Efficient and Scalable Machine Learning Methods for Robust Bayesian Optimal Experimental Design
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Go, Jinwoo
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Abstract
This thesis addresses key challenges in Bayesian Optimal Experimental Design (BOED) for complex systems, focusing on robustness, computational efficiency, and sequential design.
Estimating model parameters to understand physical systems is crucial for better comprehension and prediction. However, knowing the parameters thoroughly is difficult because we cannot access them directly. We need to estimate the model parameters through specific experiments. To evaluate each experiment, we simulate it, assess the model parameter update after the experiment, and calculate how it differs from the prior assumption. However, the optimal experiment could be sub-optimal if the prior distribution is misspecified. Additionally, updating the model parameter for high-dimensional real-world problems constrained by PDEs is computationally expensive. In sequential BOED, we need to consider sequential observations, necessitating a systematic approach to handle this problem.
To address the challenge of prior misspecification and enhance robustness, we develop a distributionally robust BOED approach using ambiguity sets to address the issue of misspecified priors. This method optimizes for the worst-case scenario within a set of plausible prior distributions, ensuring robustness without increasing computational complexity. It can be used as a log-sum-exp regularizer to alleviate the under-sample problem of estimating information gain.
Overcoming the computational burden associated with large-scale PDE-constrained problems, we introduce a computational framework for one-step BOED with derivative-informed neural operators (DINO) to enhance computational efficiency in high-dimensional settings. This approach combines dimension reduction techniques with efficient computation of the maximum a posteriori (MAP) point and posterior covariance matrix, effectively calculating various optimality criteria. It is 1000 times more efficient than solving with the Finite Element Method (FEM), even when accounting for the generating training data set for the neural network.
To tackle the sequential BOED for PDE-constrained problems, we propose a novel neural operator tailored for sequential BOED in PDE-constrained settings. We train the dynamics in the latent space with an attention model to capture the evolving dynamics. This method reduces computational cost while maintaining prediction accuracy and addresses the computational challenge of high-dimensional time-dependent simulation. It also offers a framework for balancing greedy and global optimization and interpretability.
Our contributions make BOED more robust, efficient, and applicable to complex, real-world experimental design problems involving PDEs. The developed methods offer improved robustness to prior misspecification, enhanced computational efficiency, and effective sequential design strategies. These advances have potential applications in environmental engineering, chemical engineering, and other physical systems governed by PDEs.
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Date
2024-09-18
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Dissertation