UC Santa Barbara

Computer models and simulators are widely used for understanding complex processes, whereas the computational cost can be large. This thesis introduces new efficient surrogate models for predicting expensive simulations, and adaptive designs for inversely optimizing system properties, particularly focusing on scenarios where the dimension of the inputs or outputs is large. One such scenario is the molecular simulation, which is an indispensable component in understanding the intricate relationship between molecular configurations and their associated properties. Constructing an efficient surrogate model can expedite predictions of molecular behaviors of many new chemical structures. Furthermore, it can accelerate discoveries in critical fields such as materials design, drug discovery, and chemoinformatics, through efficient designs by utilizing predictions from surrogate models and their associated assessment of prediction uncertainty. Gaussian process (GP) emulator has been used as a surrogate model for both scalar-valued and vectorized outputs from computer models. In applications like predicting molecular force fields and potential energy in \emph{ab initio} molecular dynamics simulation, the GPs can substantially improve predictive accuracy using both gradient information and functional values whereas conventional approximation methods may not work well. The computational cost of GPs, however, can be substantial. To address this challenge, Chapter 2 introduces a new approach, termed the atomized force field (AFF) model, which combines force and energy prediction in a computationally efficient manner. This model establishes a forward mapping from molecule configuration to the molecular force field and potential energy, substantially reducing computational demands by exploiting the naturally sparse covariance structure that adheres to energy conservation and atom permutation symmetry constraints. Built upon the AFF model, Chapter 3 explores novel methods to construct reverse mapping of 3D molecule structures from molecular force fields and potential energy. This approach offers fast solutions to some applications, such as finding the equilibrium state of the molecular through the minimization of atomic forces. Additionally, a Python package of the surrogate model called PyRobustGaSP is introduced in Chapter 4, for emulating computer models with massive data with robust parameter estimation and predictions.