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By querying approximate surrogate models of different fidelity as available information sources, Multi-Fidelity Bayesian Optimization (MFBO) aims at optimizing unknown functions that are costly or infeasible to evaluate. Existing MFBO methods often assume that approximate surrogates have consistently high or low fidelity across the input domain. However, approximate evaluations from the same surrogate can have different fidelity at different input regions due to data availability and model constraints, especially when considering machine learning surrogates. In this work, we investigate MFBO when multi-fidelity approximations have input-dependent fidelity. By explicitly capturing input dependency for multi-fidelity queries in a Gaussian Process (GP), our new input-dependent MFBO (iMFBO) with learnable noise models better captures the fidelity of each information source in an intuitive way. We further design a new acquisition function for iMFBO and prove that the queries selected by iMFBO have higher quality than those by naive MFBO methods, with a derived sub-linear regret bound. Experiments on both synthetic and real-world data demonstrate its superior empirical performance. 

Thanks to the rapid advances in artificial intelligence, AI for science (AI4Science) has emerged as one of the new promising research directions for modern science and engineering. In this review, we focus on recent efforts to develop knowledge-driven Bayesian learning and experimental design methods for accelerating the discovery of novel functional materials as well as enhancing the understanding of composition-process-structure-property relationships. We specifically discuss the challenges and opportunities in integrating prior scientific knowledge and physics principles with AI and machine learning (ML) models for accelerating materials and knowledge discovery. The current state-of-the-art methods in knowledge-based prior construction, model fusion, uncertainty quantification, optimal experimental design, and symbolic regression are detailed in the review, along with several detailed case studies and results in materials discovery. 

Designing and/or controlling complex systems in science and engineering relies on appropriate mathematical modeling of systems dynamics. Classical differential equation based solutions in applied and computational mathematics are often computationally demanding. Recently, the connection between reduced-order models of high-dimensional differential equation systems and surrogate machine learning models has been explored. However, the focus of both existing reduced-order and machine learning models for complex systems has been how to best approximate the high fidelity model of choice. Due to high complexity and often limited training data to derive reduced-order or machine learning surrogate models, it is critical for derived reduced-order models to have reliable uncertainty quantification at the same time. In this paper, we propose such a novel framework of Bayesian reduced-order models naturally equipped with uncertainty quantification as it learns the distributions of the parameters of the reduced-order models instead of their point estimates. In particular, we develop learnable Bayesian proper orthogonal decomposition (BayPOD) that learns the distributions of both the POD projection bases and the mapping from the system input parameters to the projected scores/coefficients so that the learned BayPOD can help predict high-dimensional systems dynamics/fields as quantities of interest in different setups with reliable uncertainty estimates. The developed learnable BayPOD inherits the capability of embedding physics constraints when learning the POD-based surrogate reduced-order models, a desirable feature when studying complex systems in science and engineering applications where the available training data are limited. Furthermore, the proposed BayPOD method is an end-to-end solution, which unlike other surrogate-based methods, does not require separate POD and machine learning steps. The results from a real-world case study of the pressure field around an airfoil. 

Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can be more efficient. In this work, we consider noisy adaptive group testing design with specific test sensitivity and specificity that select the optimal group given previous test results based on pre-selected utility function. As in prior studies on group testing, we model this problem as a sequential Bayesian Optimal Experimental Design (BOED) to adaptively design the groups for each test. We analyze the required number of group tests when using the updated posterior on the infection status and the corresponding Mutual Information (MI) as our utility function for selecting new groups. More importantly, we study how the potential bias on the ground-truth noise of group tests may affect the group testing sample complexity.