Training Physics-Guided Neural Networks with Multiple Constraints: An Application in Lake Ecology Modeling

Abstract

Lakes and reservoirs are critical components of Earth's ecosystems but are increasingly threatened by climate change and human activity, underscoring the need for reliable tools for modeling and predicting lake ecology. While machine learning has shown potential in modeling such systems, sparse environmental data often limits the ability of machine learn- ing models to produce physically consistent predictions or generalize to novel conditions. As a result, many existing approaches rely on computationally intensive physics-biogeochemical simulations to supplement training data. Physics-Guided Neural Networks (PGNN) offer a promising alternative by embedding scientific knowledge directly into the model through physical constraints applied during training. However, training these models at scale remains challenging due to the trade-offs between satisfying physical laws and fitting the data, often leading to optimization pathologies. This thesis explores the challenge of designing, training and evaluating PGNNs with up to six constraints without relying on auxillary simulation data. We assemble a suite of physics-based constraints grounded in limnological principles and evaluate their impact on neural network predictions by assessing within-distribution and zero-shot performance. To navigate the challenge of training with multiple constraints, we explore the use of multitask learning methods to counteract gradient pathologies that arise when training PGNNs. Our results suggest that multitask learning approaches can improve in-distribution performance in certain architectures, but they do not enhance zero- shot performance compared to unconstrained models. Our findings highlight the inherent complexity of scaling PGNNs and emphasize the need for principled training methodologies in data-scarce modeling contexts.