temporal coefficient $a_1$ of the POD for this test case.
• Figure 4: Results obtained based on super-resolution in time and space for the cylinder test case using PINNs from a limited set of measurements contaminated with a noise level of $c$ = 10%: (a) contours of vorticity in the $z$ direction at $t$ = 1.8 and 5.3. (b) Temporal coefficients of the POD for the 3rd, 5th and 7th modes obtained from the PINN solution in comparison with that of the reference data.
• Figure 5: PINN-simulation results for the pressure at $t = 5.3$ for the clean test case (upper left), reference data (upper right), the absolute error $\varepsilon = \left| p - \tilde{p} \right|$ (lower left) and relative absolute error $\hat{\varepsilon} = |({p - \hat{p}})/{p}|$$(\%)$ (lower right), where $p$ denotes the reference data and $\tilde{p}$ represents the PINN predictions.