arXiv subjects

Anne E. Staples

Publications and source records attributed to Anne E. Staples.

14 recordsLinked to original sources

arXiv2026

Insect-inspired modular architectures as inductive biases for reinforcement learning

Most reinforcement-learning (RL) controllers used in continuous control are architecturally centralized: observations are compressed into a single latent state from which both value estimates and actions are produced. Biological control systems are often organized differently. Insects, in particular, coordinate navigation, heading stabilization, memory, and context-dependent action selection through distributed circuits rather than a single monolithic controller. Motivated by this contrast, we study an RL policy architecture that decomposes control into interacting modules for sensory encoding, heading representation, sparse associative memory, recurrent command generation, and local motor control, with a learned arbitration mechanism that allocates motor authority across modules. The model is evaluated on a two-dimensional navigation task that require simultaneous food seeking, obstacle avoidance, and predator escape. In a six-seed predator-navigation experiment trained with Proximal Policy Optimization (PPO) for 75 updates, the modular policy achieves the strongest final mean performance among the tested controllers, with final episodic return $-2798.8\pm964.4$ versus $-3778.0\pm628.1$ for a centralized gated recurrent unit (GRU) and $-4727.5\pm772.5$ for a centralized multilayer perceptron (MLP). The modular policy also attains the lowest final value loss and stable PPO optimization statistics while driving module-assignment entropy to $0.0457\pm0.0244$, indicating highly selective control allocation. These results suggest that distributed control can serve as a useful inductive bias for RL problems involving dynamically competing behavioral objectives.

cs.LG↗

arXiv2023

Accelerated evolution of Burgers turbulence with coarse projective integration and deep learning

Simulating turbulence to stationarity is a major bottleneck in many engineering problems of practical importance. The problem can be cast as a multiscale problem involving energy redistribution processes that take place on the long large eddy turnover time scale and chaotic processes that take the much shorter time scale of the turbulent fluctuations. But the absence of a way to perform super-resolution reconstructions of the instantaneous velocity field from its lower dimensional moments has prevented the implementation of multiscale computational approaches for accelerating turbulence simulations. Here, we use an encoder-decoder recurrent neural network to learn the relationship between the instantaneous velocity field and energy spectrum for the one-dimensional stochastic Burgers equation, a common toy model of turbulence. We use the model to reconstruct the velocity field from instantaneous energy spectra in an equation-free coarse projective integration multiscale simulation scheme using a velocity-energy, fine-coarse multiscale framework. The multiscale-machine learning approach put forth here recovers the final statistically stationary turbulent Burgers velocity field up to 442 times faster in wall clock time than using direct numerical simulation alone, with 3-digit accuracy.

physics.flu-dyn↗

arXiv2020

Frequency-specific, valveless flow control in insect-mimetic microfluidic devices

Inexpensive, portable lab-on-a-chip devices would revolutionize fields like environmental monitoring and global health, but current microfluidic chips are tethered to extensive off-chip hardware. Insects, however, are self-contained and expertly manipulate fluids at the microscale using largely unexplored methods. We fabricated a series of microfluidic devices that mimic key features of insect respiratory kinematics observed by synchrotron-radiation imaging, including the collapse of portions of multiple respiratory tracts in response to a single fluctuating pressure signal. In one single-channel device, the flow rate and direction could be controlled by the actuation frequency alone, without the use of internal valves. Additionally, we fabricated multichannel chips whose individual channels responded selectively (on with a variable, frequency-dependent flow rate, or off) to a single, global actuation frequency. Our results demonstrate that insect-mimetic designs have the potential to drastically reduce the actuation overhead for microfluidic chips, and that insect respiratory systems may share features with impedance-mismatch pumps.

physics.flu-dyn↗

arXiv2014

Large Eddy Simulation of Turbulent Barotropic Flows in Spectral Space on the Sphere

Numerical simulations of atmospheric circulation models are limited by their finite spatial resolution, and so large eddy simulation (LES) is the preferred approach to study these models. In LES a low-pass filter is applied to the flow field to separate the large and small scale motions. In implicitly filtered LES the computational mesh and discretization schemes are considered to be the low-pass filter while in the explicitly filtered LES approach the filtering procedure is separated from the grid and discretization operators and allows for better control of the numerical errors. The aim of this paper is to study and compare implicitly filtered and explicitly filtered LES of atmospheric circulation models in spectral space. To achieve this goal we present the results of implicitly filtered and explicitly filtered LES of a barotropic atmosphere circulation model on the sphere in spectral space and compare them with the results obtained from direct numerical simulation (DNS). Our study shows that although in the computation of some integral quantities like total kinetic energy and total enstrophy the results obtained from implicitly filtered LES and explicitly filtered LES show the same good agreement with the DNS results, explicit filtering produces energy spectra that show better agreement with the DNS results. More importantly, explicit filtering captures the location of coherent structures over time while implicit filtering does not.

physics.flu-dyn↗

arXiv2014

Explicit Filtering in Large Eddy Simulation of Barotropic Turbulence in Spectral Space

Explicit filtering in large eddy simulation (LES) of a turbulent barotropic flow on the sphere in spectral space is studied and compared to implicit filtering. Here, a smooth filter is applied to the nondivergent barotropic vorticity equation (BVE) on the rotating sphere to divide the flow field into resolved scale (RS) and subfilter scale (SFS) motions. A portion of the SFS motions are reconstructed theoretically using the approximate deconvolution model (ADM). While the unreconstructed portion consists of the subgrid scale (SGS) motions and needs to be modeled separately. In order to investigate the effects of the explicit filtering alone no SGS model is used. It is shown that the explicit filtering accurately tracks the evolution of the coherent structures in two-dimensional turbulent flow on the rotating sphere, whereas the implicit filtering does not. It is also shown that explicit filtering improves the results of the temporal variation of the total kinetic energy and the total enstrophy and the variation of the energy spectrum with wavenumber compare to the implicit filtering. Although explicit filtering is more expensive than implicit filtering it increases the accuracy of the computations and improves the results, particularly where the location of coherent structures is concerned, a topic of particular importance in LES of atmospheric flows for climate and weather applications.

physics.flu-dyn↗

arXiv2014

A posteriori analysis of low-pass spatial filters for approximate deconvolution large eddy simulations of homogeneous incompressible flows

The goal of this paper is twofold: first, it investigates the effect of low-pass spatial filters for approximate deconvolution large eddy simulation (AD-LES) of turbulent incompressible flows. Second, it proposes the hyper-differential filter as a means of increasing the accuracy of the AD-LES model without increasing the computational cost. Box filters, Padé filters, and differential filters with a wide range of parameters are studied in the AD-LES framework. The AD-LES model, in conjunction with these spatial filters, is tested in the numerical simulation of the three-dimensional Taylor-Green vortex problem. The numerical results are benchmarked against direct numerical simulation (DNS) data. An under-resolved numerical simulation is also used for comparison purposes. Four criteria are used to investigate the AD-LES model equipped with these spatial filters: (i) the time series of the volume-averaged enstrophy; (ii) the volume-averaged third-order structure function; (iii) the $L^2$-norm of the velocity and vorticity errors; and (iv) the volume-averaged velocity and vorticity correlation coefficients. According to these criteria, the numerical results yield the following two conclusions: first, the AD-LES model equipped with any of these spatial filters yields accurate results at a fraction of the computational cost of DNS. Second, the most accurate results are obtained with the hyper-differential filter, followed by the differential filter. We demonstrate that the results highly depend on the selection of the filtering procedure. Although a careful parameter choice makes each class of filters used in this study competitive, it seems that filters whose transfer function resembles that of the Fourier cut-off filter (such as the hyper-differential filters) tend to perform best.

physics.flu-dyn↗

arXiv2013

An Efficient Coarse Grid Projection Method for Quasigeostrophic Models of Large-Scale Ocean Circulation

This paper puts forth a coarse grid projection (CGP) multiscale method to accelerate computations of quasigeostrophic (QG) models for large scale ocean circulation. These models require solving an elliptic sub-problem at each time step, which takes the bulk of the computational time. The method we propose here is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for solving the elliptic sub-problem and potential vorticity equations in the QG flow solvers. After solving the elliptic sub-problem on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. The potential vorticity field is then updated on the fine grid with savings in computational time due to the reduced number of grid points for the elliptic solver. The method is applied to both single layer barotropic and two-layer stratified QG ocean models for mid-latitude oceanic basins in the beta plane, which are standard prototypes of more realistic ocean dynamics. The method is found to accelerate these computations while retaining the same level of accuracy in the fine-resolution field. A linear acceleration rate is obtained for all the cases we consider due to the efficient linear-cost fast Fourier transform based elliptic solver used. We expect the speed-up of the CGP method to increase dramatically for versions of the method that use other, suboptimal, elliptic solvers, which are generally quadratic cost. It is also demonstrated that numerical oscillations due to lower grid resolutions, in which the Munk scales are not resolved adequately, are effectively eliminated with CGP method.

physics.flu-dyn↗

arXiv2012

High-order methods for decaying two-dimensional homogeneous isotropic turbulence

Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is investigated for direct numerical simulations (DNS) of homogeneous isotropic two-dimensional decaying turbulent flows. The numerical accuracy of compact difference, explicit central difference, Arakawa, and dispersion-relation-preserving schemes are analyzed and compared with the Fourier-Galerkin pseudospectral scheme. In addition, several explicit Runge-Kutta schemes for time integration are investigated. We demonstrate that the centered schemes suffer from spurious Nyquist signals that are generated almost instantaneously and propagate into much of the field when the numerical resolution is insufficient. We further show that the order of the scheme becomes increasingly important for increasing cell Reynolds number. Surprisingly, the sixth-order schemes are found to be in perfect agreement with the pseudospectral method. Considerable reduction in computational time compared to the pseudospectral method is also reported in favor of the finite difference schemes. Among the fourth-order schemes, the compact scheme provides better accuracy than the others for fully resolved computations. The fourth-order Arakawa scheme provides more accurate results for under-resolved computations, however, due to its conservation properties. Our results show that, contrary to conventional wisdom, difference methods demonstrate superior performance in terms of accuracy and efficiency for fully resolved DNS computations of the complex flows considered here. For under-resolved simulations, however, the choice of difference method should be made with care.

physics.flu-dyn↗

arXiv2012

Stationary two-dimensional turbulence statistics using a Markovian forcing scheme

In this study we investigate the statistics of two-dimensional stationary turbulence using a Markovian forcing scheme, which correlates the forcing process in the current time step to the previous time step according to a defined memory coefficient. In addition to the Markovian forcing mechanism, the hyperviscous dissipation mechanism for small scales and the Ekman friction type of linear damping mechanism for the large scales are included in the model. We examine the effects of various dissipation and forcing parameters on the turbulence statistics in both wave space and physical space. Our analysis includes the effects of the effective forcing scale, the bandwidth of the forcing, the memory correlation coefficient, and the forcing amplitude, along with the large scale friction and small scale dissipation coefficients. Scaling exponents of structure functions and energy spectra are calculated, and the role of the parameters associated with the Markovian forcing is discussed. We found that the scaling exponents are approximately invariant and show a universal behavior for the various forms of forcing schemes used. We found, however, that the final states strongly depend on the large scale friction mechanism considered. When the large scale friction mechanism is included in the model with a high friction coefficient, we demonstrate that the behavior is no longer universal. Our analysis also shows that the second-order vorticity structure function has an asymptotic scaling exponent for larger dissipation. Additionally, we confirmed that vorticity behaves as a passive scalar when the dissipation mechanism becomes less effective. Finally, although turbulence is not believed to have a separation of time scales in the dynamics of the velocity field, we conjectured that a separation of time scales exists in the dynamics of the energy spectrum.

physics.flu-dyn↗

arXiv2012

A coarse-grid projection method for accelerating incompressible flow computations

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

physics.flu-dyn↗

arXiv2012

An improved model for reduced-order physiological fluid flows

An improved one-dimensional mathematical model based on Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension, and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest fifty-five arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.

physics.flu-dyn↗

arXiv2012

Dynamics of pulsatile flows through elastic microtubes

We investigate the dynamics of pressure driven transient flows of incompressible Newtonian fluids through circular microtubes having thin elastic walls under the long-wavelength and small deformation assumptions, which are valid for many industrial and biological processes. An analytical solution of the coupled fluid and solid equations is found using Navier slip boundary conditions and is shown to include some existing Womersley solutions as limiting cases. The effect of the slip length at the fluid-solid interface is analyzed for oscillatory pressure gradients using a range of slip ratio and frequency parameters. The solutions for elastic and rigid walls are compared for the cases with and without slip boundary conditions for a broad range of the relevant parameters. It is shown that the elastic behavior of the microtube couples nonlinearly with the slip velocity, which greatly enhances the achievable flow rate and pumping efficacy compared to the inelastic case. In addition, it is observed that increasing the slip length produces less shear stress, which is consistent with the nearly frictionless interfaces observed in many microscale experiments.

physics.flu-dyn↗

arXiv2011

Approximate deconvolution large eddy simulation of a barotropic ocean circulation model

This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does not employ additional phenomenological arguments to the model. The new approximate deconvolution model is tested in the numerical simulation of the wind-driven circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics. The model employs the barotropic vorticity equation driven by a symmetric double-gyre wind forcing, which yields a four-gyre circulation in the time mean. The approximate deconvolution model yields the correct four-gyre circulation structure predicted by a direct numerical simulation, on a coarser mesh but at a fraction of the computational cost. This first step in the numerical assessment of the new model shows that approximate deconvolution could represent a viable tool for under-resolved computations in the large eddy simulation of more realistic turbulent geophysical flows.

physics.ao-ph↗

arXiv2011

On the Steady State Distributions for Turbulence

We propose explicit forms for the steady state distributions governing fully developed turbulence in two and three spatial dimensions. We base our proposals on the crucial importance of the area and volume preserving diffeomorphisms in the space of velocities. We argue that these distributions can lead to the relevant (Kolmogorov and Kraichnan) scaling laws.

physics.flu-dyn↗