Adaptive Multi-Fidelity Modeling for Efficient Design Exploration Under Uncertainty

This thesis work introduces a novel multi-fidelity modeling framework, which is designed to address the practical challenges encountered in Aerospace vehicle design when 1) multiple low-fidelity models exist, 2) each low-fidelity model may only be correlated with the high-fidelity model in part of the design domain, and 3) models may contain noise or uncertainty. The proposed approach approximates a high-fidelity model by consolidating multiple low-fidelity models using the localized Galerkin formulation. Also, two adaptive sampling methods are developed to efficiently construct an accurate model. The first acquisition formulation, expected effectiveness, searches for the global optimum and is useful for modeling engineering objectives. The second acquisition formulation, expected usefulness, identifies feasible design domains and is useful for constrained design exploration. The proposed methods can be applied to any engineering systems with complex and demanding simulation models

Epistemic Modeling Uncertainty of Rapid Neural Network Ensembles for Adaptive Learning

Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network models are trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty caused due to lack of training samples. This uncertainty estimation is crucial information for successful goal-oriented adaptive learning in an aerospace system design exploration. However, the costs of training the ensemble models often become prohibitive and pose a computational challenge, especially when the models are not trained in parallel during adaptive learning. In this work, a new type of emulator embedded neural network is presented using the rapid neural network paradigm. Unlike the conventional neural network training that optimizes the weights and biases of all the network layers by using gradient-based backpropagation, rapid neural network training adjusts only the last layer connection weights by applying a linear regression technique. It is found that the proposed emulator embedded neural network trains near-instantaneously, typically without loss of prediction accuracy. The proposed method is demonstrated on multiple analytical examples, as well as an aerospace flight parameter study of a generic hypersonic vehicle

A Machine Learning Framework for Hypersonic Vehicle Design Exploration

The design of Hypersonic Vehicles (HVs) requires meeting multiple unconventional and often conflicting design requirements in a hostile, high-energy environment. The most fundamental difference between ordinary aerospace design and hypersonic flight is that the extreme conditions of hypersonic flight require parts to perform multiple functions and be tightly integrated, resulting in significant coupled effects. Critical couplings among the disciplines of aerodynamics, structures, propulsion, and thermodynamics must be investigated in the early stages of design exploration to reduce the risk of requiring major design changes and cost overruns later. In addition, due to a lack of validated test data within the coupled high-dimensional design domains, concept design exploration of HVs poses unprecedented challenges, especially in terms of computational costs and decision-making under uncertainty. A common design exploration technique is to sample the expensive physics-based models in a design of experiments and then use the sample data to train an inexpensive metamodel. Conventional metamodels include Polynomial Chaos Expansion, kriging, and neural networks. However, many simulation evaluations are needed for the design of experiments because of the large number of independent parameters for each design and the complex responses resulting from interactions across multiple disciplines. Because each simulation is expensive, the total costs are often computationally intractable. Computational cost reduction is often achieved using Multi-Fidelity (MF) modeling and Active Learning (AL). MF models supplement High-Fidelity (HF) simulations with less accurate but inexpensive Low-Fidelity (LF) simulations. AL generates training data in an iterative process: rebuilding the metamodel after each HF sample is added, and then using the metamodel to select the next HF sample. Location-specific uncertainty information is critical for making this determination. To address the technical challenges in HV concept design exploration, this work presents a novel machine learning framework. This framework combines NN architectures which robustly integrate LF models with high, low, or unknown accuracy; an ensemble technique to estimate epistemic modeling uncertainty for active learning; and a method for rapidly training neural networks so computational modeling costs remain low. These techniques are demonstrated to enable rapid and meaningful exploration of various hypersonic vehicle design concepts

Epistemic Modeling Uncertainty of Rapid Neural Network Ensembles for Adaptive Learning

Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network models are trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty caused due to lack of training samples. This uncertainty estimation is crucial information for successful goal-oriented adaptive learning in an aerospace system design exploration. However, the costs of training the ensemble models often become prohibitive and pose a computational challenge, especially when the models are not trained in parallel during adaptive learning. In this work, a new type of emulator embedded neural network is presented using the rapid neural network paradigm. Unlike the conventional neural network training that optimizes the weights and biases of all the network layers by using gradient-based backpropagation, rapid neural network training adjusts only the last layer connection weights by applying a linear regression technique. It is found that the proposed emulator embedded neural network trains near-instantaneously, typically without loss of prediction accuracy. The proposed method is demonstrated on multiple analytical examples, as well as an aerospace flight parameter study of a generic hypersonic vehicle