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Abstract When building predictive models for real-world applications, many data are discarded because conventional learning algorithms cannot utilize it, although such data could be very informative. This paper focuses on representation learning using two types of additional data: privileged information (PI) and unlabeled data. PI refers to data available only during training but not at test time. Existing methods transfer the knowledge embedded in PI via supervised mechanisms, making them unable to use unlabeled data. In contrast, self-supervised learning methods can use unlabeled data but cannot learn from PI. While these techniques appear complementary, as we demonstrate, combining them is non-trivial. This paper introduces the privileged information regularized (PIReg) self-supervised learning framework, which utilizes both PI and unlabeled data to learn better representations. 

Abstract Prediction of dynamic environmental variables in unmonitored sites remains a long-standing challenge for water resources science. The majority of the world’s freshwater resources have inadequate monitoring of critical environmental variables needed for management. Yet, the need to have widespread predictions of hydrological variables such as river flow and water quality has become increasingly urgent due to climate and land use change over the past decades, and their associated impacts on water resources. Modern machine learning methods increasingly outperform their process-based and empirical model counterparts for hydrologic time series prediction with their ability to extract information from large, diverse data sets. We review relevant state-of-the art applications of machine learning for streamflow, water quality, and other water resources prediction and discuss opportunities to improve the use of machine learning with emerging methods for incorporating watershed characteristics and process knowledge into classical, deep learning, and transfer learning methodologies. The analysis here suggests most prior efforts have been focused on deep learning frameworks built on many sites for predictions at daily time scales in the United States, but that comparisons between different classes of machine learning methods are few and inadequate. We identify several open questions for time series predictions in unmonitored sites that include incorporating dynamic inputs and site characteristics, mechanistic understanding and spatial context, and explainable AI techniques in modern machine learning frameworks. 

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. 

Representation Learning), a novel multimodal meta-learning framework for few-shot learning in heterogeneous systems, designed for science and engineering problems where entities share a common underlying forward model but exhibit heterogeneity due to entity-specific characteristics. TAM-RL leverages an amortized training process with a modulation network and a base network to learn task-specific modulation parameters, enabling efficient adaptation to new tasks with limited data. We evaluate TAM-RL on two real-world environmental datasets: Gross Primary Product (GPP) prediction and streamflow forecasting, demonstrating significant improvements over existing meta-learning methods. On the FLUXNET dataset, TAM-RL improves RMSE by 18.9% over MMAML with just one month of few-shot data, while for streamflow prediction, it achieves an 8.21% improvement with one year of data. Synthetic data experiments further validate TAM-RL’s superior performance in heterogeneous task distributions, outperforming the baselines in the most heterogeneous setting. Notably, TAM-RL offers substantial computational efficiency, with at least 3x faster training times compared to gradient-based meta-learning approaches while being much simpler to train due to reduced complexity. Ablation studies highlight the importance of pretraining and adaptation mechanisms in TAM-RL’s performance. Keywords: Representation Learning, meta-learning, few-shot learning, environmental applications, time-series. DOI:10.1137/1.9781611978520.2 

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. Traditional time series approaches for prediction often focus on either autoregressive modeling, which relies solely on past observations of the target “endogenous variables”, or forward modeling, which considers only current covariate drivers “exogenous variables”. However, effectively integrating past endogenous and past exogenous with current exogenous variables remains a significant challenge. In this paper, we propose ExoTST, a novel transformer-based framework that effectively incorporates current exogenous variables alongside past context for improved time series prediction. To integrate exogenous information efficiently, ExoTST leverages the strengths of attention mechanisms and introduces a novel cross-temporal modality fusion module. This module enables the model to jointly learn from both past and current exogenous series, treating them as distinct modalities. By considering these series separately, ExoTST provides robustness and flexibility in handling data uncertainties that arise from the inherent distribution shift between historical and current exogenous variables. Extensive experiments on real-world carbon flux datasets and time series benchmarks demonstrate ExoTST's superior performance compared to state-of-the-art baselines, with improvements of up to 10% in prediction accuracy. Moreover, ExoTST exhibits strong robustness against missing values and noise in exogenous drivers, maintaining consistent performance in real-world situations where these imperfections are common. 

Time series modeling, a crucial area in science, often encounters challenges when training Machine Learning (ML) models like Recurrent Neural Networks (RNNs) using the conventional mini-batch training strategy that assumes independent and identically distributed (IID) samples and initializes RNNs with zero hidden states. The IID assumption ignores temporal dependencies among samples, resulting in poor performance. This paper proposes the Message Propagation Through Time (MPTT) algorithm to effectively incorporate long temporal dependencies while preserving faster training times relative to the stateful algorithms. MPTT utilizes two memory modules to asynchronously manage initial hidden states for RNNs, fostering seamless information exchange between samples and allowing diverse mini-batches throughout epochs. MPTT further implements three policies to filter outdated and preserve essential information in the hidden states to generate informative initial hidden states for RNNs, facilitating robust training. Experimental results demonstrate that MPTT outperforms seven strategies on four climate datasets with varying levels of temporal dependencies. 

In recent years, the increasing threat of devastating wildfires has underscored the need for effective prescribed fire management. Process-based computer simulations have traditionally been employed to plan prescribed fires for wildfire prevention. However, even simplified process models are too compute-intensive to be used for real-time decision-making. Traditional ML methods used for fire modeling offer computational speedup but struggle with physically inconsistent predictions, biased predictions due to class imbalance, biased estimates for fire spread metrics (e.g., burned area, rate of spread), and limited generalizability in out-of-distribution wind conditions. This paper introduces a novel machine learning (ML) framework that enables rapid emulation of prescribed fires while addressing these concerns. To overcome these challenges, the framework incorporates domain knowledge in the form of physical constraints, a hierarchical modeling structure to capture the interdependence among variables of interest, and also leverages pre-existing source domain data to augment training data and learn the spread of fire more effectively. Notably, improvement in fire metric (e.g., burned area) estimates offered by our framework makes it useful for fire managers, who often rely on these estimates to make decisions about prescribed burn management. Furthermore, our framework exhibits better generalization capabilities than the other ML-based fire modeling methods across diverse wind conditions and ignition patterns. 

Accurate and timely crop mapping is essential for yield estimation, insurance claims, and conservation efforts. Over the years, many successful machine learning models for crop mapping have been developed that use just the multispectral imagery from satellites to predict crop type over the area of interest. However, these traditional methods do not account for the physical processes that govern crop growth. At a high level, crop growth can be envisioned as physical parameters, such as weather and soil type, acting upon the plant, leading to crop growth, which can be observed via satellites. In this paper, we propose a Weather-based Spatio-Temporal segmentation network with ATTention (WSTATT), a deep learning model that leverages this understanding of crop growth by formulating it as an inverse model that combines weather (Daymet) and satellite imagery (Sentinel-2) to generate accurate crop maps. We show that our approach provides significant improvements over existing algorithms that solely rely on spectral imagery by comparing segmentation maps and F1 classification scores. Furthermore, effective use of attention in WSTATT architecture enables the detection of crop types earlier in the season (up to 5 months in advance), which is very useful for improving food supply projections. We finally discuss the impact of weather by correlating our results with crop phenology to show that WSTATT is able to capture the physical properties of crop growth. 

Many environmental systems (e.g., hydrology basins) can be modeled as an entity whose response (e.g., streamflow) depends on drivers (e.g., weather) conditioned on their characteristics (e.g., soil properties). We introduce Entity-aware Conditional Variational Inference (EA-CVI), a novel probabilistic inverse modeling approach, to deduce entity characteristics from observed driver-response data. EA-CVI infers probabilistic latent representations that can accurately predict responses for diverse entities, particularly in out-of-sample few-shot settings. EA-CVI's latent embeddings encapsulate diverse entity characteristics within compact, low-dimensional representations. EA-CVI proficiently identifies dominant modes of variation in responses and offers the opportunity to infer a physical interpretation of the underlying attributes that shape these responses. EA-CVI can also generate new data samples by sampling from the learned distribution, making it useful in zero-shot scenarios. EA-CVI addresses the need for uncertainty estimation, particularly during extreme events, rendering it essential for data-driven decision-making in real-world applications. Extensive evaluations on a renowned hydrology benchmark dataset, CAMELS-GB, validate EA-CVI's abilities. 

Accurate and timely crop mapping is essential for yield estimation, insurance claims, and conservation efforts. Over the years, many successful machine learning models for crop mapping have been developed that use just the multispectral imagery from satellites to predict crop type over the area of interest. However, these traditional methods do not account for the physical processes that govern crop growth. At a high level, crop growth can be envisioned as physical parameters, such as weather and soil type, acting upon the plant, leading to crop growth which can be observed via satellites. In this paper, we propose a weather-based Spatio-Temporal segmentation network with ATTention (WSTATT), a deep learning model that leverages this understanding of crop growth by formulating it as an inverse model that combines weather (Daymet) and satellite imagery (Sentinel-2) to generate accurate crop maps. We show that our approach provides significant improvements over existing algorithms that solely rely on spectral imagery by comparing segmentation maps and F1 classification scores. Furthermore, effective use of attention in WSTATT architecture enables the detection of crop types earlier in the season (up to 5 months in advance), which is very useful for improving food supply projections. We finally discuss the impact of weather by correlating our results with crop phenology to show that WST