Robert Ladwig

Runlong Yu, Chonghao Qiu, Robert Ladwig et al.

Physics-guided machine learning (PGML) has become a prevalent approach in studying scientific systems due to its ability to integrate scientific theories for enhancing machine learning (ML) models. However, most PGML approaches are tailored to isolated and relatively simple tasks, which limits their applicability to complex systems involving multiple interacting processes and numerous influencing features. In this paper, we propose a \textit{\textbf{P}hysics-\textbf{G}uided \textbf{F}oundation \textbf{M}odel (\textbf{PGFM})} that combines pre-trained ML models and physics-based models and leverages their complementary strengths to improve the modeling of multiple coupled processes. To effectively conduct pre-training, we construct a simulated environmental system that encompasses a wide range of influencing features and various simulated variables generated by physics-based models. The model is pre-trained in this system to adaptively select important feature interactions guided by multi-task objectives. We then fine-tune the model for each specific task using true observations, while maintaining consistency with established physical theories, such as the principles of mass and energy conservation. We demonstrate the effectiveness of this methodology in modeling water temperature and dissolved oxygen dynamics in real-world lakes. The proposed PGFM is also broadly applicable to a range of scientific fields where physics-based models are being used.

Runlong Yu, Chonghao Qiu, Robert Ladwig et al.

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.

Runlong Yu, Robert Ladwig, Xiang Xu et al.

Accurate prediction of dissolved oxygen (DO) concentrations in lakes requires a comprehensive study of phenological patterns across ecosystems, highlighting the need for precise selection of interactions amongst external factors and internal physical-chemical-biological variables. This paper presents the Multi-population Cognitive Evolutionary Search (MCES), a novel evolutionary algorithm for complex feature interaction selection problems. MCES allows models within every population to evolve adaptively, selecting relevant feature interactions for different lake types and tasks. Evaluated on diverse lakes in the Midwestern USA, MCES not only consistently produces accurate predictions with few observed labels but also, through gene maps of models, reveals sophisticated phenological patterns of different lake types, embodying the innovative concept of "AI from nature, for nature".

Shiyuan Luo, Runlong Yu, Chonghao Qiu et al.

The discovery of environmental knowledge depends on labeled task-specific data, but is often constrained by the high cost of data collection. Existing machine learning approaches usually struggle to generalize in data-sparse or atypical conditions. To this end, we propose an Augmentation-Adaptive Self-Supervised Learning (A$^2$SL) framework, which retrieves relevant observational samples to enhance modeling of the target ecosystem. Specifically, we introduce a multi-level pairwise learning loss to train a scenario encoder that captures varying degrees of similarity among scenarios. These learned similarities drive a retrieval mechanism that supplements a target scenario with relevant data from different locations or time periods. Furthermore, to better handle variable scenarios, particularly under atypical or extreme conditions where traditional models struggle, we design an augmentation-adaptive mechanism that selectively enhances these scenarios through targeted data augmentation. Using freshwater ecosystems as a case study, we evaluate A$^2$SL in modeling water temperature and dissolved oxygen dynamics in real-world lakes. Experimental results show that A$^2$SL significantly improves predictive accuracy and enhances robustness in data-scarce and atypical scenarios. Although this study focuses on freshwater ecosystems, the A$^2$SL framework offers a broadly applicable solution in various scientific domains.