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Estimating mutual correlations between random variables or data streams is essential for intelligent behavior and decision-making. As a fundamental quantity for measuring statistical relationships, mutual information has been extensively…

A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure…

The computational prediction of the structure and stability of hybrid organic-inorganic interfaces provides important insights into the measurable properties of electronic thin film devices, coatings, and catalyst surfaces and plays an…

The objective of this Philosophiae Doctor (Ph.D) thesis is to propose an efficient approach for optimizing a multidisciplinary black-box model when the optimization problem is constrained and involves a large number of mixed integer design…

Design optimization techniques are often used at the beginning of the design process to explore the space of possible designs. In these domains illumination algorithms, such as MAP-Elites, are promising alternatives to classic optimization…

Efficient optimization of molecules with targeted properties remains a significant challenge due to the vast size and discrete nature of chemical compound space. Conventional machine-learning-based optimization approaches typically require…

Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density…

Large-scale numerical simulations underpin modern scientific discovery but remain constrained by prohibitive computational costs. AI surrogates offer acceleration, yet adoption in mission-critical settings is limited by concerns over…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research -- unimportant input variables and…

Machine learning has been effective at detecting patterns and predicting the response of systems that behave free of natural laws. Examples include learning crowd dynamics, recommender systems and autonomous mobility. There also have been…

Operator-based neural network architectures such as DeepONets have emerged as a promising tool for the surrogate modeling of physical systems. In general, towards operator surrogate modeling, the training data is generated by solving the…

Hyperparameter optimization (HPO) is a fundamental problem in automatic machine learning (AutoML). However, due to the expensive evaluation cost of models (e.g., training deep learning models or training models on large datasets), vanilla…

The performance of deep neural networks crucially depends on good hyperparameter configurations. Bayesian optimization is a powerful framework for optimizing the hyperparameters of DNNs. These methods need sufficient evaluation data to…

Accurate simulations of the oceans are crucial in understanding the Earth system. Despite their efficiency, simulations at lower resolutions must rely on various uncertain parameterizations to account for unresolved processes. However,…

We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…

A surrogate function is often employed to reduce the number of objective function evaluations for optimization. However, the effect of using a surrogate model in evolutionary approaches has not been theoretically investigated. This paper…

Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based…

Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically involves high-dimensional spaces of possibly correlated…

Distributed learning offers a practical solution for the integrative analysis of multi-source datasets, especially under privacy or communication constraints. However, addressing prospective distributional heterogeneity and ensuring…