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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. 

Abstract. Water quality in lakes is an emergent property of complex biotic and abiotic processes that differ across spatial and temporal scales. Water quality is also a determinant of ecosystem services that lakes provide and is thus of great interest to ecologists. Machine learning and other computer science techniques are increasingly being used to predict water quality dynamics as well as to gain a greater understanding of water quality patterns and controls. To benefit the sciences of both ecology and computer science, we have created a benchmark dataset of lake water quality time series and vertical profiles. LakeBeD-US contains over 500 million unique observations of lake water quality collected by multiple long-term monitoring programs across 17 water quality variables from 21 lakes in the United States. There are two published versions of LakeBeD-US: the “Ecology Edition” published in the Environmental Data Initiative repository (https://doi.org/10.6073/pasta/c56a204a65483790f6277de4896d7140, McAfee et al., 2024) and the “Computer Science Edition” published in the Hugging Face repository (https://doi.org/10.57967/hf/3771, Pradhan et al., 2024). Each edition is formatted in a manner conducive to inquiries and analyses specific to each domain. For ecologists, LakeBeD-US: Ecology Edition provides an opportunity to study the spatial and temporal dynamics of several lakes with varying water quality, ecosystem, and landscape characteristics. For computer scientists, LakeBeD-US: Computer Science Edition acts as a benchmark dataset that enables the advancement of machine learning for water quality prediction. 

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 Photosynthetic acclimation to both warming and elevated CO₂of boreal trees remains a key uncertainty in modelling the response of photosynthesis to future climates. We investigated the impact of increased growth temperature and elevated CO₂on photosynthetic capacity (V_cmaxandJ_max) in mature trees of two North American boreal conifers, tamarack and black spruce. We show thatV_cmaxandJ_maxat a standard temperature of 25°C did not change with warming, whileV_cmaxandJ_maxat their thermal optima (T_opt) and growth temperature (T_g) increased. Moreover,V_cmaxandJ_maxat either 25°C,T_optorT_gdecreased with elevated CO₂. TheJ_max/V_cmaxratio decreased with warming when assessed at bothT_optandT_gbut did not significantly vary at 25°C. TheJ_max/V_cmaxincreased with elevated CO₂at either reference temperature. We found no significant interaction between warming and elevated CO₂on all traits. If this lack of interaction between warming and elevated CO₂on theV_cmax,J_maxandJ_max/V_cmaxratio is a general trend, it would have significant implications for improving photosynthesis representation in vegetation models. However, future research is required to investigate the widespread nature of this response in a larger number of species and biomes. 

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The data are associated with the following manuscript: Hanson, P. C., Ladwig, R., Buelo, C., Albright, E. A., Delany, A. D., & Carey, C. (2023). Legacy phosphorus and ecosystem memory control future water quality in a eutrophic lake. Lake water and ice observational data and lake bathymetry are from the North Temperate Lakes Long Term Ecological Research program. Brief abstract of the work: To investigate how water quality in Lake Mendota might respond to nutrient pollution reduction, we used computer models to simulate the elimination of phosphorus inputs from the catchment and track water quality change. The data herein are used to drive and calibrate the model. In addition, model code and simulation output are included as "other entities." 

Abstract Soil and atmospheric droughts increasingly threaten plant survival and productivity around the world. Yet, conceptual gaps constrain our ability to predict ecosystem‐scale drought impacts under climate change. Here, we introduce the ecosystem wilting point (Ψ EWP ), a property that integrates the drought response of an ecosystem's plant community across the soil–plant–atmosphere continuum. Specifically, Ψ EWP defines a threshold below which the capacity of the root system to extract soil water and the ability of the leaves to maintain stomatal function are strongly diminished. We combined ecosystem flux and leaf water potential measurements to derive the Ψ EWP of a Quercus‐Carya forest from an “ecosystem pressure–volume (PV) curve,” which is analogous to the tissue‐level technique. When community predawn leaf water potential (Ψ pd ) was above Ψ EWP (=−2.0 MPa), the forest was highly responsive to environmental dynamics. When Ψ pd fell below Ψ EWP , the forest became insensitive to environmental variation and was a net source of carbon dioxide for nearly 2 months. Thus, Ψ EWP is a threshold defining marked shifts in ecosystem functional state. Though there was rainfall‐induced recovery of ecosystem gas exchange following soaking rains, a legacy of structural and physiological damage inhibited canopy photosynthetic capacity. Although over 16 growing seasons, only 10% of Ψ pd observations fell below Ψ EWP , the forest is commonly only 2–4 weeks of intense drought away from reaching Ψ EWP , and thus highly reliant on frequent rainfall to replenish the soil water supply. We propose, based on a bottom‐up analysis of root density profiles and soil moisture characteristic curves, that soil water acquisition capacity is the major determinant of Ψ EWP , and species in an ecosystem require compatible leaf‐level traits such as turgor loss point so that leaf wilting is coordinated with the inability to extract further water from the soil.