Developing data-driven subgrid-scale (SGS) models for large eddy simulations (LESs) 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 $10\times$ higher Reynolds number.

Transfer learning (TL), which enables neural networks (NNs) to generalize out-of-distribution via targeted re-training, is becoming a powerful tool in scientific machine learning (ML) applications such as weather/climate prediction and turbulence modeling. Effective TL requires knowing (1) how to re-train NNs? and (2) what physics are learned during TL? Here, we present novel analyses and a framework addressing (1)–(2) for a broad range of multi-scale, nonlinear, dynamical systems. Our approach combines spectral (e.g. Fourier) analyses of such systems with spectral analyses of convolutional NNs, revealing physical connections between the systems and what the NN learns (a combination of low-, high-, band-pass filters and Gabor filters). Integrating these analyses, we introduce a general framework that identifies the best re-training procedure for a given problem based on physics and NN theory. As test case, we explain the physics of TL in subgrid-scale modeling of several setups of 2D turbulence. Furthermore, these analyses show that in these cases, the shallowest convolution layers are the best to re-train, which is consistent with our physics-guided framework but is against the common wisdom guiding TL in the ML literature. Our work provides a new avenue for optimal and explainable TL, and a step toward fully explainable NNs, for wide-ranging applications in science and engineering, such as climate change modeling.

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. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling 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.

An electrohydrodynamic (EHD) flow in a point-to-ring corona configuration is investigated experimentally and via a multiphysics computational model. The model couples the ion transport equation and the Navier-Stokes equations (NSE) to solve for the spatiotemporal distribution of electric field, flow field, and charge density. The numerical simulation results are validated against experimental measurements of the cathode voltage, ion concentration, and velocity profiles. The maximum flow velocity is at the centerline, and it decays rapidly with radial distance due to the viscous and electric forces acting on the partially ionized gas. To understand this coupling, 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 $X\ge 1$, the electric force dominates the flow dynamics, while in the $X\ll 1$ region, the balance of viscous and inertial terms yields traditional pipe flow characteristics. This approach expands on the analytical model of Guan et al. by adding a description of the developing flow region. The approach allows the model to be used for the entire EHD domain, providing insights into the near-field flow in the corona region.