This paper introduces a \textit{Process-Guided Learning (Pril)} framework that integrates physical models with recurrent neural networks (RNNs) to enhance the prediction of dissolved oxygen (DO) concentrations in lakes, which is crucial for sustaining water quality and ecosystem health. Unlike traditional RNNs, which may deliver high accuracy but often lack physical consistency and broad applicability, the \textit{Pril} method incorporates differential DO equations for each lake layer, modeling it as a first-order linear solution using a forward Euler scheme with a daily timestep. However, this method is sensitive to numerical instabilities. When drastic fluctuations occur, the numerical integration is neither mass-conservative nor stable. Especially during stratified conditions, exogenous fluxes into each layer cause significant within-day changes in DO concentrations. To address this challenge, we further propose an \textit{Adaptive Process-Guided Learning (April)} model, which dynamically adjusts timesteps from daily to sub-daily intervals with the aim of mitigating the discrepancies caused by variations in entrainment fluxes. \textit{April} uses a generator-discriminator architecture to identify days with significant DO fluctuations and employs a multi-step Euler scheme with sub-daily timesteps to effectively manage these variations. We have tested our methods on a wide range of lakes in the Midwestern USA, and demonstrated robust capability in predicting DO concentrations even with limited training data. While primarily focused on aquatic ecosystems, this approach is broadly applicable to diverse scientific and engineering disciplines that utilize process-based models, such as power engineering, climate science, and biomedicine.

Predicting dissolved oxygen (DO) concentrations in north temperate lakes requires a comprehensive study of phenological patterns across various ecosystems, which highlights the significance of selecting phenological features and feature interactions. Process-based models are limited by partial process knowledge or oversimplified feature representations, while machine learning models face challenges in efficiently selecting relevant feature interactions for different lake types and tasks, especially under the infrequent nature of DO data collection. In this paper, we propose a Nature-Guided Cognitive Evolution (NGCE) strategy, which represents a multi-level fusion of adaptive learning with natural processes. Specifically, we utilize metabolic process-based models to generate simulated DO labels. Using these simulated labels, we implement a multi-population cognitive evolutionary search, where models, mirroring natural organisms, adaptively evolve to select relevant feature interactions within populations for different lake types and tasks. These models are not only capable of undergoing crossover and mutation mechanisms within intra-populations but also, albeit infrequently, engage in inter-population crossover. The second stage involves refining these models by retraining them with real observed labels. We have tested the performance of our NGCE strategy in predicting daily DO concentrations across a wide range of lakes in the Midwest, USA. These lakes, varying in size, depth, and trophic status, represent a broad spectrum of north temperate lakes. Our findings demonstrate that NGCE not only produces accurate predictions with few observed labels but also, through gene maps of models, reveals sophisticated phenological patterns of different lakes.