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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. 

We present a framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the system dynamics at multiple temporal scales and captures their interactions. This framework consists of an inverse and a forward model. The inverse model is used to empirically resolve the system’s temporal modes from data (physical model simulations, observed data, or a combination of them from the past), and these states are then used in the forward model to predict streamflow. Experiments on several catchments from the National Weather Service North Central River Forecast Center show that FHNN outperforms standard baselines, including physicsbased models and transformer-based approaches. The model demonstrates particular effectiveness in catchments with low runoff ratios and colder climates. We further validate FHNN on the CAMELS (Catchment Attributes and MEteorology for Large-sample Studies), which is a widely used continental-scale hydrology benchmark dataset, confirming consistent performance improvements for 1-7 day streamflow forecasts across diverse hydrological conditions. Additionally, we show that FHNN can maintain accuracy even with limited training data through effective pre-training strategies and training global models.Not Available 

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. 

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. 

We present a knowledge‐guided machine learning framework for operational hydrologic forecasting at the catchment scale. Our approach, a Factorized Hierarchical Neural Network (FHNN), has two main components: inverse and forward models. The inverse model uses observed precipitation, temperature, and streamflow data to generate a representation of the current underlying catchment state. The forward model predicts streamflow using the learned catchment state. The FHNN architecture is designed to model multi‐scale processes and capture their interactions, a critical ability for flood modeling. FHNN also improves forecasts based on real‐time data through an inference‐based data integration approach using inverse modeling. FHNN's data integration approach improves forecasts in response to observed data more efficiently than data assimilation methods that require computationally intensive optimization. We compare the FHNN to a leading deep learning alternative (autoregressive LSTM) on the large‐sample CAMELS‐US data set, and operational flood forecast data from the US National Weather Service (NWS). Official NWS flood forecasts are generated by expert human forecasters using a physics‐based model, in a human‐in‐the‐loop process. Thus, we assess the flood forecast ability of FHNN by directly comparing its performance against these NWS expert‐derived forecasts. The human forecaster creates a more accurate forecast within the first 12–18 hr of a forecast's issuance, but FHNN has significantly better predictions thereafter. This research lays the groundwork for leveraging the predictive performance of AI‐based models with the expertise in forecasting agencies to produce better river forecasts. 

In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to minibatch training, temporal relationships between training segments within the batch (intra-batch) as well as between batches (inter-batch) are not considered, which can lead to limited performance. Stateful RNNs aim to address this issue by passing hidden states between batches. Since Stateful RNNs ignore intra-batch temporal dependency, there exists a trade-off between training stability and capturing temporal dependency. In this paper, we provide a quantitative comparison of different Stateful RNN modeling strategies, and propose two strategies to enforce both intra- and inter-batch temporal dependency. First, we extend Stateful RNNs by defining a batch as a temporally ordered set of training segments, which enables intra-batch sharing of temporal information. While this approach significantly improves the performance, it leads to much larger training times due to highly sequential training. To address this issue, we further propose a new strategy which augments a training segment with an initial value of the target variable from the timestep right before the starting of the training segment. In other words, we provide an initial value of the target variable as additional input so that the network can focus on learning changes relative to that initial value. By using this strategy, samples can be passed in any order (mini-batch training) which significantly reduces the training time while maintaining the performance. In demonstrating the utility of our approach in hydrological modeling, we observe that the most significant gains in predictive accuracy occur when these methods are applied to state variables whose values change more slowly, such as soil water and snowpack, rather than continuously moving flux variables such as streamflow. 

There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML) techniques. This paper provides a structured overview of such techniques. Application-centric objective areas for which these approaches have been applied are summarized, and then classes of methodologies used to construct physics-guided ML models and hybrid physics-ML frameworks are described. We then provide a taxonomy of these existing techniques, which uncovers knowledge gaps and potential crossovers of methods between disciplines that can serve as ideas for future research. 

Physics-based models are often used to study engineering and environmental systems. The ability to model these systems is the key to achieving our future environmental sustainability and improving the quality of human life. This article focuses on simulating lake water temperature, which is critical for understanding the impact of changing climate on aquatic ecosystems and assisting in aquatic resource management decisions. General Lake Model (GLM) is a state-of-the-art physics-based model used for addressing such problems. However, like other physics-based models used for studying scientific and engineering systems, it has several well-known limitations due to simplified representations of the physical processes being modeled or challenges in selecting appropriate parameters. While state-of-the-art machine learning models can sometimes outperform physics-based models given ample amount of training data, they can produce results that are physically inconsistent. This article proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physics-based models (by over 20% even with very little training data), while generating outputs consistent with physical laws. An important aspect of our PGRNN approach lies in its ability to incorporate the knowledge encoded in physics-based models. This allows training the PGRNN model using very few true observed data while also ensuring high prediction accuracy. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where physics-based (also known as mechanistic) models are used.