The rise of modern machine learning (ML) has profoundly reshaped hydrologic modeling by delivering unprecedented predictive accuracy. Models such as the Long Short-Term Memory (LSTM) network and, more recently, deep state-space architectures have achieved remarkable success in the classical rainfall–runoff (RR) problem, setting new benchmarks within the hydrologic science community. In contrast to the traditional principle of parsimony (Occam’s razor) that guides scientific modeling, these neural network–based approaches often rely on large, heterogeneous datasets to train a single massive architecture following neural scaling laws. However, improvements in predictive performance have not necessarily been accompanied by advances in physical or conceptual understanding, thereby limiting the acceptance of deep learning models among physics-based modelers and their contribution to scientific insight.

To address this gap, the Mass-Conserving Perceptron (MCP)—a physically interpretable computational unit—has been proposed to bridge the divide between physics-based and machine-learning–based modeling approaches. This talk, based on a series of four manuscripts on the MCP, first illustrates how the inherent isomorphic relationship between a simple mass-conserving physical system and a gated recurrent neural network led to the conceptual development of this framework. As a proof of concept, the MCP-based model is evaluated for rainfall–runoff simulation at the humid Leaf River catchment in Mississippi, exploring the behavioral expressivity and physical interpretability achievable by a single MCP node enabled by its learnable, time-varying gating mechanism. Next, I will demonstrate how this physically interpretable single-node MCP can be used to construct both traditional hydrologic model architectures and modern deep neural networks and compare their performance against conceptual rainfall–runoff (CRR) models and LSTMs at the catchment scale. Finally, I will present recent progress from a large-sample investigation across 513 CAMELS-US catchments, highlighting the potential of MCP as a theory-informed and physically grounded ML framework for large-sample hydrology—emphasizing mechanistic understanding, parsimony, and interpretability toward developing future “models of everywhere.”

Overall, this series of studies suggests a paradigm shift from emphasizing predictive accuracy to advancing scientific understanding. It paves the way for several future research directions, including the development and modification of parsimonious, physically interpretable neural networks—such as the Kolmogorov–Arnold Network inspired by the Kolmogorov neural network existence theorem—at the catchment scale, as well as exploring neural network compression through pruning, trained quantization, and Huffman coding within emerging paradigms such as tinyML and neural evolution.