Generalizable Physics-constrained Modeling using Learning and Inference assisted by Feature Space Engineering

Abstract

This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to as Learning and Inference assisted by Feature Engineering (LIFE), is based on the hypothesis that robustness and generalizability demand a meticulously-designed feature space that is informed by the underlying physics, and a carefully constructed features-to-augmentation map. The critical components of this approach are : (1) Identification of relevant physics-informed features in appropriate functional forms to enable significant overlap in feature space for a wide variety of cases to promote generalizability; (2) Explicit control over feature space to locally infer the augmentation without affecting other feature space regions, especially when limited data is available; (3) Maintaining consistency across the learning and prediction environments to make the augmentation case-agnostic; (4) Tightly-coupled inference and learning by constraining the augmentation to be learnable throughout the inference process to avoid significant loss of information (and hence accuracy). To demonstrate the viability of this approach, it is used in the modeling of bypass transition. The augmentation is developed on skin friction data from two flat plate cases from the ERCOFTAC dataset. The augmented model is then applied to a variety of flat plate cases which are characterized by different freestream turbulence intensities, pressure gradients, and Reynolds numbers. The predictive capability of the augmented model is also tested on single-stage high-pressure-turbine cascade cases, and the model performance is analyzed from the perspective of information contained in the feature space. The results show consistent improvements across these cases, as long as the physical phenomena in question are well-represented in the training.

Frame invariant neural network closures for Kraichnan turbulence

“…Moreover, neural networks have also been utilized to learn the optimal map between filtered and unfiltered variables in the approximate deconvolution framework for SGS modeling [26,27]. Apart from SGS closure modeling, machine learning (ML) and in particular DL is being increasingly applied for different problems in fluid mechanics, like superresolution of turbulent flows [28,29], Reynolds-Average Navier-Stokes (RANS) closure modeling [30][31][32], and reduced-order modeling [33][34][35][36].…”

Promoting global stability in data-driven models of quadratic nonlinear dynamics

“…into both model reduction [48,90] and system identification [19,49,91,92]. Precisely in this way, the energy-preserving constraint in Eq.…”

PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence

“…Examples of reduced-order PDE models in fluid mechanics include the Reynolds-averaged Navier-Stokes (RANS) equations and Large-eddy Simulation (LES) equations. Recent research has explored using deep learning models for the closure of these equations [52,53,49,39,40,62,22,58,54,41]. In parallel, other classes of machine learning methods have also been developed for PDEs such as the physics-informed neural networks (PINNs) [47,48].…”

“…[4] recently numerically optimized a linear PDE with a neural network source term using adjoint methods. [54,41], [22], and [58] use adjoint methods to calibrate nonlinear PDE models with neural network terms. [4,54,41,22,58] do not include a mathematical analysis of the adjoint method for PDE models with neural network terms.…”