arXiv subjects

Samuel J. Grauer

Publications and source records attributed to Samuel J. Grauer.

12 recordsLinked to original sources

arXiv2026

Ultra-high-speed chemiluminescence tomography of spinning-mode detonation waves

This work presents a chemiluminescence tomography campaign to reconstruct time-resolved, three-dimensional reacting structures in detonation waves propagating through ethylene-based mixtures at 1 atm. Images of chemiluminescence are recorded simultaneously by five cameras through a cylindrical sapphire test section, and a custom calibration procedure is developed to account for refraction through the cylinder. The images are combined to reconstruct an effective emission source term field at megahertz rates. Reconstructions are reported for a persistent spinning detonation, a failed spinning detonation, and a case with counter-propagating transverse fronts. The reconstructed fields enable visualization of wave morphologies, determination of the axial and azimuthal wave speeds, and estimation of key geometric and kinematic parameters. These results demonstrate time-resolved chemiluminescence tomography as a non-intrusive tool for resolving volumetric detonation dynamics that are difficult to infer from point, planar, or line-of-sight diagnostics.

physics.optics↗

arXiv2026

Degree-of-freedom and optimization-dynamic effects on the observability of Kuramoto-Sivashinsky systems

Simulations of chaotic systems can only produce high-fidelity trajectories if the initial and boundary conditions are well specified. When these conditions are unknown but measurements are available, variational state estimation can reconstruct a trajectory that is consistent with both the data and the governing equations. A key open question is how many measurements are required for accurate reconstruction, making the full system trajectory observable from sparse data. We establish observability criteria for variational state estimation applied to the Kuramoto-Sivashinsky equation by linking its observability to embedding theory for dissipative dynamical systems. For a system whose attractor lies on an inertial manifold of dimension $d_M$, we show that $m \geq d_M$ measurements ensures local observability from an arbitrarily good initial guess, and $m \geq 2d_M + 1$ implies global observability using a gradient-based smoother since the only critical point on $M$ is the global minimum. We also analyze optimization-dynamic limitations that persist even when these topological conditions are met, including drift off the manifold, degeneracy of the Hessian, negative curvature, and vanishing gradients. To address these issues, we introduce a robust reconstruction strategy that combines non-convex Newton updates with a novel pseudo-projection step. Numerical simulations of the Kuramoto-Sivashinsky equation validate our analysis and show practical limits of observability for chaotic systems with low-dimensional inertial manifolds.

math.DS↗

arXiv2026

On the joint estimation of flow fields and particle properties from Lagrangian data

We numerically investigate the feasibility and limits of jointly estimating flow fields and unknown particle properties (e.g., position, size, and density) from Lagrangian particle tracking (LPT) data. LPT offers time-resolved, volumetric measurements of particle trajectories, which are markers of the carrier fluid motion. However, experimental tracks are spatially sparse and potentially noisy, and the problem of reconstructing flow fields may be further complicated by inertial particle transport, such that particle slip velocities must be determined to access the velocity field of the carrier fluid. To address this problem, we develop a data assimilation framework that couples an Eulerian representation of the flow with Lagrangian particle models, enabling the simultaneous inference of carrier fields and particle properties under the governing equations of disperse multiphase flow. We show that flow fields and particle properties can be jointly estimated in three representative regimes: (1) In a turbulent boundary layer with noisy tracer tracks (St to 0), flow fields and true particle positions are jointly estimated, which amounts to a physics-informed particle tracking problem; (2) in homogeneous isotropic turbulence seeded with inertial particles (St ~ 1-5), we demonstrate simultaneous recovery of flow states and particle diameters, showing the feasibility of implicit particle characterization; and (3) in a compressible, shock-dominated flow, we report the first joint reconstructions of velocity, pressure, density, and inertial particle properties (diameter and density), highlighting both the potential and certain limits of joint estimation in supersonic regimes. A systematic sensitivity study reveals how the seeding density, noise level, and Stokes number govern reconstruction accuracy for our method.

physics.flu-dyn↗

arXiv2026

Neural inference of fluid-structure interactions from sparse off-body measurements

We report a novel physics-informed neural framework for reconstructing unsteady fluid-structure interactions (FSI) from sparse, single-phase observations of the flow. Our approach combines a modal surface model with coordinate neural representations of the fluid and solid states, constrained by the fluid's governing equations and interface conditions. Using only off-body Lagrangian particle tracks and a moving-wall boundary condition, the method infers both flow fields and structural motion. It does not require a constitutive model for the solid or measurements of surface position, although including these can improve performance. We demonstrate the approach numerically on two canonical FSI benchmarks: vortex-induced oscillations of a 2D flapping plate and pulse-wave propagation in a 3D flexible pipe. We also demonstrate it on flow around a swimming fish. In all cases, the framework achieves accurate reconstructions of flow states and structural deformations despite acute data sparsity near the moving interface. A key result is that reconstructions remain robust to over-parameterization. This work extends physics-informed neural networks to coupled fluid-structure dynamics learned from single-phase observations, and it provides a pathway toward quantitative FSI analysis when flow measurements are sparse and structural measurements are asynchronous or unavailable.

physics.flu-dyn↗

arXiv2026

Open-source BOS tomography dataset of high-speed flow over a flight body

We present an open-source background-oriented schlieren dataset with 70 views of high-speed flow over a flight body. Sample analyses are performed using a neural-implicit reconstruction technique (NIRT) with total variation regularization as well as data assimilation via the 3D compressible Euler equations. Limited-data reconstructions based on nine views resolve sharp shocks that are consistent with the geometry, reproduce validation deflections with high fidelity, and exhibit minimal artifacts. Data assimilation recovers unmeasured fields, marking the first demonstration of 3D state estimation directly from experimental schlieren measurements. The NIRT also enables efficient uncertainty quantification, providing insight into well-resolved flow features and guiding design-of-experiments efforts. Public access to the data and code repositories is detailed at the end of this correspondence.

physics.flu-dyn↗

arXiv2025

Neural optical flow for planar and stereo PIV

Neural optical flow (NOF) offers improved accuracy and robustness over existing OF methods for particle image velocimetry (PIV). Unlike other OF techniques, which rely on discrete displacement fields, NOF parameterizes the physical velocity field using a continuous neural-implicit representation. This formulation enables efficient data assimilation and ensures consistent regularization across views for stereo PIV. The neural-implicit architecture provides significant data compression and supports a space-time formulation, facilitating the analysis of both steady and unsteady flows. NOF incorporates a differentiable, nonlinear image-warping operator that relates particle motion to intensity changes between frames. Discrepancies between the advected intensity field and observed images form the data loss, while soft constraints, such as Navier-Stokes residuals, enhance accuracy and enable direct pressure inference from PIV images. Additionally, mass continuity can be imposed as a hard constraint for both 2D and 3D flows. Implicit regularization is achieved by tailoring the network's expressivity to match a target flow's spectral characteristics. Results from synthetic planar and stereo PIV datasets, as well as experimental planar data, demonstrate NOF's effectiveness compared to state-of-the-art wavelet-based OF and CC methods. Additionally, we highlight its potential broader applicability to techniques like background-oriented schlieren, molecular tagging velocimetry, and other advanced measurement systems.

physics.flu-dyn↗

arXiv2025

Unsupervised neural-implicit laser absorption tomography for quantitative imaging of unsteady flames

This paper presents a novel neural-implicit approach to laser absorption tomography (LAT) with an experimental demonstration. A coordinate neural network is used to represent thermochemical state variables as continuous functions of space and time. Unlike most existing neural methods for LAT, which rely on prior simulations and supervised training, our approach is based solely on LAT measurements, utilizing a differentiable observation operator with line parameters provided in a standard spectroscopy database format. Although reconstructing scalar fields from multi-beam absorbance data is an inherently ill-posed, nonlinear inverse problem, our continuous space-time parameterization supports physics-inspired regularization strategies and enables data assimilation. Synthetic and experimental tests are conducted to validate the method, demonstrating robust performance and reproducibility. We show that our neural-implicit approach to LAT can capture the dominant spatial modes of an unsteady flame from very sparse measurement data, indicating its potential to reveal combustion instabilities in measurement domains with minimal optical access.

physics.optics↗

arXiv2024

Forward and inverse modeling of depth-of-field effects in background-oriented schlieren

We report a novel "cone-ray" model of background-oriented schlieren (BOS) imaging that accounts for depth-of-field effects. Reconstructions of the density field performed with this model are far more robust to the blur associated with a finite aperture than conventional reconstructions, which presume a "thin-ray" pinhole camera. Our model is characterized and validated using forward evaluations based on simulated and experimental BOS measurements of buoyancy-driven flow and hypersonic flow over a sphere. Moreover, we embed the model in a neural reconstruction algorithm, which is demonstrated with a total variation penalty as well as the compressible Euler equations. Our cone-ray technique dramatically improves the accuracy of BOS reconstructions: the shock interface is well-resolved in all our tests, irrespective of the camera's aperture setting, which spans f-numbers from 22 down to 4.

physics.flu-dyn↗

arXiv2023

Flow reconstruction and particle characterization from inertial Lagrangian tracks

This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are illuminated, imaged (typically with multiple cameras), localized in 3D, and then tracked across a series of frames. The resultant "tracks" are spatially sparse, and a reconstruction algorithm is commonly employed to determine dense Eulerian velocity and pressure fields that are consistent with the data as well as the equations governing fluid dynamics. Existing LPT reconstruction algorithms presume that the particles perfectly follow the flow, but this assumption breaks down for inertial particles, which can exhibit lag or ballistic motion and may impart significant momentum to the surrounding fluid. We report an LPT reconstruction strategy that incorporates the transport physics of both the carrier fluid and particle phases, which may be parameterized to account for unknown particle properties like size and density. Our method enables the reconstruction of unsteady flow states and determination of particle properties from LPT data and the coupled governing equations for both phases. We use a neural solver to represent flow states and data-constrained polynomials to represent the tracks (though we note that our technique is compatible with a variety of solvers). Numerical tests are performed to demonstrate the reconstruction of forced isotropic turbulence and a cone-cylinder shock structure from inertial tracks that exhibit significant lag, streamline crossing, and preferential sampling.

physics.flu-dyn↗

arXiv2023

Stochastic particle advection velocimetry (SPAV): theory, simulations, and proof-of-concept experiments

Particle tracking velocimetry (PTV) is widely used to measure time-resolved, three-dimensional velocity and pressure fields in fluid dynamics research. Inaccurate localization and tracking of particles is a key source of error in PTV, especially for single camera defocusing, plenoptic imaging, and digital in-line holography (DIH) sensors. To address this issue, we developed stochastic particle advection velocimetry (SPAV): a statistical data loss that improves the accuracy of PTV. SPAV is based on an explicit particle advection model that predicts particle positions over time as a function of the estimated velocity field. The model can account for non-ideal effects like drag on inertial particles. A statistical data loss that compares the tracked and advected particle positions, accounting for arbitrary localization and tracking uncertainties, is derived and approximated. We implement our approach using a physics-informed neural network, which simultaneously minimizes the SPAV data loss, a Navier-Stokes physics loss, and a wall boundary loss, where appropriate. Results are reported for simulated and experimental DIH-PTV measurements of laminar and turbulent flows. Our statistical approach significantly improves the accuracy of PTV reconstructions compared to a conventional data loss, resulting in an average reduction of error close to 50%. Furthermore, our framework can be readily adapted to work with other data assimilation techniques like state observer, Kalman filter, and adjoint-variational methods.

physics.flu-dyn↗

arXiv2023

Flow field tomography with uncertainty quantification using a Bayesian physics-informed neural network

We report a new approach to flow field tomography that uses the Navier-Stokes and advection-diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a series of line-of-sight (LoS) integrated measurements using a wide array of imaging modalities. The high-dimensional flow field is reconstructed from low-dimensional measurements by inverting a projection model that comprises path integrals along each LoS through the region of interest. Regularization techniques are needed to obtain realistic estimates, but current methods rely on truncating an iterative solution or adding a penalty term that is incompatible with the flow physics to varying degrees. Physics-informed neural networks (PINNs) are new tools for inverse analysis that enable regularization of the flow field estimates using the governing physics. We demonstrate how a PINN can be leveraged to reconstruct a 2D flow field from sparse LoS-integrated measurements with no knowledge of the boundary conditions by incorporating the measurement model into the loss function used to train the network. The resulting reconstructions are remarkably superior to reconstructions produced by state-of-the-art algorithms, even when a PINN is used for post-processing. However, as with conventional iterative algorithms, our approach is susceptible to semi-convergence when there is a high level of noise. We address this issue through the use of a Bayesian PINN, which facilitates comprehensive uncertainty quantification of the reconstructions, enables the use of a more intuitive loss function, and reveals the source of semi-convergence.

physics.flu-dyn↗

arXiv2023

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

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 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 used to characterize high-speed flows. Images of a background pattern, positioned behind the target flow, are processed using 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 BOS workflows 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 was not previously available. We demonstrate our approach by reconstructing synthetic data that corresponds to analytical and numerical phantoms as well as experimental measurements. Our physics-informed reconstructions are significantly more accurate than conventional BOS estimates. Further, 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.

physics.flu-dyn↗