Machine Learning for Computational Optimization

Abstract

The exponential growth of computational power has transformed our ability to model and interact with the world, from simulating trillions of atoms in complex molecular dynamics studies to processing billions of financial transactions daily. Despite this progress, computational resources remain fundamentally bounded, creating a critical challenge for applications like climate modeling, where accurate simulations could require orders of magnitude more computing power than currently available. This limitation drives researchers to develop approximations that trade computational cost for solution quality. This thesis investigates how machine learning algorithms can optimize this cost-quality trade-off in computationally constrained environments. We advance the state of the art through two primary approaches: (1) developing novel machine learning-based emulators that enhance computational efficiency while maintaining solution quality, and (2) creating adaptive computational reasoning models that optimize resource allocation across different approximation fidelities. In ice-sheet modeling—our central case study—we show how Gaussian Process emulators combined with multi-fidelity experimental design can produce accurate sea-level rise predictions while reducing computational costs by up to 70%. By unifying concepts from computational approximation, resource allocation, and machine learning, this thesis provides a comprehensive framework for understanding and addressing computational constraints in scientific modeling. Our results demonstrate practical pathways to improve climate science predictions, particularly for ice-sheet dynamics and resulting sea-level rise forecasts, which are critical for developing effective climate change mitigation strategies. }