Physics as the Inductive Bias for Causal Discovery

2026-02-03

AI Summary

Traditional causal discovery methods in dynamic systems are often constrained by assumptions of acyclicity or stationarity, rendering them ill-suited for real-world complexities such as feedback loops, cyclic interactions, and nonstationarity. This work proposes a hybrid causal discovery framework that integrates physical knowledge with data-driven learning by embedding known physical mechanisms as inductive biases into a stochastic differential equation (SDE) model: the drift term encodes established ordinary differential equation (ODE) dynamics, while the diffusion term captures unknown causal couplings. By systematically incorporating partial physical priors into dynamic causal discovery for the first time, the approach overcomes conventional limitations and substantially enhances the identifiability and robustness of the inferred causal graph. Coupled with sparsity-inducing maximum likelihood estimation, the proposed algorithm outperforms state-of-the-art purely data-driven baselines across multiple dynamic system benchmarks, yielding more accurate, stable, and physically consistent causal structures.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Causal discovery is often a data-driven paradigm to analyze complex real-world systems. In parallel, physics-based models such as ordinary differential equations (ODEs) provide mechanistic structure for many dynamical processes. Integrating these paradigms potentially allows physical knowledge to act as an inductive bias, improving identifiability, stability, and robustness of causal discovery in dynamical systems. However, such integration remains challenging: real dynamical systems often exhibit feedback, cyclic interactions, and non-stationary data trend, while many widely used causal discovery methods are formulated under acyclicity or equilibrium-based assumptions. In this work, we propose an integrative causal discovery framework for dynamical systems that leverages partial physical knowledge as an inductive bias. Specifically, we model system evolution as a stochastic differential equation (SDE), where the drift term encodes known ODE dynamics and the diffusion term corresponds to unknown causal couplings beyond the prescribed physics. We develop a scalable sparsity-inducing MLE algorithm that exploits causal graph structure for efficient parameter estimation. Under mild conditions, we establish guarantees to recover the causal graph. Experiments on dynamical systems with diverse causal structures show that our approach improves causal graph recovery and produces more stable, physically consistent estimates than purely data-driven state-of-the-art baselines.

Problem

• causal discovery
• dynamical systems
• feedback
• non-stationarity
• acyclicity

Innovation

• inductive bias
• stochastic differential equation
• causal discovery
• dynamical systems
• sparsity-inducing MLE