Generalized Polynomial Chaos for Data-Driven Model Generation and Validation

Barron Associates, in partnership with the Hume Center at Virginia Tech, proposes to develop a comprehensive model generation and validation approach that leverages recent advances in generalized polynomial chaos (gPC) theory. Similar to neural-network-based artificial intelligence/machine learning (AI/ML) approaches, solutions based on gPC theory learn by adjusting the weights in a linear combination of nonlinear functions that operate on input data. gPC offers a number of distinct advantages over typical AI/ML formulations, which are important for this application. Foremost among them is that, gPC representations can be learned from analytical models, high-fidelity simulation data, hardware-in-the-loop data, flight-test data, or any combination thereof. Moreover, algorithms for learning parameters of a gPC model have a very direct and computationally efficient form. This efficient form can be used to conduct the repeated model generation and evaluation steps required for cross-validation. Once a model structure has been defined, each new batch of available data can be used to refine and validate the model. In Phase II, a general-purpose model generation and validation toolset will be constructed that packages these techniques in an easy-to-use software application. Approved for Public Release | 21-MDA-11013 (19 Nov 21)