# Adaptive Process-Guided Learning: An Application in Predicting Lake DO Concentrations

arXiv: https://arxiv.org/abs/2411.12973 · HTML: https://mlsanity.com/paper/2411.12973/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 20 Nov 2024.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [Predicting Water Temperature Dynamics of Unmonitored Lakes with Meta Transfer Learning](https://mlsanity.com/paper/2011.05369/) (2020)
- [Knowledge-guided Machine Learning: Current Trends and Future Prospects](https://mlsanity.com/paper/2403.15989/) (2024)
- [Evolution-based Feature Selection for Predicting Dissolved Oxygen Concentrations in Lakes](https://mlsanity.com/paper/2403.18923/) (2024)

## Built on by (most cited first, 9 of 9)

- [Physics-Guided Foundation Model for Scientific Discovery: An Application to Aquatic Science](https://mlsanity.com/paper/2502.06084/) (2025)
- [RAG for Geoscience: What We Expect, Gaps and Opportunities](https://mlsanity.com/paper/2508.11246/) (2025)
- [Foundation Models for Environmental Science: A Survey of Emerging Frontiers](https://mlsanity.com/paper/2504.04280/) (2025)
- [A Survey of Foundation Models for Environmental Science](https://mlsanity.com/paper/2503.03142/) (2025)
- [X-MethaneWet: A Cross-scale Global Wetland Methane Emission Benchmark Dataset for Advancing Science Discovery with AI](https://mlsanity.com/paper/2505.18355/) (2025)
- [Learning to Retrieve for Environmental Knowledge Discovery: An Augmentation-Adaptive Self-Supervised Learning Framework](https://mlsanity.com/paper/2509.14563/) (2025)
- [Geo-Aware Models for Stream Temperature Prediction across Different Spatial Regions and Scales](https://mlsanity.com/paper/2510.09500/) (2025)
- [CHAM-net: A Contrastive Hierarchical Adaptive Meta-network for Robust Global Methane Flux Prediction](https://mlsanity.com/paper/2606.00338/) (2026)
- [PIER: Physics-Informed Environmental Retrieval for Time-Series Modeling](https://mlsanity.com/paper/2607.20230/) (2026)

## Abstract (arXiv)

This paper introduces a textitProcess-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 textitPril 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 textitAdaptive 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. textitApril 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.