Tayal, Kshitij2025-01-282025-01-282024-08https://hdl.handle.net/11299/269587University of Minnesota Ph.D. dissertation. August 2024. Major: Computer Science. Advisor: Vipin Kumar. 1 computer file (PDF); x, 82 pages.Machine learning (ML) has revolutionized various aspects of our lives, including decision-making, entertainment, and social recommendations. The power of ML models lies in their capability to automatically identify patterns in training data. Given their demonstrated effectiveness in computer vision and natural language processing, there’s a growing interest in leveraging ML for environmental science advancements. However, environmental science datasets present unique challenges. They are often heterogeneous, encompassing a broad spectrum of static and dynamic variables, and pose difficulties in handling temporal dynamics due to their inherent complexities.This thesis presents a comprehensive exploration of latent space modeling techniques developed to improve the accuracy and efficiency of environmental and hydrological predictions. The crux of this research lies in developing and applying machine learning models that can effectively integrate and analyze various data types, ranging from static to time-series data, and overcome the limitations of traditional models in predicting complex environmental systems. The first part of the thesis introduces the Invertibility-Aware-Long Short-Term Memory (IA-LSTM) model, which integrates aspects of Invertible Networks and LSTM.This model is specifically designed to predict lake temperatures across various systems, demonstrating significant improvements in prediction accuracy, especially in scenarios with missing static features. The effectiveness of IA-LSTM is validated through its application to temperature profiles of lakes in the Midwestern U.S., showcasing its ability to outperform baseline models and capture data heterogeneity. The second part delves into the Koopman Invertible Autoencoders (KIA), a model based on the Koopman operator theory. KIA is adept at capturing both forward and backward dynamics in infinite-dimensional Hilbert space, leading to more precise long-term predictions. This model’s utility is shown through its application to climate datasets, where it achieves a significant improvement in long-term prediction capability, demonstrating its robustness against noise. The final part of the thesis introduces the Koopman Invertible Disentangling Autoencoder (KIDA), a model that disentangles inherent characteristics from other dynamic factors in hydrological systems. KIDA utilizes the Koopman operator to model complex hydrological systems, enabling the accurate recovery of multiple disentangled variation factors. Applied to a hydrometeorological dataset, KIDA outperforms competing methods in reconstructing characteristics and exhibits superior robustness to distortion. The findings of this thesis demonstrate the potential of advanced machine learning in environmental applications and also pave the way for future research in this rapidly growing domain.enThesis or Dissertation