Shaoming Xu

Jaideep Pathak, Yair Cohen, Piyush Garg et al.

Storm-scale convection-allowing models (CAMs) are an important tool for predicting the evolution of thunderstorms and mesoscale convective systems that result in damaging extreme weather. By explicitly resolving convective dynamics within the atmosphere they afford meteorologists the nuance needed to provide outlook on hazard. Deep learning models have thus far not proven skilful at km-scale atmospheric simulation, despite being competitive at coarser resolution with state-of-the-art global, medium-range weather forecasting. We present a generative diffusion model called StormCast, which emulates the high-resolution rapid refresh (HRRR) model-NOAA's state-of-the-art 3km operational CAM. StormCast autoregressively predicts 99 state variables at km scale using a 1-hour time step, with dense vertical resolution in the atmospheric boundary layer, conditioned on 26 synoptic variables. We present evidence of successfully learnt km-scale dynamics including competitive 1-6 hour forecast skill for composite radar reflectivity alongside physically realistic convective cluster evolution, moist updrafts, and cold pool morphology. StormCast predictions maintain realistic power spectra for multiple predicted variables across multi-hour forecasts. Together, these results establish the potential for autoregressive ML to emulate CAMs -- opening up new km-scale frontiers for regional ML weather prediction and future climate hazard dynamical downscaling.

Shaoming Xu, Ankush Khandelwal, Xiang Li et al.

In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to mini-batch 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 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.

Shaoming Xu, Ankush Khandelwal, Arvind Renganathan et al.

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 solutions. 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.

Shaoming Xu, Arvind Renganathan, Ankush Khandelwal et al.

Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.

Ankush Khandelwal, Shaoming Xu, Xiang Li et al.

Streamflow prediction is one of the key challenges in the field of hydrology due to the complex interplay between multiple non-linear physical mechanisms behind streamflow generation. While physics based models are rooted in rich understanding of the physical processes, a significant performance gap still remains which can be potentially addressed by leveraging the recent advances in machine learning. The goal of this work is to incorporate our understanding of hydrological processes and constraints into machine learning algorithms to improve the predictive performance. Traditional ML models for this problem predict streamflow using weather drivers as input. However there are multiple intermediate processes that interact to generate streamflow from weather drivers. The key idea of the approach is to explicitly model these intermediate processes that connect weather drivers to streamflow using a multi-task learning framework. While our proposed approach requires data about intermediate processes during training, only weather drivers will be needed to predict the streamflow during testing phase. We assess the efficacy of the approach on a simulation dataset generated by the SWAT model for a catchment located in the South Branch of the Root River Watershed in southeast Minnesota. While the focus of this paper is on improving the performance given data from a single catchment, methodology presented here is applicable to ML-based approaches that use data from multiple catchments to improve performance of each individual catchment.

Xiaowei Jia, Jacob Zwart, Jeffrey Sadler et al.

This paper proposes a physics-guided machine learning approach that combines advanced machine learning models and physics-based models to improve the prediction of water flow and temperature in river networks. We first build a recurrent graph network model to capture the interactions among multiple segments in the river network. Then we present a pre-training technique which transfers knowledge from physics-based models to initialize the machine learning model and learn the physics of streamflow and thermodynamics. We also propose a new loss function that balances the performance over different river segments. We demonstrate the effectiveness of the proposed method in predicting temperature and streamflow in a subset of the Delaware River Basin. In particular, we show that the proposed method brings a 33\%/14\% improvement over the state-of-the-art physics-based model and 24\%/14\% over traditional machine learning models (e.g., Long-Short Term Memory Neural Network) in temperature/streamflow prediction using very sparse (0.1\%) observation data for training. The proposed method has also been shown to produce better performance when generalized to different seasons or river segments with different streamflow ranges.

Jared Willard, Xiaowei Jia, Shaoming Xu et al.

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.