Estimating density, velocity, and pressure fields in supersonic flows using physics-informed BOS

Joseph P. Molnar, Lakshmi Venkatakrishnan, Bryan E. Schmidt, Timothy A. Sipkens, Samuel J. Grauer

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We report a new workflow for background-oriented schlieren (BOS), termed “physics-informed BOS,” to extract density, velocity, and pressure fields from a pair of reference and distorted images. Our method uses a physics-informed neural network (PINN) to produce flow fields that simultaneously satisfy the measurement data and governing equations. For the high-speed, approximately inviscid flows of interest in this work, we specify a physics loss based on the Euler and irrotationality equations. BOS is a quantitative fluid visualization technique that is commonly used to characterize compressible flow. Images of a background pattern, positioned behind the measurement volume, are processed with computer vision and tomography algorithms to determine the density field. Crucially, BOS features a series of ill-posed inverse problems that require supplemental information (i.e., in addition to the images) to accurately reconstruct the flow. Current methods for BOS rely upon interpolation of the images or a penalty term to promote a globally- or piecewise-smooth solution. However, these algorithms are invariably incompatible with the flow physics, leading to errors in the density field. Physics-informed BOS directly reconstructs all the flow fields using a PINN that includes the BOS measurement model and governing equations. This procedure improves the accuracy of density estimates and also yields velocity and pressure data, which were not previously available. We demonstrate our approach by reconstructing synthetic data that corresponds to analytical and numerical phantoms as well as a single pair of experimental measurements. Our physics-informed reconstructions are significantly more accurate than conventional BOS estimates. Furthermore, to the best of our knowledge, this work represents the first use of a PINN to reconstruct a supersonic flow from experimental data of any kind.

Original languageEnglish (US)
Article number14
JournalExperiments in Fluids
Issue number1
StatePublished - Jan 2023

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • General Physics and Astronomy
  • Fluid Flow and Transfer Processes


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