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Methods based on upward canopy gap fractions are widely employed to measure in-situ effective LAI (Le) as an alternative to destructive sampling. However, these measurements are limited to point-level and are not practical for scaling up to larger areas. To address the point-to-landscape gap, this study introduces an innovative approach, named NeRF-LAI, for corn and soybean Le estimation that combines gap-fraction theory with the neural radiance field (NeRF) technology, an emerging neural network-based method for implicitly representing 3D scenes using multi-angle 2D images. The trained NeRF-LAI can render downward photorealistic hemispherical depth images from an arbitrary viewpoint in the 3D scene, and then calculate gap fractions to estimate Le. To investigate the intrinsic difference between upward and downward gaps estimations, initial tests on virtual corn fields demonstrated that the downward Le matches well with the upward Le, and the viewpoint height is insensitive to Le estimation for a homogeneous field. Furthermore, we conducted intensive real-world experiments at controlled plots and farmer-managed fields to test the effectiveness and transferability of NeRF-LAI in real-world scenarios, where multi-angle UAV oblique images from different phenological stages were collected for corn and soybeans. Results showed the NeRF-LAI is able to render photorealistic synthetic images with an average peak signal-to-noise ratio (PSNR) of 18.94 for the controlled corn plots and 19.10 for the controlled soybean plots. We further explored three methods to estimate Le from calculated gap fractions: the 57.5° method, the five-ring-based method, and the cell-based method. Among these, the cell-based method achieved the best performance, with the r2 ranging from 0.674 to 0.780 and RRMSE ranging from 1.95 % to 5.58 %. The Le estimates are sensitive to viewpoint height in heterogeneous fields due to the difference in the observable foliage volume, but they exhibit less sensitivity to relatively homogeneous fields. Additionally, the cross-site testing for pixel-level LAI mapping showed the NeRF-LAI significantly outperforms the VI-based models, with a small variation of RMSE (0.71 to 0.95 m2/m2) for spatial resolution from 0.5 m to 2.0 m. This study extends the application of gap fraction-based Le estimation from a discrete point scale to a continuous field scale by leveraging implicit 3D neural representations learned by NeRF. The NeRF-LAI method can map Le from raw multi-angle 2D images without prior information, offering a potential alternative to the traditional in-situ plant canopy analyzer with a more flexible and efficient solution. 

Abstract Accurate and cost-effective quantification of the carbon cycle for agroecosystems at decision-relevant scales is critical to mitigating climate change and ensuring sustainable food production. However, conventional process-based or data-driven modeling approaches alone have large prediction uncertainties due to the complex biogeochemical processes to model and the lack of observations to constrain many key state and flux variables. Here we propose a Knowledge-Guided Machine Learning (KGML) framework that addresses the above challenges by integrating knowledge embedded in a process-based model, high-resolution remote sensing observations, and machine learning (ML) techniques. Using the U.S. Corn Belt as a testbed, we demonstrate that KGML can outperform conventional process-based and black-box ML models in quantifying carbon cycle dynamics. Our high-resolution approach quantitatively reveals 86% more spatial detail of soil organic carbon changes than conventional coarse-resolution approaches. Moreover, we outline a protocol for improving KGML via various paths, which can be generalized to develop hybrid models to better predict complex earth system dynamics. 

Training machine learning (ML) models for scientific problems is often challenging due to limited observation data. To overcome this challenge, prior works commonly pre-train ML models using simulated data before having them fine-tuned with small real data. Despite the promise shown in initial research across different domains, these methods cannot ensure improved performance after fine-tuning because (i) they are not designed for extracting generalizable physics-aware features during pre-training, (ii) the features learned from pre-training can be distorted by the fine-tuning process. In this paper, we propose a new learning method for extracting, preserving, and adapting physics-aware features. We build a knowledge-guided neural network (KGNN) model based on known dependencies amongst physical variables, which facilitate extracting physics-aware feature representation from simulated data. Then we fine-tune this model by alternately updating the encoder and decoder of the KGNN model to enhance the prediction while preserving the physics-aware features learned through pre-training. We further propose to adapt the model to new testing scenarios via a teacher-student learning framework based on the model uncertainty. The results demonstrate that the proposed method outperforms many baselines by a good margin, even using sparse training data or under out-of-sample testing scenarios. 

Training machine learning (ML) models for scientific problems is often challenging due to limited observation data. To overcome this challenge, prior works commonly pre-train ML models using simulated data before having them fine-tuned with small real data. Despite the promise shown in initial research across different domains, these methods cannot ensure improved performance after fine-tuning because (i) they are not designed for extracting generalizable physics-aware features during pre-training, (ii) the features learned from pre-training can be distorted by the fine-tuning process. In this paper, we propose a new learning method for extracting, preserving, and adapting physics-aware features. We build a knowledge-guided neural network (KGNN) model based on known dependencies amongst physical variables, which facilitate extracting physics-aware feature representation from simulated data. Then we fine-tune this model by alternately updating the encoder and decoder of the KGNN model to enhance the prediction while preserving the physics-aware features learned through pre-training. We further propose to adapt the model to new testing scenarios via a teacher-student learning framework based on the model uncertainty. The results demonstrate that the proposed method outperforms many baselines by a good margin, even using sparse training data or under out-of-sample testing scenarios. 

Accurate prediction of water quality and quantity is crucial for sustainable development and human well-being. However, existing data-driven methods often suffer from spatial biases in model performance due to heterogeneous data, limited observations, and noisy sensor data. To overcome these challenges, we propose Fair-Graph, a novel graph-based recurrent neural network that leverages interrelated knowledge from multiple rivers to predict water flow and temperature within large-scale stream networks. Additionally, we introduce node-specific graph masks for information aggregation and adaptation to enhance prediction over heterogeneous river segments. To reduce performance disparities across river segments, we introduce a centralized coordination strategy that adjusts training priorities for segments. We evaluate the prediction of water temperature within the Delaware River Basin, and the prediction of streamflow using simulated data from U.S. National Water Model in the Houston River network. The results showcase improvements in predictive performance and highlight the proposed model's ability to maintain spatial fairness over different river segments. 

Spatio-temporal machine learning is critically needed for a variety of societal applications, such as agricultural monitoring, hydrological forecast, and traffic management. These applications greatly rely on regional features that characterize spatial and temporal differences. However, spatio-temporal data often exhibit complex patterns and significant data variability across different locations. The labels in many real-world applications can also be limited, which makes it difficult to separately train independent models for different locations. Although meta learning has shown promise in model adaptation with small samples, existing meta learning methods remain limited in handling a large number of heterogeneous tasks, e.g., a large number of locations with varying data patterns. To bridge the gap, we propose task-adaptive formulations and a model-agnostic meta-learning framework that transforms regionally heterogeneous data into location-sensitive meta tasks. We conduct task adaptation following an easy-to-hard task hierarchy in which different meta models are adapted to tasks of different difficulty levels. One major advantage of our proposed method is that it improves the model adaptation to a large number of heterogeneous tasks. It also enhances the model generalization by automatically adapting the meta model of the corresponding difficulty level to any new tasks. We demonstrate the superiority of our proposed framework over a diverse set of baselines and state-of-the-art meta-learning frameworks. Our extensive experiments on real crop yield data show the effectiveness of the proposed method in handling spatial-related heterogeneous tasks in real societal applications. 

This paper proposes a physics-guided neural network model to predict crop yield and maintain the fairness over space. Failures to preserve the spatial fairness in predicted maps of crop yields can result in biased policies and intervention strategies in the distribution of assistance or subsidies in supporting individuals at risk. Existing methods for fairness enforcement are not designed for capturing the complex physical processes that underlie the crop growing process, and thus are unable to produce good predictions over large regions under different weather conditions and soil properties. More importantly, the fairness is often degraded when existing methods are applied to different years due to the change of weather conditions and farming practices. To address these issues, we propose a physics-guided neural network model, which leverages the physical knowledge from existing physics-based models to guide the extraction of representative physical information and discover the temporal data shift across years. In particular, we use a reweighting strategy to discover the relationship between training years and testing years using the physics-aware representation. Then the physics-guided neural network will be refined via a bi-level optimization process based on the reweighted fairness objective. The proposed method has been evaluated using real county-level crop yield data and simulated data produced by a physics-based model. The results demonstrate that this method can significantly improve the predictive performance and preserve the spatial fairness when generalized to different years.