Hierarchically Disentangled Recurrent Network for Factorizing System Dynamics of Multi-scale Systems: An application on Hydrological Systems

TL;DR

This work tackles multi-scale, data-assimilative streamflow forecasting by introducing the Factorized Hierarchical Neural Network (FHNN), which learns latent states at slow, medium, and fast temporal scales via an inverse encoder and uses them in a forward generator to predict future flow. The method addresses limitations of LSTM and Transformer approaches in data-scarce, path-dependent hydrological systems by explicitly modeling multi-scale states and enabling data assimilation through state-based conditioning. Key contributions include (i) a novel FHNN architecture with a three-scale state encoder and a conditional LSTM decoder, (ii) two data-scarcity strategies—global multi-basin modeling and simulation-data pretraining with SAC-SMA—(iii) extensive validation on NCRFC hydrological basins and the CAMELS benchmark showing superior predictive performance, especially for low-runoff and cold basins, and (iv) interpretable visualizations of learned multi-scale states. Overall, FHNN demonstrates data-efficient, high-accuracy hydrologic forecasting and provides a framework potentially transferable to other complex, multi-scale dynamical systems requiring latent state factorization and data assimilation.

Abstract

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 physics-based 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.

Figures (4)

• Figure 1: Schematic of different modeling approaches for streamflow forecasting illustrating each approach's inputs, processes, and outputs. (a) Process-based Forward Models use weather forecasts to estimate catchment states and generate streamflow forecasts. (b) ML-based Forward Models (e.g., LSTM) directly use weather forecasts to predict streamflow forecasts. (c) ML-based Autoregressive Forward Models utilize weather forecasts and historical streamflow data for streamflow forecasting. (d) The proposed FHNN framework integrates an Inverse Model that generates catchment state representations from historical weather and streamflow data, which are then used alongside weather forecasts in a Forward Model to produce streamflow forecasts, capturing dynamics at multiple temporal scales (slow, medium, fast)
• Figure 2: (a) Graphical model representation of FHNN for time series data. The model illustrates the relationships between latent variables ($z_0$ to $z_l$), observed variables ($x$ and $y$), and model parameters ($\phi$ and $\theta$). It shows the generative process ($p_{\theta}(\boldsymbol{Y^t}|\boldsymbol{z}, \boldsymbol{X^t})$) and the inference process ($q_{\phi}(\boldsymbol{z}|\boldsymbol{X^{t-1}}, \boldsymbol{Y^{t-1}}$), depicting how past observations influence the current latent state and how the current latent state and inputs generate the output. This structure enables FHNN to capture multi-scale temporal dependencies and generate predictions., (b) Architecture of FHNN for streamflow prediction. The model processes historical weather and streamflow data at three different timescales (fast, medium, and slow) using parallel BiLSTM layers, capturing temporal dependencies at various resolutions. The final hidden states from each timescale ($h_f$, $h_m$, $h_s$) are combined with forecasted weather data to generate streamflow predictions for future time steps. This design allows the model to integrate both short-term fluctuations and long-term trends in the input data for more accurate streamflow forecasting.
• Figure 3: Performance difference between FHNN and LSTM-AR models plotted against (a) Runoff Ratio, (b) Annual Average Temperature, and (c) Annual Precipitation across different catchments.
• Figure 4: Visualization of FHNN's inferred fast, medium, and slow states for seven river basins. Each row represents a basin, with columns showing the mean of hidden state dimensions over time for each temporal scale. Fast states (left) exhibit high variability, medium states (center) show smoothed patterns, and slow states (right) capture long-term trends.