Functional network reconstruction and dependency quantification from time series

Develop accurate and reliable methodologies to reconstruct functional networks from time-series data and to quantify statistical dependencies between nodes, ensuring that inferred relationships are robust despite noise, indirect measurements, and potential confounding influences.

Background

Time series from complex systems are widely used both to infer underlying network topology and to map statistical influences between signals. Correlation-based methods can yield spurious relationships, and causal inference techniques impose strong modeling assumptions and computational demands. Bayesian approaches offer principled inference but are often limited to small networks due to high computational cost. Despite progress, reliably reconstructing functional networks and quantifying dependencies from empirical time series remains unresolved.

References

Although substantial progress has been made, the reconstruction and quantification of dependencies in functional networks remains an open problem.

— Prediction and inference in complex networks: a brief review and perspectives  (2512.07439 - Rodrigues, 8 Dec 2025) in Section “Network reconstruction and statistical dependencies”

Consequently, inferring effective interaction statistics directly from abundance data for species-rich communities remains a major unresolved challenge in community ecology.

— Consistent determination of stability regimes in natural ecological communities from abundance time series  (2609.30154 - Megías et al., 24 Sep 2026) in Introduction, paragraph beginning “Temporal data partially break this degeneracy”

This complete estimator partition, rather than the pooled 12-of-24 fraction, is the informative result: NM-H2 is measure-dependent, and the mechanism underlying the partition remains unresolved.

— Bringing analytic rigor to agentic AI for science: The Brain Researcher platform for neuroimaging data analysis  (2608.19902 - Chen et al., 20 Aug 2026) in Figure 1 caption, Fig.\ref{fig:leading-case}B

It is still unknown whether these issues can be resolved with better methods, or if there are fundamental limits on what TSCD can achieve.

— One Thing Leads to Another: The Essentials of Time Series Causal Discovery  (2610.13430 - Butler et al., 9 Oct 2026) in Section VI, “Research Outlook,” p. 14

Finding general-purpose pipelines for TSCD, that can automatically analyse a given problem context, design and test methods to be used, and deploy those solutions, remains an open problem.

— One Thing Leads to Another: The Essentials of Time Series Causal Discovery  (2610.13430 - Butler et al., 9 Oct 2026) in Section VII, “Conclusion,” p. 14