Deep Chaos ODE for Advanced Hydrological Modelling: Integrating Deep Learning and Polynomial Chaos into Data-Driven Hydrology

Hydrological systems are governed by nonlinear dynamical processes for which the governing equations are often only partially known, simplified, or subject to structural uncertainty. While physics-based hydrological models encode valuable domain knowledge, they frequently struggle to capture complex dynamics and nonstationary behavior. At the same time, purely data-driven approaches lack physical interpretability and often fail when applied beyond the conditions represented in the training data. This motivates the development of learning frameworks that combine physical structure, data-driven flexibility, and explicit uncertainty awareness.

To address this challenge, this project focuses on physics-informed deep learning of dynamical systems for hydrological modeling, with particular emphasis on Deep Chaos Ordinary Differential Equations (Deep Chaos ODEs). These models integrate neural networks into continuous-time dynamical system formulations, allowing unresolved or poorly understood hydrological processes to be learned from data while preserving known physical and causal structures. By embedding learning directly into differential equation models, the approach supports interpretability, causal consistency, and improved generalization in hydrological simulations.

Building on concepts from neural ODEs and dynamical systems theory, the research investigates how chaotic dynamics, nonlinear feedbacks, and system sensitivity can be represented within hybrid physics–learning models. In addition to improving predictive performance, the framework aims to provide quantified uncertainty and reliability assessments for model outputs. As an exploratory component, the project evaluates Out-of-Distribution (OOD) detection methods to identify hydrological conditions under which learned models operate outside their trained or validated domain, thereby supporting uncertainty quantification and risk-aware model deployment.

The motivating application of this research lies in data-driven hydrology, where observational data are often limited, noisy, and heterogeneous, and where predictive reliability is critical for scientific understanding and decision-making. More broadly, the project contributes to the development of interpretable, physics-informed learning approaches for complex dynamical systems, advancing the integration of deep learning, uncertainty quantification, and domain knowledge in environmental modeling.