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

Runlong Yu, Chonghao Qiu, Robert Ladwig, Paul C. Hanson, Yiqun Xie, Yanhua Li, Xiaowei Jia

Abstract

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.

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

Abstract

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.

Paper Structure

This paper contains 19 sections, 14 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Preliminaries on Process-based Model
  4. Process-Guided Learning
  5. Adaptive Process-Guided Learning
  6. Analysis of numerical instabilities
  7. Adaptive timestep adjustment
  8. Refinement of mass conservation loss
  9. Experimental Evaluation
  10. Data preparation
  11. Baselines
  12. Implementation details
  13. Experimental results
  14. Performance comparison
  15. Time-series analysis
  16. ...and 4 more sections

Figures (8)

  • Figure 1: Seasonal variations and diurnal fluctuations in DO concentrations.
  • Figure 2: Overall framework of the April model.
  • Figure 3: Clustering of lakes based on depth and surface area.
  • Figure 4: Time-series analysis of DO concentrations: comparing predictions, physical process-based simulation, and observed values.
  • Figure 5: Physical consistency analysis of epilimnion DO concentration predictions: evaluating RMSE and DO mass inconsistency.
  • ...and 3 more figures