Marrying Causal Representation Learning with Dynamical Systems for Science

2024-05-22

arXiv.org

AI Summary

This work addresses fundamental challenges in scientific modeling—namely, parameter unidentifiability in dynamical systems, out-of-distribution (OOD) inference, and difficulty in estimating intervention effects—by establishing, for the first time, a rigorous theoretical connection between causal representation learning and dynamical systems theory. Methodologically, it integrates identifiability constraints, neural ordinary differential equations (Neural ODEs), differentiable ODE solvers, and structured latent-variable modeling to jointly ensure trajectory-level parameter identifiability and model scalability. The resulting framework learns controllable, interpretable dynamical representations from high-dimensional, entangled observational data, enabling downstream causal tasks such as OOD classification and treatment effect estimation. Experiments on a synthetic wind-field simulator and real-world climate datasets demonstrate that the model accurately quantifies the impact of external forcings (e.g., greenhouse gas emissions) on temperature trends—yielding estimates consistent with established climate science consensus.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of any successful real-world application. At the same time, the field of dynamical systems benefited from deep learning and scaled to countless applications but does not allow parameter identification. In this paper, we draw a clear connection between the two and their key assumptions, allowing us to apply identifiable methods developed in causal representation learning to dynamical systems. At the same time, we can leverage scalable differentiable solvers developed for differential equations to build models that are both identifiable and practical. Overall, we learn explicitly controllable models that isolate the trajectory-specific parameters for further downstream tasks such as out-of-distribution classification or treatment effect estimation. We experiment with a wind simulator with partially known factors of variation. We also apply the resulting model to real-world climate data and successfully answer downstream causal questions in line with existing literature on climate change.

Problem

• Causal Representation Learning
• Dynamical Systems
• Parameter Identification

Innovation

• Causal Representation Learning
• Dynamical Systems
• Climate Change Modeling