Communications Physics Article in Press
Deep Koopman operators for causal discovery
This paper leverages deep learning and Koopman theory to introduce Kausal, a novel deep Koopman operator-based framework for causal discovery. Kausal demonstrates superior ability in disentangling complex, nonlinear cause-effect mechanisms in dynamical systems, including real-world climate phenomena.
Executive Impact: Kausal's Edge in Enterprise AI
Kausal provides unparalleled insights into complex system dynamics, enabling more accurate predictions, optimized decision-making, and robust explainable AI across critical enterprise applications.
0.67
AUROC (Rössler Oscillator)
AUROC score demonstrating Kausal's strong performance in causal direction identification for nonlinear Rössler systems (Table 2).
0.64
AUROC (ENSO Model)
AUROC score showing Kausal's effectiveness in complex real-world inspired climate models (Table 2).
✓
Time-Evolving Causality
Kausal's ability to track dynamically evolving causal graphs, unlike many existing methods (Page 13).
8+
Experiments & Benchmarks
Evaluated across 3 increasingly complex dynamical systems and 4 additional experiments (Page 7, 11).
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
Kausal's Foundational Approach
Kausal combines deep learning and Koopman operator theory to linearize nonlinear dynamics for robust causal discovery.
Enterprise Process Flow
Estimate Embeddings (Deep Learning)
→
Approximate Koopman Operator (DMD)
→
Infer Causal Measures (Prediction Error Difference)
Nonlinear Dynamics Simplified
Via Koopman Operators
Koopman theory transforms finite-dimensional nonlinear dynamics into an infinite-dimensional linear operator acting on observables, simplifying causal inference.
Benchmarking Kausal's Capabilities
Kausal demonstrates superior performance compared to traditional statistical and deep learning-based methods in various causal discovery tasks.
| Feature | Kausal (DL-Koopman) | Traditional (e.g., PCMCI+, VARLINGAM) | DL Baselines (e.g., cLSTM, TSCI) |
|---|---|---|---|
| Handles Nonlinear Dynamics | |||
| Detects Time-Evolving Causality | |||
| Scales to High-Dimensional Systems |
|
||
| Provides Interpretable Latent Space |
|
|
|
| AUROC (Rössler Oscillator) | 0.67 | 0.50-0.58 | 0.52-0.58 |
0.67 AUROC
Rössler Oscillator Performance
Kausal achieves an AUROC score of 0.67 on the coupled Rössler oscillators, significantly outperforming baselines and demonstrating robust causal direction identification.
Kausal in Action: Climate Science
Kausal provides robust insights for complex real-world phenomena, exemplified by its successful application to climate dynamics.
Real-world Climate Dynamics: Identifying ENSO Events
Kausal successfully identified major El Niño and La Niña events from 1982-83, 1997-98, and 2014-16 in real-world ocean reanalysis data. This demonstrates the framework's robustness and scalability for complex, observed climate phenomena.
Key Learnings:
- Major ENSO events accurately tracked
- Robustness in observed, noisy climate data
- Highlights importance of deep learning for complex nonlinearities
0.64 AUROC
ENSO Model Performance
Kausal maintains a strong AUROC score of 0.64 on the eXtended nonlinear Recharge Oscillator (XRO) model, showcasing its generalizability to high-dimensional, complex climate systems.
Advanced ROI Calculator
Estimate the potential efficiency gains and cost savings by integrating Kausal's advanced causal discovery into your enterprise workflows.
Estimated Annual Savings
$0
Annual Hours Reclaimed
0
Your Kausal Implementation Roadmap
Our structured approach ensures a seamless integration of Kausal into your existing enterprise architecture, maximizing impact with minimal disruption.
Phase 1: Data Integration & Model Setup
Securely integrate your proprietary time-series data, configure Kausal's deep learning embeddings, and initialize the Koopman operator. This phase focuses on establishing a robust data pipeline and foundational model architecture.
Phase 2: Causal Graph Discovery & Validation
Execute Kausal's algorithms to uncover underlying causal structures in your dynamics. Validate discovered relationships against domain expertise and establish statistical significance using bootstrapping.
Phase 3: Predictive Modeling & Actionable Insights
Leverage the identified causal mechanisms for improved forecasting and scenario planning. Translate insights into explainable decision-making and optimize control strategies within your enterprise systems.
Unlock Deeper Insights. Drive Smarter Decisions.
Ready to transform your understanding of complex system dynamics? Schedule a complimentary strategy session with our AI experts to explore how Kausal can be tailored for your specific enterprise challenges.
Ready to Get Started?
Book Your Free Consultation.
Let's Discuss Your AI Strategy!
Lets Discuss Your Needs
Select a Date
Sun
Mon
Tue
Wed
Thu
Fri
Sat