Yifei Guan, Steven L. Brunton, Igor Novosselov
Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory and the reduced-order modeling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh-Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.
Yifei Guan, Ravi Sankar Vaddi, Alberto Aliseda, Igor Novosselov
An electrohydrodynamic (EHD) flow in a point-to-ring corona configuration is investigated experimentally, analytically and via a multiphysics numerical model. The interaction between the accelerated ions and the neutral gas molecules is modeled as an external body force in the Navier-Stokes equation (NSE). The gas flow characteristics are solved from conservation principles with spectral methods. The analytical and numerical simulation results are compared against experimental measurements of the cathode voltage, ion concentration, and velocity profiles. A nondimensional parameter, X, is formulated as the ratio of the local electric force to the inertial term in the NSE. In the region of X > 1, the electric force dominates the flow dynamics, while in the X << 1 region, the balance of viscous and inertial terms yields traditional pipe flow characteristics.
Yifei Guan, James Riley, Igor Novosselov
The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number.
Yifei Guan, Pedram Hassanzadeh, Tapio Schneider, Oliver Dunbar, Daniel Zhengyu Huang, Jinlong Wu, Ignacio Lopez-Gomez
Different approaches to using data-driven methods for subgrid-scale closure modeling have emerged recently. Most of these approaches are data-hungry, and lack interpretability and out-of-distribution generalizability. Here, we use {online} learning to address parametric uncertainty of well-known physics-based large-eddy simulation (LES) closures: the Smagorinsky (Smag) and Leith eddy-viscosity models (1 free parameter) and the Jansen-Held (JH) backscattering model (2 free parameters). For 8 cases of 2D geophysical turbulence, optimal parameters are estimated, using ensemble Kalman inversion (EKI), such that for each case, the LES' energy spectrum matches that of direct numerical simulation (DNS). Only a small training dataset is needed to calculate the DNS spectra (i.e., the approach is {data-efficient}). We find the optimized parameter(s) of each closure to be constant across broad flow regimes that differ in dominant length scales, eddy/jet structures, and dynamics, suggesting that these closures are {generalizable}. In a-posteriori tests based on the enstrophy spectra and probability density functions (PDFs) of vorticity, LES with optimized closures outperform the baselines (LES with standard Smag, dynamic Smag or Leith), particularly at the tails of the PDFs (extreme events). In a-priori tests, the optimized JH significantly outperforms the baselines and optimized Smag and Leith in terms of interscale enstrophy and energy transfers (still, optimized Smag noticeably outperforms standard Smag). The results show the promise of combining advances in physics-based modeling (e.g., JH) and data-driven modeling (e.g., {online} learning with EKI) to develop data-efficient frameworks for accurate, interpretable, and generalizable closures.
Yifei Guan, Pedram Hassanzadeh
Physics-based closures such as eddy-viscosity and backscattering models are widely used for large-eddy simulation (LES) of geophysical turbulence for applications including weather and climate prediction. However, these closures have parameters that are often chosen empirically. Here, for the first time, we semi-analytically derive the parameters of the Leith and Smagorinsky eddy-viscosity closures and the Jansen-Held backscattering closure for 2D geophysical turbulence. The semi-analytical derivation provides these parameters up to a constant that can be estimated from the turbulent kinetic energy spectrum of a few snapshots of direct numerical simulation (DNS) or other high-fidelity (eddy resolving) simulations, or even obtained from earlier analytical work based on renormalization group. The semi-analytically estimated closure parameters agree with those obtained from online (a-posteriori) learning in several setups of 2D geophysical turbulence in our earlier work. LES with closures that use these parameters can correctly reproduce the key statistics of DNS, including those of the extreme events and interscale energy and enstrophy transfers, and outperform the baselines (dynamic Leith and Smagorinsky and the latter with standard parameter).
Qi Wang, Yifei Guan, Junyu Huang, Jian Wu
The two-dimensional regular and chaotic electro-convective flow states of a dielectric liquid between two infinite parallel planar electrodes are investigated using a two-relaxation-time lattice Boltzmann method. Positive charges injected at the metallic planar electrode located at the bottom of the dielectric liquid layer are transported towards the grounded upper electrode by the synergy of the flow and the electric field. The various flow states can be characterized by a non-dimensional parameter, the electric Rayleigh number. Gradually increasing the electric Rayleigh number, the flow system sequentially evolves via quasi-periodic, periodic, and chaotic flow states with five identified bifurcations. The turbulence kinetic energy spectrum is shown to follow the -3 law as the flow approaches turbulence. The spectrum is found to follow a -5 law when the flow is periodic.
Yifei Guan, Ashesh Chattopadhyay, Adam Subel, Pedram Hassanzadeh
There is a growing interest in developing data-driven subgrid-scale (SGS) models for large-eddy simulation (LES) using machine learning (ML). In a priori (offline) tests, some recent studies have found ML-based data-driven SGS models that are trained on high-fidelity data (e.g., from direct numerical simulation, DNS) to outperform baseline physics-based models and accurately capture the inter-scale transfers, both forward (diffusion) and backscatter. While promising, instabilities in a posteriori (online) tests and inabilities to generalize to a different flow (e.g., with a higher Reynolds number, Re) remain as major obstacles in broadening the applications of such data-driven SGS models. For example, many of the same aforementioned studies have found instabilities that required often ad-hoc remedies to stabilize the LES at the expense of reducing accuracy. Here, using 2D decaying turbulence as the testbed, we show that deep fully convolutional neural networks (CNNs) can accurately predict the SGS forcing terms and the inter-scale transfers in a priori tests, and if trained with enough samples, lead to stable and accurate a posteriori LES-CNN. Further analysis attributes these instabilities to the disproportionally lower accuracy of the CNNs in capturing backscattering when the training set is small. We also show that transfer learning, which involves re-training the CNN with a small amount of data (e.g., 1%) from the new flow, enables accurate and stable a posteriori LES-CNN for flows with 16x higher Re (as well as higher grid resolution if needed). These results show the promise of CNNs with transfer learning to provide stable, accurate, and generalizable LES for practical use.
Yifei Guan, Adam Subel, Ashesh Chattopadhyay, Pedram Hassanzadeh
We demonstrate how incorporating physics constraints into convolutional neural networks (CNNs) enables learning subgrid-scale (SGS) closures for stable and accurate large-eddy simulations (LES) in the small-data regime (i.e., when the availability of high-quality training data is limited). Using several setups of forced 2D turbulence as the testbeds, we examine the {\it a priori} and {\it a posteriori} performance of three methods for incorporating physics: 1) data augmentation (DA), 2) CNN with group convolutions (GCNN), and 3) loss functions that enforce a global enstrophy-transfer conservation (EnsCon). While the data-driven closures from physics-agnostic CNNs trained in the big-data regime are accurate and stable, and outperform dynamic Smagorinsky (DSMAG) closures, their performance substantially deteriorate when these CNNs are trained with 40x fewer samples (the small-data regime). We show that CNN with DA and GCNN address this issue and each produce accurate and stable data-driven closures in the small-data regime. Despite its simplicity, DA, which adds appropriately rotated samples to the training set, performs as well or in some cases even better than GCNN, which uses a sophisticated equivariance-preserving architecture. EnsCon, which combines structural modeling with aspect of functional modeling, also produces accurate and stable closures in the small-data regime. Overall, GCNN+EnCon, which combines these two physics constraints, shows the best {\it a posteriori} performance in this regime. These results illustrate the power of physics-constrained learning in the small-data regime for accurate and stable LES.
Yifei Guan, Adrien Bouhon, Oleg V. Yazyev
Two-dimensional systems with $C_{2}\mathcal{T}$ ($P\mathcal{T}$) symmetry exhibit the Euler class topology $E\in\mathbb{Z}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating phases in the presence of an external magnetic field, we reveal the robust gaplessness of the Hofstadter butterfly spectrum in the flat-band limit, while for the dispersive bands the gapping of the Landau levels is controlled by a hidden symmetry. We also find that the Euler class $E$ of a two-band subspace gives a lower bound for the Chern numbers of the magnetic subgaps. Our study provides new fundamental insights into the fragile topology of flat-band systems going beyond the special case of $E=1$ as e.g.~in twisted bilayer graphene, thus opening the way to a very rich, still mainly unexplored, topological landscape with higher Euler classes.
Yifei Guan, Oleg V. Yazyev
Real-world samples of graphene often exhibit various types of out-of-plane disorder -- ripples, wrinkles and folds -- introduced at the stage of growth and transfer processes. These complex out-of-plane defects resulting from the interplay between self-adhesion of graphene and its bending rigidity inevitably lead to the scattering of charge carriers thus affecting the electronic transport properties of graphene. We address the ballistic charge-carrier transmission across the models of out-of-plane defects using tight-binding and density functional calculations while fully taking into account lattice relaxation effects. The observed transmission oscillations in commensurate graphene wrinkles are attributed to the interference between intra- and interlayer transport channels, while the incommensurate wrinkles show vanishing backscattering and retain the transport properties of flat graphene. The suppression of backscattering reveals the crucial role of lattice commensuration in the electronic transmission. Our results provide guidelines to controlling the transport properties of graphene in presence of this ubiquitous type of disorder.
Owen Hutchinson, Katerina Kostova, Jian Wu, Yifei Guan
Turbulent convection is ubiquitous in fluid systems. In particular, multi-physical convection problems involve mass, heat, and particle transfer. When the particles are charged and driven by a high-voltage electric field, both buoyancy and electric forces contribute to driving and maintaining the convection. In this work, we perform numerical analysis using a high-fidelity Fourier-Chebyshev spectral solver. We further derive the dynamical systems governing the kinetic energy, the enstrophy, the potential energy, and the electric energy analytically. Using the simulated data, we apply a long short-term memory recurrent neural network to predict the chaotic time series of domain-average energy terms. Finally, we perform a data-driven modal decomposition to show the coherent structures that contain energy and enstrophy in 2D turbulent convection.
Yifei Guan, Lucas Amoudruz, Sergey Litvinov, Karan Jakhar, Rambod Mojgani, Petros Koumoutsakos, Pedram Hassanzadeh
Accurate subgrid-scale closures are essential for weather/climate models, where predicting extreme events is critical. Traditional closures have structural errors, e.g., producing excessive diffusion that dampens extremes. Artificial intelligence has gained attention for closure modeling, but the prediction of extreme events remains challenging. Supervised offline learning needs abundant high-fidelity training data and can lead to instabilities. Online learning algorithms are emerging as an alternative, but reliance on differentiable numerical solvers or scalable optimizers hinders broad use. Here, we introduce SMARL to develop closures for canonical prototypes of atmospheric/oceanic turbulence, using only the enstrophy spectrum, estimated from a few high-fidelity samples, as reward. This reward ensures that the model captures the cascades of scales in these simulations. These online-learned closures enable stable simulations, with up to five orders of magnitude fewer degrees of freedom, that reproduce high-fidelity simulation statistics and capture in particular extremes. We interpret the closures by analyzing the SMARL policy and demonstrate generalization to other flows. The results highlight SMARL as a potent tool for developing closures capable of capturing extremes in atmospheric/oceanic flows, opening new capabilities for effective climate modeling.
Ravi Sankar Vaddi, Yifei Guan, Alexander Mamishev, Igor Novosselov
Electrohydrodynamic (EHD) thrust is produced when ionized fluid is accelerated in an electric field due to the momentum transfer between the charged species and neutral molecules. We extend the previously reported analytical model that couples space charge, electric field, and momentum transfer to derive thrust force in 1D planar coordinates. The electric current density in the model can be expressed in the form of Mott-Gurney law. After the correction for the drag force, the EHD thrust model yields good agreement with the experimental data from several independent studies. The EHD thrust expression derived from the first principles can be used in the design of propulsion systems and can be readily implemented in the numerical simulations.
Ravi Sankar Vaddi, Yifei Guan, Igor Novosselov
Ultrafine particle behavior in electro-hydrodynamic (EHD) flow induced by corona discharge is studied experimentally and numerically. The EHD flow serves as a primary particle aspiration/sampling mechanism, the collector does not require any additional flow generation. Multiphysics numerical model couples the ion transport equation and the Navier-Stokes equations (NSE) to solve for the spatiotemporal distribution of electric field, charge density, and flow field, the results are compared with experimental velocity profiles at the exit. The computed velocity and flow rate data are in good agreement with the experimental data; the maximum velocity is located at the axis and ranges from 1 m/s to 4 m/s as a function of corona voltage. Experimentally evaluated particle transmission trends for ambient and NaCl nanoparticles particles in the 20 nm - 150 nm range are in good agreement with the theoretical models. However, for particles in the 10 nm - 20 nm size range, the transmission is lower due to the increased particle charging resulted from their exposure to the high-intensity electric field and high charge density in the EHD driven flow. These conditions yield a high probability of particles below 20 nm to acquire and hold a unit charge. The transmission is lower for smaller particle (10 nm) due to their high charge to mass ratio, and it increases as the single-charged particles grow in mass up to 20 nm, resulting in their lower electrical mobility. For particles larger than 20 nm, the electrical mobility increases again as they can acquire multiple charges. The results shed insight into interaction of nanoparticle and ions in high electrical field environment, that occur in primary EHD driven flows and in the secondary flows generated by corona discharge.
Yifei Guan, Junyu Huang, Jian Wu
The 1D hydrostatic base state of electroconvection driven by unipolar charge injection between two parallel electrodes is investigated using a finite difference method. A boundary layer near the anode surface is derived analytically. The computational grid is required to resolve this boundary layer to maintain high order accuracy.
Yifei Guan, Igor Novosselov
Numerical simulation of Electroconvective vortices behavior in the presence of Couette flow between two infinitely long electrodes is investigated. The two-relaxation-time Lattice Boltzmann Method with fast Poisson solver solves for the spatiotemporal distribution of flow field, electric field, and charge density. Couette cross-flow is applied to the solutions after the electroconvective vortices are established. Increasing cross-flow velocity deforms the vortices and eventually suppresses them when threshold values of shear stress are reached.
Yifei Guan, Igor Novosselov
Electroconvective flow between two infinitely long parallel electrodes is investigated via a multiphysics computational model. The model solves for spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann Method for fluid and charge transport coupled to Fast Fourier Transport Poisson solver for the electric potential. The segregated model agrees with the previous analytical and numerical results providing a robust approach for modeling electrohydrodynamic flows.
Adam Subel, Ashesh Chattopadhyay, Yifei Guan, Pedram Hassanzadeh
Developing data-driven subgrid-scale (SGS) models for large eddy simulations (LES) has received substantial attention recently. Despite some success, particularly in a priori (offline) tests, challenges have been identified that include numerical instabilities in a posteriori (online) tests and generalization (i.e., extrapolation) of trained data-driven SGS models, for example to higher Reynolds numbers. Here, using the stochastically forced Burgers turbulence as the test-bed, we show that deep neural networks trained using properly pre-conditioned (augmented) data yield stable and accurate a posteriori LES models. Furthermore, we show that transfer learning enables accurate/stable generalization to a flow with 10x higher Reynolds number.
Karan Jakhar, Yifei Guan, Pedram Hassanzadeh
By combining AI and fluid physics, we discover a closed-form closure for 2D turbulence from small direct numerical simulation (DNS) data. Large-eddy simulation (LES) with this closure is accurate and stable, reproducing DNS statistics including those of extremes. We also show that the new closure could be derived from a 4th-order truncated Taylor expansion. Prior analytical and AI-based work only found the 2nd-order expansion, which led to unstable LES. The additional terms emerge only when inter-scale energy transfer is considered alongside standard reconstruction criterion in the sparse-equation discovery.
Yifei Guan, Oleg V. Yazyev, Alexander Kruchkov
In this work we address the re-entrance of magic-angle phenomena (band flatness and quantum-geometric transport) in twisted bilayer graphene (TBG) subjected to strong magnetic fluxes $\pm Φ_0$, $\pm 2 Φ_0$, $\pm 3 Φ_0$... ($Φ_0 = h/e$ is the flux quantum per moiré cell). The moiré translation invariance is restored at the integer fluxes, for which we calculate the TBG band structure using accurate atomistic models with lattice relaxations. Similarly to the zero-flux physics outside the magic angle condition, the reported effect breaks down rapidly with the twist. We conclude that the magic-angle physics re-emerges in high magnetic fields, witnessed by the appearance of flat electronic bands distinct from Landau levels, and manifesting non-trivial quantum geometry. We further discuss the possible flat-band quantum geometric contribution to the superfluid weight in strong magnetic fields (28 T at 1.08$^\circ$ twist), according to Peotta-Törmä mechanism.