Research map / Probabilistic and scientific modeling / Dynamical systems
Neural Persistence Dynamics
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Learns a latent ODE over vectorized per-time-point persistent homology diagrams (plus PointNet++ features) of collective-behavior point clouds and regresses governing-equation parameters from the latent path, outperforming PSK and crocker stacks.
Problem
Inferring parameters of governing equations for collective behavior (D'Orsogna, Vicsek, volume exclusion) from time-evolving point clouds without tracking individual trajectories, which is hard to scale and existing topological methods handle poorly.
Approach
Model the dynamics of vectorized persistence diagrams per time point with a variational latent ODE (attention-based mTAN encoder), then regress governing-equation parameters from the latent path, with stability results for vectorized persistent homology justifying the continuous latent model.
Key results
- On dorsogna-1k, joint model (PH+PointNet++) reaches VE 0.931 and SMAPE 0.067, versus PSK 0.828/0.096 and crocker stacks 0.746/0.150.
- On vicsek-10k, PH-only variant reaches VE 0.579 and SMAPE 0.146 versus PSK 0.466/0.173.
- On volex-10k, the joint model reaches VE 0.871 and SMAPE 0.081 versus PSK 0.509/0.190.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PointNet++ representations to PH representations (ablation) | Neural Persistence Dynamics · dorsogna-1k | VE: 0.851±0.008 -> 0.931±0.004 | Helped |
| Add PointNet++ representations to PH representations (ablation) | Neural Persistence Dynamics · vicsek-10k | VE: 0.579±0.034 -> 0.576±0.030 | No clear effect |
| Model latent dynamics with a latent ODE (ablation) | Neural Persistence Dynamics · vicsek-10k | VE: 0.512±0.020 -> 0.576±0.030 | Helped |
| Model latent dynamics with a latent ODE (ablation) | Neural Persistence Dynamics · dorsogna-1k | SMAPE: 0.098±0.004 -> 0.067±0.002 | Helped |
| Use PH representations instead of PointNet++ representations (ablation) | Neural Persistence Dynamics · vicsek-10k | VE: 0.274±0.085 -> 0.579±0.034 | Helped |
| Use PH+PointNet++ instead of PointNet++ alone (ablation) | Neural Persistence Dynamics · dorsogna-1k | SMAPE: 0.132±0.018 -> 0.067±0.002 | Helped |
| Include H1 with H0 features (ablation) | Neural Persistence Dynamics (PH-only) · dorsogna-1k | VE: 0.819 ± 0.015 -> 0.844 ± 0.021 | Helped |
| Include H1 and H2 with H0 features (ablation) | Neural Persistence Dynamics (PH-only) · dorsogna-1k | VE: 0.819 ± 0.015 -> 0.846 ± 0.011 | Helped |
| Include H2 in addition to H0 and H1 features (ablation) | Neural Persistence Dynamics (PH-only) · dorsogna-1k | VE: 0.844 ± 0.021 -> 0.846 ± 0.011 | No clear effect |
| Use PH-only instead of PH+PointNet++ representations (ablation) | Neural Persistence Dynamics · dorsogna-10k | VE: 0.689±0.021 -> 0.680±0.025 | Hurt |
| Use PH-only instead of PH+PointNet++ representations (ablation) | Neural Persistence Dynamics · vicsek-10k | VE: 0.576±0.030 -> 0.579±0.034 | No clear effect |
| Use PH-only instead of PH+PointNet++ representations (ablation) | Neural Persistence Dynamics · volex-10k | SMAPE: 0.081±0.006 -> 0.082±0.007 | No clear effect |
Surprising findings
- PointNet++ representations alone perform poorly on vicsek-10k (VE 0.274) yet reasonably on dorsogna-1k (VE 0.816), while PH works on both.
- Even without latent dynamics, the attention-based regression baseline already exceeds the PSK state of the art.
Limitations
- Relies on Vietoris-Rips persistent homology, whose complex becomes prohibitively large when the number of points grows (especially for H2).
- Stability guarantees do not apply when point cardinality changes over time (as in volex-10k).
Experimental setup
Datasets: dorsogna-1k dorsogna-10k vicsek-10k volex-10k
Benchmarks: dorsogna-1k dorsogna-10k vicsek-10k volex-10k
Metrics: variance explained (VE) SMAPE
Baselines: PSK Crocker Stacks PointNet++ w/o dynamics baseline
Builds on: neural ODE mTAN exponential structure elements path signature kernel crocker stacks
Closest papers by meaning
- TRENDy: Temporal Regression of Effective Nonlinear Dynamics (ICLR 2025 · similarity 0.87)
- Meta-Dynamical State Space Models for Integrative Neural Data Analysis (ICLR 2025 · similarity 0.87)
- Identifying latent state transitions in non-linear dynamical systems (ICLR 2025 · similarity 0.87)
- Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems (NeurIPS 2026 · similarity 0.87)
- Back to the Continuous Attractor (NeurIPS 2024 · similarity 0.86)
- Let's do the time-warp-attend: Learning topological invariants of dynamical systems (ICLR 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.