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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 Physics-Guided Foundation Model (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. 

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”. 

Abstract As a key water quality parameter, dissolved oxygen (DO) concentration, and particularly changes in bottom water DO is fundamental for understanding the biogeochemical processes in lake ecosystems. Based on two machine learning (ML) models, Gradient Boost Regressor (GBR) and long‐short‐term‐memory (LSTM) network, this study developed three ML model approaches: direct GBR; direct LSTM; and a 2‐step mixed ML model workflow combining both GBR and LSTM. They were used to simulate multi‐year surface and bottom DO concentrations in five lakes. All approaches were trained with readily available environmental data as predictors. Indices of lake thermal structure and mixing provided by a one‐dimensional (1‐D) hydrodynamic model were also included as predictors in the ML models. The advantages of each ML approach were not consistent for all the tested lakes, but the best one of them was defined that can estimate DO concentration with coefficient of determination (R²) up to 0.6–0.7 in each lake. All three approaches have normalized mean absolute error (NMAE) under 0.15. In a polymictic lake, the 2‐step mixed model workflow showed better representation of bottom DO concentrations, with a highest true positive rate (TPR) of hypolimnetic hypoxia detection of over 90%, while the other workflows resulted in, TPRs are around 50%. In most of the tested lakes, the predicted surface DO concentrations and variables indicating stratified conditions (i.e., Wedderburn number and the temperature difference between surface and bottom water) are essential for simulating bottom DO. The ML approaches showed promising results and could be used to support short‐ and long‐term water management plans. 

Abstract. Hypolimnetic oxygen depletion during summer stratification in lakes can lead to hypoxic and anoxic conditions. Hypolimnetic anoxia is a water quality issue with many consequences, including reduced habitat for cold-water fish species, reduced quality of drinking water, and increased nutrient and organic carbon (OC) release from sediments. Both allochthonous and autochthonous OC loads contribute to oxygen depletion by providing substrate for microbial respiration; however, their relative contributions to oxygen depletion across diverse lake systems remain uncertain. Lake characteristics, such as trophic state, hydrology, and morphometry, are also influential in carbon-cycling processes and may impact oxygen depletion dynamics. To investigate the effects of carbon cycling on hypolimnetic oxygen depletion, we used a two-layer process-based lake model to simulate daily metabolism dynamics for six Wisconsin lakes over 20 years (1995–2014). Physical processes and internal metabolic processes were included in the model and were used to predict dissolved oxygen (DO), particulate OC (POC), and dissolved OC (DOC). In our study of oligotrophic, mesotrophic, and eutrophic lakes, we found autochthony to be far more important than allochthony to hypolimnetic oxygen depletion. Autochthonous POC respiration in the water column contributed the most towards hypolimnetic oxygen depletion in the eutrophic study lakes. POC water column respiration and sediment respiration had similar contributions in the mesotrophic and oligotrophic study lakes. Differences in terms of source of respiration are discussed with consideration of lake productivity and the processing and fates of organic carbon loads. 

This repository includes the setup and output from the analysis ran on Lake Mendota to explore the trophic cascade caused by invasion of spiny water flea in 2010. Scripts to run the model are located under /src, and the processed results for the discussion of the paper are located under /data_processed.</p> 

Abstract Water temperature, ice cover, and lake stratification are important physical properties of lakes and reservoirs that control mixing as well as bio-geo-chemical processes and thus influence the water quality. We used an ensemble of vertical one-dimensional hydrodynamic lake models driven with regional climate projections to calculate water temperature, stratification, and ice cover under the A1B emission scenario for the German drinking water reservoir Lichtenberg. We used an analysis of variance method to estimate the contributions of the considered sources of uncertainty on the ensemble output. For all simulated variables, epistemic uncertainty, which is related to the model structure, is the dominant source throughout the simulation period. Nonetheless, the calculated trends are coherent among the five models and in line with historical observations. The ensemble predicts an increase in surface water temperature of 0.34 K per decade, a lengthening of the summer stratification of 3.2 days per decade, as well as decreased probabilities of the occurrence of ice cover and winter inverse stratification by 2100. These expected changes are likely to influence the water quality of the reservoir. Similar trends are to be expected in other reservoirs and lakes in comparable regions.