We present a framework for modeling multi-scale processes, and study its performance in the context of stream-flow 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.

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.