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Structural Inference of Dynamical Systems with Conjoined State Space Models
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Proposes SICSM, which combines selective SSM (Mamba) residual blocks for trajectory dynamics with a JSP-GFN posterior over graph structure to infer interaction structure from irregularly sampled and partially observed dynamical system trajectories.
Problem
Structural inference of directed interaction graphs from trajectories of dynamical systems that are irregularly sampled and partially observed (unobserved nodes).
Approach
Uses selective SSM (Mamba) blocks with input-dependent step size to model node dynamics under irregular intervals, aggregates outputs of multiple residual blocks as input to a joint structure-parameter GFN that samples adjacency matrices as posterior approximation.
Key results
- On Springs Simulations and NetSims with 10 time steps, SICSM maintains AUROC above 85% while baselines decline substantially.
- On VN_SP_30 with only 60% of nodes observed, SICSM keeps AUROC above 80%, while NRI and ACD drop below 75%.
- In biological networks BF and TF, SICSM surpasses baselines by roughly 5-10% AUROC across sampling levels.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SICSM for irregularly sampled trajectories | Structural inference methods on Springs Simulations and NetSim · Springs Simulations and NetSim, irregular sampling | AUROC: above 85% | Helped |
| Use SICSM instead of baseline methods | Structural inference on BF and TF · BF and TF, irregular sampling | AUROC: 5-10% | Helped |
| Use SICSM for inference with partially observed nodes | Structural inference on VN_SP_30 · VN_SP_30, 60% of nodes observed | AUROC: above 80%; below 75% | Helped |
| Use outputs from multiple Residual Blocks instead of only the final encoder block (ablation) | SICSM · VN_SP_15, 12-node sampling | structural inference accuracy | Helped |
Surprising findings
- Traditional VAE-based methods (NRI, ACD, MPM, iSIDG, RCSI) often perform no better than random guessing under irregular sampling.
Limitations
- Ablation suggests single-block output blurs hop distinctions; authors note possible need for adaptive weighting of block outputs.
- Future work on mutable structures and emerging nodes is not addressed.
- SubTB conditions are only satisfied approximately with fixed-length partial trajectories, so theoretical guarantees are weaker.
Experimental setup
Datasets: Springs Simulations NetSims BoolODE synthetic biological networks (LI, LL, CY, BF, TF, BF-CV) StructInfer Vascular Networks (VN_SP, VN_NS)
Benchmarks: Springs Simulations NetSims LI LL CY BF TF BF-CV VN_SP_15 VN_SP_30 VN_SP_50 VN_SP_100
Metrics: AUROC AUPRC SHD F1-score
Baselines: NRI MPM ACD iSIDG RCSI JSP-GFN CUTS SIDEC
Builds on: Mamba Generative Flow Networks JSP-GFN Neural Relational Inference
Closest papers by meaning
- Benchmarking Structural Inference Methods for Interacting Dynamical Systems with Synthetic Data (NeurIPS 2024 · similarity 0.89)
- Theoretical Foundations of Deep Selective State-Space Models (NeurIPS 2024 · similarity 0.88)
- Gated Inference Network: Inference and Learning State-Space Models (NeurIPS 2024 · similarity 0.87)
- Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling (NeurIPS 2026 · similarity 0.87)
- Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning (NeurIPS 2026 · similarity 0.86)
- eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling (NeurIPS 2024 · similarity 0.86)
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