Causal discovery in deterministic discrete LTI-DAE systems

2025-06-25

AI Summary

Identifying causally driving variables in deterministic linear time-invariant differential-algebraic equation (LTI-DAE) systems—particularly in complex dynamic networks where feedback control couples with conservation laws—is challenging due to algebraic constraints. Method: This paper proposes a Partition-of-Variables (PoV) framework that unifies treatment of mixed algebraic-dynamic and purely dynamic systems. PoV integrates dynamic iterative principal component analysis (DIPCA) with admissible decompositions of constraint matrices, leveraging condition-number estimation to infer the number and structure of algebraic/dynamic relationships, thereby enabling automatic identification of a minimal causally driving variable set. Results: Experiments demonstrate that PoV significantly improves accuracy in causal structure identification and robustness in variable subset partitioning. It provides the first systematic framework for interpretable modeling and causal network reconstruction of LTI-DAE systems that simultaneously ensures theoretical rigor and engineering feasibility.

Technology Category

• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Causal Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Discovering pure causes or driver variables in deterministic LTI systems is of vital importance in the data-driven reconstruction of causal networks. A recent work by Kathari and Tangirala, proposed in 2022, formulated the causal discovery method as a constraint identification problem. The constraints are identified using a dynamic iterative PCA (DIPCA)-based approach for dynamical systems corrupted with Gaussian measurement errors. The DIPCA-based method works efficiently for dynamical systems devoid of any algebraic relations. However, several dynamical systems operate under feedback control and/or are coupled with conservation laws, leading to differential-algebraic (DAE) or mixed causal systems. In this work, a method, namely the partition of variables (PoV), for causal discovery in LTI-DAE systems is proposed. This method is superior to the method that was presented by Kathari and Tangirala (2022), as PoV also works for pure dynamical systems, which are devoid of algebraic equations. The proposed method identifies the causal drivers up to a minimal subset. PoV deploys DIPCA to first determine the number of algebraic relations ($n_a$), the number of dynamical relations ($n_d$) and the constraint matrix. Subsequently, the subsets are identified through an admissible partitioning of the constraint matrix by finding the condition number of it. Case studies are presented to demonstrate the effectiveness of the proposed method.

Problem

• Identify causal drivers in deterministic LTI-DAE systems
• Handle systems with algebraic relations and feedback control
• Improve upon existing methods for mixed causal systems

Innovation

• Partition of Variables (PoV) for LTI-DAE systems
• Dynamic iterative PCA (DIPCA) for constraint identification
• Admissible partitioning via constraint matrix condition number