arXiv subjects

Jeff D. Eldredge

Publications and source records attributed to Jeff D. Eldredge.

At least 19 recordsLinked to original sources

arXiv2026

Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes

The Stokes-flow hydrodynamics of an irregular microparticle is encoded by its grand resistance matrix, a 6x6 tensor whose translational and rotational blocks (A and C) govern settling, diffusion, and orientational transport. Empirical drag correlations compress these tensors to a single scalar, discarding drag's orientation dependence and the rotational response. We present an SO(3)-equivariant neural network that predicts the full symmetric positive-definite A and C blocks from a particle's spherical-harmonic surface representation, equivariant by construction to floating-point precision. Trained on 1.1x10^5 random shapes from near-spherical to very rough, with a sealed test set of 18,000, it achieves 1.4% and 2.7% mean relative error on the two blocks while evaluating each shape 4-5 orders of magnitude faster than the regularised-Stokeslet solver that generated its labels. A spectral-convergence study confirms the representation is faithful: truncating a shape at spherical-harmonic degree 15 changes its resistance by a median of 0.14% (translation) and 0.38% (rotation), while the training shapes, generated band-limited at degree 15, carry no truncation error. Across 1.16x10^6 orientation-sampled settling, rotation and diffusion events, the surrogate reveals lateral drift up to 11 deg, rotational misalignment up to 46 deg, and shape-induced diffusion spreads of 30% (translational) and 2.4x (rotational), all identically zero under any scalar or spheroid reduction. Even the orientation-averaged scalar friction the correlations target, accurate to 1.7-2.8% (median; 2.2-3.2% mean), carries no tensor orientation, whereas the surrogate reproduces that scalar to ~1% while supplying the full anisotropic tensors. A fast, equivariant tensor surrogate can replace both solver and scalar approximation in atmospheric dust transport, microplastic fate and colloidal Brownian dynamics.

physics.flu-dyn↗

arXiv2026

Vertical vortex gust encounters of a delta wing

The present study analyzes encounters of a vertical vortex with a tailless NACA 0012 delta wing with a sweep angle of 60 degrees at an angle of attack of 10 degrees and Reynolds number 1000 using direct numerical simulations. Motivated by the need to fly in complex settings such as urban canyons, mountainous areas, wildfires, or vehicle swarms, we focus on the influence of a vertical vortex gust on the delta wing, complementing previous efforts that predominantly studied spanwise and streamwise vortex encounters. The vertical orientation can impose strong transient loads on all six degrees of freedom, and particular attention is devoted to connecting these loads to the flow response. By varying the gust's lateral position, size, and strength, we find a fundamental process that characterizes vertical vortex gust encounters. The gust consistently imprints a low-pressure core on the wing surface. The evolving core creates an adverse pressure gradient that distorts the baseline skin-friction pattern and induces separation that lifts the boundary layers. These lifted boundary layers are elongated and twisted by the gust's strain into lobed vortical structures, which are shown by force element analysis to make a critical contribution to the lift. As the gust's lateral position is varied from root to tip, the low-pressure core and the induced flow separation are increasingly localized around the leading edge closest to the gust, modifying the lobe evolution and leading to complex dependence of the force and moment response on gust position compared to the largely monotonic dependence on gust size and strength.

physics.flu-dyn↗

arXiv2026

Quantification and Classification of Carbon Nanotubes in Electron Micrographs using Vision Foundation Models

Accurate characterization of carbon nanotube morphologies in electron microscopy images is vital for exposure assessment and toxicological studies, yet current workflows rely on slow, subjective manual segmentation. This work presents a unified framework leveraging vision foundation models to automate the quantification and classification of CNTs in electron microscopy images. First, we introduce an interactive quantification tool built on the Segment Anything Model (SAM) that segments particles with near-perfect accuracy using minimal user input. Second, we propose a novel classification pipeline that utilizes these segmentation masks to spatially constrain a DINOv2 vision transformer, extracting features exclusively from particle regions while suppressing background noise. Evaluated on a dataset of 1,800 TEM images, this architecture achieves 95.5% accuracy in distinguishing between four different CNT morphologies, significantly outperforming the current baseline despite using a fraction of the training data. Crucially, this instance-level processing allows the framework to resolve mixed samples, correctly classifying distinct particle types co-existing within a single field of view. These results demonstrate that integrating zero-shot segmentation with self-supervised feature learning enables high-throughput, reproducible nanomaterial analysis, transforming a labor-intensive bottleneck into a scalable, data-driven process.

cs.CV↗

arXiv2026

A practical guide to estimation and uncertainty quantification of aerodynamic flows

Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or the non-uniqueness of the underlying mapping. Knowledge of this uncertainty can be as important for decision-making as that of the state itself. Uncertainty tracking is challenged by the often-nonlinear relationship between the measurements and the flow state. For example, a collection of passing vortices leaves a footprint in wall pressure that depends nonlinearly on the vortices' strengths and positions. In this paper, we outline recent approaches to flow estimation and illuminate them with worked examples and selected case studies. We review relevant probability tools, including sampling and estimation, in the powerful setting of Bayesian inference and demonstrate these in static flow estimation examples. We then review unsteady examples and illustrate the application of sequential estimation, and particularly, the ensemble Kalman filter. Finally, we discuss uncertainty quantification in neural network approximations of the mappings between sensor measurements and flow states. Recent aerodynamic applications have shown that the flow state can be encoded into a very low-dimensional latent space. We discuss the uncertainty implications of this encoding.

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arXiv2025

Attention on flow control: transformer-based reinforcement learning for lift regulation in highly disturbed flows

A linear flow control strategy designed for weak disturbances may not remain effective in sequences of strong disturbances due to nonlinear interactions, but it is sensible to leverage it for developing a better strategy. In the present study, we propose a transformer-based reinforcement learning (RL) framework to learn an effective control strategy for regulating aerodynamic lift in arbitrarily long gust sequences via pitch control. The random gusts produce intermittent, high-variance flows observed only through limited surface pressure sensors, making this control problem inherently challenging compared to stationary flows. The transformer addresses the challenge of partial observability from the limited surface pressures. We demonstrate that the training can be accelerated with two techniques -- pretraining with an expert policy (here, linear control) and task-level transfer learning (here, extending a policy trained on isolated gusts to multiple gusts). We show that the learned strategy outperforms the best proportional control, with the performance gap widening as the number of gusts increases. The control strategy learned in an environment with a small number of successive gusts is shown to effectively generalize to an environment with an arbitrarily long sequence of gusts. We investigate the pivot configuration and show that quarter-chord pitching control can achieve superior lift regulation with substantially less control effort compared to mid-chord pitching control. Through a decomposition of the lift, we attribute this advantage to the dominant added-mass contribution accessible via quarter-chord pitching.

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arXiv2025

Model-Based Reinforcement Learning for Control of Strongly-Disturbed Unsteady Aerodynamic Flows

The intrinsic high dimension of fluid dynamics is an inherent challenge to control of aerodynamic flows, and this is further complicated by a flow's nonlinear response to strong disturbances. Deep reinforcement learning, which takes advantage of the exploratory aspects of reinforcement learning (RL) and the rich nonlinearity of a deep neural network, provides a promising approach to discover feasible control strategies. However, the typical model-free approach to reinforcement learning requires a significant amount of interaction between the flow environment and the RL agent during training, and this high training cost impedes its development and application. In this work, we propose a model-based reinforcement learning (MBRL) approach by incorporating a novel reduced-order model as a surrogate for the full environment. The model consists of a physics-augmented autoencoder, which compresses high-dimensional CFD flow field snaphsots into a three-dimensional latent space, and a latent dynamics model that is trained to accurately predict the long-time dynamics of trajectories in the latent space in response to action sequences. The accuracy and robustness of the model are demonstrated in the scenario of a pitching airfoil within a highly disturbed environment. Additionally, an application to a vertical-axis wind turbine in a disturbance-free environment is discussed in the Appendix Based on the model trained in the pitching airfoil problem, we realize an MBRL strategy to mitigate lift variation during gust-airfoil encounters. We demonstrate that the policy learned in the reduced-order environment translates to an effective control strategy in the full CFD environment.

physics.flu-dyn↗

arXiv2025

Low-Order Flow Reconstruction and Uncertainty Quantification in Disturbed Aerodynamics Using Sparse Pressure Measurements

This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying response of sensors to gust-airfoil interactions, uncovering valuable insights into optimal sensor placement. To address uncertainties in deep learning predictions, we implement probabilistic regression strategies to model both epistemic and aleatoric uncertainties. Epistemic uncertainty, reflecting the model's confidence in its predictions, is modeled using Monte Carlo dropout, as an approximation to the variational inference in the Bayesian framework, treating the neural network as a stochastic entity. On the other hand, aleatoric uncertainty, arising from noisy input measurements, is captured via learned statistical parameters, which propagates measurement noise through the network into the final predictions. Our results showcase the efficacy of this dual uncertainty quantification strategy in accurately predicting aerodynamic behavior under extreme conditions while maintaining computational efficiency, underscoring its potential to improve online sensor-based flow estimation in real-world applications.

cs.LG↗

arXiv2024

Bayesian Inference for Estimating Heat Sources through Temperature Assimilation

This paper introduces a Bayesian inference framework for two-dimensional steady-state heat conduction, focusing on the estimation of unknown distributed heat sources in a thermally-conducting medium with uniform conductivity. The goal is to infer heater locations, strengths, and shapes using temperature assimilation in the Euclidean space, employing a Fourier series to represent each heater's shape. The Markov Chain Monte Carlo (MCMC) method, incorporating the random-walk Metropolis-Hasting algorithm and parallel tempering, is utilized for posterior distribution exploration in both unbounded and wall-bounded domains. Strong correlations between heat strength and heater area prompt caution against simultaneously estimating these two quantities. It is found that multiple solutions arise in cases where the number of temperature sensors is less than the number of unknown states. Moreover, smaller heaters introduce greater uncertainty in estimated strength. The diffusive nature of heat conduction smooths out any deformations in the temperature contours, especially in the presence of multiple heaters positioned near each other, impacting convergence. In wall-bounded domains with Neumann boundary conditions, the inference of heater parameters tends to be more accurate than in unbounded domains.

stat.AP↗

arXiv2024

Deep reinforcement learning of airfoil pitch control in a highly disturbed environment using partial observations

This study explores the application of deep reinforcement learning (RL) to design an airfoil pitch controller capable of minimizing lift variations in randomly disturbed flows. The controller, treated as an agent in a partially observable Markov decision process, receives non-Markovian observations from the environment, simulating practical constraints where flow information is limited to force and pressure sensors. Deep RL, particularly the TD3 algorithm, is used to approximate an optimal control policy under such conditions. Testing is conducted for a flat plate airfoil in two environments: a classical unsteady environment with vertical acceleration disturbances (i.e., a Wagner setup) and a viscous flow model with pulsed point force disturbances. In both cases, augmenting observations of the lift, pitch angle, and angular velocity with extra wake information (e.g., from pressure sensors) and retaining memory of past observations enhances RL control performance. Results demonstrate the capability of RL control to match or exceed standard linear controllers in minimizing lift variations. Special attention is given to the choice of training data and the generalization to unseen disturbances.

physics.flu-dyn↗

arXiv2024

Bayesian inference of vorticity in unbounded flow from limited pressure measurements

We study the instantaneous inference of an unbounded planar flow from sparse noisy pressure measurements. The true flow field comprises one or more regularized point vortices of various strength and size. We interpret the true flow's measurements with a vortex estimator, also consisting of regularized vortices, and attempt to infer the positions and strengths of this estimator assuming little prior knowledge. The problem often has several possible solutions, many due to a variety of symmetries. To deal with this ill-posedness and to quantify the uncertainty, we develop the vortex estimator in a Bayesian setting. We use Markov-chain Monte Carlo and a Gaussian mixture model to sample and categorize the probable vortex states in the posterior distribution, tailoring the prior to avoid spurious solutions. Through experiments with one or more true vortices, we reveal many aspects of the vortex inference problem. With fewer sensors than states, the estimator infers a manifold of equally-possible states. Using one more sensor than states ensures that no cases of rank deficiency arise. Uncertainty grows rapidly with distance when a vortex lies outside of the vicinity of the sensors. Vortex size cannot be reliably inferred, but the position and strength of a larger vortex can be estimated with a much smaller one. In estimates of multiple vortices their individual signs are discernible because of the non-linear coupling in the pressure. When the true vortex state is inferred from an estimator of fewer vortices, the estimate approximately aggregates the true vortices where possible.

physics.flu-dyn↗

arXiv2023

An adaptive ensemble filter for heavy-tailed distributions: tuning-free inflation and localization

Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version - the ensemble Kalman filter (EnKF) - that have been designed under Gaussian assumptions result in degraded performance. t-distributions are a parametric family of distributions whose tail-heaviness is modulated by a degree of freedom $ν$. Interestingly, Cauchy and Gaussian distributions correspond to the extreme cases of a t-distribution for $ν= 1$ and $ν= \infty$, respectively. Leveraging tools from measure transport (Spantini et al., SIAM Review, 2022), we present a generalization of the EnKF whose prior-to-posterior update leads to exact inference for t-distributions. We demonstrate that this filter is less sensitive to outlying synthetic observations generated by the observation model for small $ν$. Moreover, it recovers the Kalman filter for $ν= \infty$. For nonlinear state-space models with heavy-tailed noise, we propose an algorithm to estimate the prior-to-posterior update from samples of joint forecast distribution of the states and observations. We rely on a regularized expectation-maximization (EM) algorithm to estimate the mean, scale matrix, and degree of freedom of heavy-tailed \textit{t}-distributions from limited samples (Finegold and Drton, arXiv preprint, 2014). Leveraging the conditional independence of the joint forecast distribution, we regularize the scale matrix with an $l1$ sparsity-promoting penalization of the log-likelihood at each iteration of the EM algorithm. By sequentially estimating the degree of freedom at each analysis step, our filter can adapt its prior-to-posterior update to the tail-heaviness of the data. We demonstrate the benefits of this new ensemble filter on challenging filtering problems.

stat.CO↗

arXiv2022

A low-rank ensemble Kalman filter for elliptic observations

We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic partial differential equations, such as the pressure Poisson equation (PPE) in incompressible fluid flows, distance localization cannot be applied, as we cannot disentangle slowly decaying physical interactions from spurious long-range correlations. This is particularly true for the PPE, in which distant vortex elements couple nonlinearly to induce pressure. Instead, these inverse problems have a low effective dimension: low-dimensional projections of the observations strongly inform a low-dimensional subspace of the state space. We derive a low-rank factorization of the Kalman gain based on the spectrum of the Jacobian of the observation operator. The identified eigenvectors generalize the source and target modes of the multipole expansion, independently of the underlying spatial distribution of the problem. Given rapid spectral decay, inference can be performed in the low-dimensional subspace spanned by the dominant eigenvectors. This low-rank EnKF is assessed on dynamical systems with Poisson observation operators, where we seek to estimate the positions and strengths of point singularities over time from potential or pressure observations. We also comment on the broader applicability of this approach to elliptic inverse problems outside the context of filtering.

physics.flu-dyn↗

arXiv2022

Experimental quantification of unsteady leading-edge flow separation

We propose here a method to experimentally quantify unsteady leading-edge flow separation on aerofoils with finite thickness. The methodology relies on the computation of a leading-edge suction parameter based on measured values of the partial circulation around the leading-edge and the stagnation point location. We validate the computation of the leading-edge suction parameter for both numerical and experimental data under steady and unsteady flow conditions. The leading-order approximation of the definition of the leading-edge suction parameter is proven to be sufficiently accurate for the application to thin aerofoils such as the NACA0009 without a-priori knowledge of the stagnation point location. The higher-order terms including the stagnation point location are required to reliably compute the leading-edge suction parameter on thicker aerofoils such as the NACA0015. The computation of the leading-edge suction parameter from inviscid flow theory does not assume the Kutta condition to be valid at the trailing edge which allows us to compute its value for separated flows. The relation between the leading-edge suction parameter and the evolution of the shear layer height is studied in two different unsteady flow conditions, a fixed aerofoil in a fluctuating free-stream velocity and a pitching aerofoil in a steady free-stream. We demonstrate here that the instantaneous value of the leading-edge suction parameter based on the partial circulation around the leading edge is unambiguously defined for a given flow field and can serve as a directly quantitative measure of the degree of unsteady flow separation at the leading edge.

physics.flu-dyn↗

arXiv2022

Planar potential flow on Cartesian grids

Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential flows in two dimensions and its use in a vortex model for simulating unsteady aerodynamic flows. For flows consisting of vortex elements, the treatment follows the vortex-in-cell approach and solves the streamfunction-vorticity Poisson equation on a Cartesian grid after transferring the circulation from the vortices onto the grid. For sources and sinks, an analogous approach can be followed using the scalar potential. The combined velocity field due to vortices, sinks, and sources can then be obtained using the Helmholtz decomposition. In this work, we use several key tools that ensure the approach works on arbitrary geometries, with and without sharp edges. Firstly, the immersed boundary projection method is used to account for bodies in the flow and the resulting body-forcing Lagrange multiplier is identified as the bound vortex sheet strength. Secondly, sharp edges are treated by decomposing the vortex sheet strength into a singular and smooth part. To enforce the Kutta condition, the smooth part can then be constrained to remove the singularity introduced by the sharp edge. These constraints and the Poisson equation are formulated as a saddle-point system and solved using the Schur complement method. The lattice Green's function is used to efficiently solve the discrete Poisson equation with unbounded boundary conditions. The method and its accuracy are demonstrated for several problems.

physics.flu-dyn↗

arXiv2021

A method of immersed layers on Cartesian grids, with application to incompressible flows

The immersed boundary method (IBM) of Peskin (J. Comput. Phys., 1977), and derived forms such as the projection method of Taira and Colonius (J. Comput. Phys., 2007), have been useful for simulating flow physics in problems with moving interfaces on stationary grids. However, in their interface treatment, these methods do not distinguish one side from the other, but rather, apply the motion constraint to both sides, and the associated interface force is an inseparable mix of contributions from each side. In this work, we define a discrete Heaviside function, a natural companion to the familiar discrete Dirac delta function (DDF), to define a masked version of each field on the grid which, to within the error of the DDF, takes the intended value of the field on the respective sides of the interface. From this foundation we develop discrete operators and identities that are uniformly applicable to any surface geometry. We use these to develop extended forms of prototypical partial differential equations, including Poisson, convection-diffusion, and incompressible Navier-Stokes, that govern the discrete masked fields. These equations contain the familiar forcing term of the IBM, but also additional terms that regularize the jumps in field quantities onto the grid and enable us to individually specify the constraints on field behavior on each side of the interface. Drawing the connection between these terms and the layer potentials in elliptic problems, we refer to them generically as immersed layers. We demonstrate the application of the method to several representative problems, including two-dimensional incompressible flows inside a rotating cylinder and external to a rotating square.

physics.flu-dyn↗

arXiv2020

Lift Coefficient Estimation for a Rapidly Pitching Airfoil

We develop a method for estimating the instantaneous lift coefficient on a rapidly pitching airfoil that uses a small number of pressure sensors and a measurement of the angle of attack. The approach assimilates four surface pressure measurements with a modified nonlinear state space model (Goman-Khrabrov model) through a Kalman filter. The error of lift coefficient estimates based only on a weighted-sum of the measured pressures are found to be noisy and biased, which leads to inaccurate estimates. The estimate is improved by including the predictive model in an conventional Kalman filter. The Goman-Khrabrov model is shown to be a linear parameter-varying system and can therefore be used in the Kalman filter without the need for linearization. Additional improvement is realized by modifying the algorithm to provide more accurate estimate of the lift coefficient. The improved Kalman filtering approach results in a bias-free lift coefficient estimate that is more precise than either the pressure-based estimate or the Goman-Khrabrov model on their own. The new method will enable performance enhancements in aerodynamic systems whose performance relies on lift.

physics.flu-dyn↗

arXiv2020

The mean transport of inertial particles in viscous streaming flows

Viscous streaming has emerged as an effective method to transport, trap, and cluster inertial particles in a fluid. Previous work has shown that this transport is well described by the Maxey-Riley equation augmented with a term representing Saffman lift. However, in its straightforward application to viscous streaming flows, the equation suffers from severe numerical stiffness due to the wide disparity between the time scales of viscous response, oscillation period, and slow mean transport, posing a severe challenge for drawing physical insight on mean particle trajectories. In this work, we develop equations that directly govern the mean transport of particles in oscillatory viscous flows. The derivation of these equations relies on a combination of three key techniques. In the first, we develop an inertial particle velocity field via a small Stokes number expansion of the particle's deviation from that of the fluid. This expansion clearly reveals the primary importance of Faxén correction and Saffman lift in effecting the trapping of particles in streaming cells. Then, we apply Generalized Lagrangian Mean theory to unambiguously decompose the transport into fast and slow scales, and ultimately, develop the Lagrangian mean velocity field to govern mean transport. Finally, we carry out an expansion in small oscillation amplitude to simplify the governing equations and to clarify the hierarchy of first- and second-order influences, and particularly, the crucial role of Stokes drift in the mean transport. We demonstrate the final set of equations on the transport of both fluid and inertial particles in configurations involving one and two weakly oscillating cylinders. Notably, the new equations allow numerical time steps that are $O(10^3)$ larger than the existing approach with little sacrifice in accuracy, allowing more efficient predictions of transport.

physics.flu-dyn↗

arXiv2020

Ensemble-filtered vortex modeling of strongly disturbed aerodynamic flows

The task of dynamic flow estimation is to construct an approximation of an evolving flow---and particularly, its response to disturbances---using measurements from available sensors. Building from previous work by Darakananda et al.~(Phys Rev Fluids 2018), we further develop an ensemble Kalman filter (EnKF) framework for aerodynamic flows based on an ensemble of randomly-perturbed inviscid vortex models of flow about an infinitely-thin plate. In the forecast step, vortex elements in each ensemble member are advected by the flow and new elements are released from each edge of the plate; the elements are aggregated to maintain an efficient representation. The vortex elements and leading edge constraint are corrected in the analysis step by assimilating the surface pressure differences across the plate measured from the truth system. We show that the overall framework can be physically interpreted as a series of adjustments to the position and shape of an elliptical region of uncertainty associated with each vortex element. In this work, we compare the previously-used stochastic EnKF with the ensemble transform Kalman filter (ETKF), which uses a deterministic analysis step. We examine the response of the flat plate at $20^\circ$ in two perturbed flows, with truth data obtained from high-fidelity simulation at Reynolds number 500. In the first case, we apply a sequence of large-amplitude pulses near the leading edge of the plate to mimic flow actuation. In the second, we place the plate in a vortex street wake behind a cylinder. In both cases, we show that the vortex-based framework accurately estimates the pressure distribution and normal force, with no {\em a priori} knowledge of the perturbations. We show that the ETKF is consistently more robust than the stochastic EnKF. Finally, we examine the mapping from measurements to state update in the analysis step through SVD of the Kalman gain.

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