Guiding Applications
Turbulence, Convection, and Clouds in Climate Models
Lead: Schneider - Closure models for unresolved turbulence, convection, and clouds represent the dominant uncertainties in climate predictions. Diverse data, for example, data from high-resolution simulations and satellite observations of temperature, humidity, and cloud cover, are now available and are informative about these processes, albeit usually only indirectly. They are underutilized in climate modeling due to the challenge of harnessing heterogeneous multi-fidelity data. We use the methodological framework to learn ML-based closure models in recently developed physics-based TCC models from diverse data, quantify their uncertainties, and propagate the uncertainties into climate predictions.
Bias-Aware Stochastic Turbulence Closure Models
Lead: Colonius - Correct predictions of the statistics of turbulent flows are adequate for many engineering design problems. However, important design optimization tasks are beyond reach, either due to the expense of high-fidelity turbulence simulations such as large-eddy-simulation (LES), or due to the lack of required accuracy for low-cost statistical closure models (i.e., Reynolds-averaged Navier stokes, RANS). We will introduce a new closure paradigm to accurately predict the mean and low-order statistics, using RANS-type models, based on an ensemble of lower-fidelity LES-type simulations on meshes of varying refinement.
Using ML ideas, the ensemble space is interrogated to capture models of statistical bias caused by the coarse resolution. In particular the bias model and gain operator are learned by combining ideas from data assimilation and ML. The assimilation framework initially uses (partial) truth data from fully-resolved simulations that includes both individual realizations and their statistics, but the framework is flexible enough to incorporate experimental data when available. Recent ideas regarding inpainting in computer vision are closely related to data assimilation.
Stochastic Particle Dynamics In Complex Fluids
Lead: Brenner - Many models of complex fluids and materials are modeled by stochastic particle dynamics, whereby particles interact via interaction potentials with stochastic forcing emulating thermal fluctuations.
Examples range from Stokesian dynamics to the interactions of colloidal particles to the dynamics of bubbles in turbulent flows. Any description of the dynamics is necessarily probabilistic; yet up until now, it has been impossible to characterize these distributions in strongly interacting systems. We investigate how to use ML-based representations to parameterize the probability distribution of such dense particle systems, fitting a distribution parameterized by outputs of neural operators. After validating accuracy we use these systems for an array of applications, including both forward and inverse problems. Examples include: parameterizing rheology of dense suspensions, and designing the characteristics of the suspension to achieve target rheologies; advance the state of art for particle tracking in high speed movies of dense suspensions with confocal microscopy; finding the interaction potentials for particles from their tracks alone. An application of the latter is deducing effective potentials of bubbles in turbulent fluid flows.
Free-Boundary and Free-Discontinuity Problems
Lead: Bhattacharya - Many physical phenomena are formulated as free-boundary (melting and solidification, contact lines, adhesive fronts, dislocation loops) and free-discontinuity (fracture) problems. Instabilities, nucleation, heterogeneities, and pinning/depinning lead to complex morphologies (dendrites, riverine fracture surface) and topology changes that necessitate high spatial and temporal resolution that make full-scale simulations currently beyond reach. Experimental observations of interfaces and cracks deep inside the material are also difficult and expensive, despite rapid advances in x-ray tomography and related techniques. However, one has (indirect and noisy) data in terms of surface fluxes, low-resolution tomography, and short-time or small-domain simulations. The ML-based closure models being developed will enable full-scale simulations with quantified uncertainties. Further, fast predictors of the approximate trajectory can be used as surrogates for planning and controlling experiments.