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TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: Stochastic population dynamics · 0 citations (OpenAlex)

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Proposes TracingFlow, a simulation-free flow matching framework that solves a second-order (acceleration-cost) optimal transport problem (DOAT) for trajectory inference from snapshots, with lineage barcode priors.

Problem

Trajectory inference from sparse temporal snapshots (e.g., scRNA-seq) with first-order, memoryless velocity fields cannot capture momentum, time-delayed responses, or lineage-consistent dynamics; velocities are unobserved.

Approach

Formulates a Dynamical Optimal Acceleration Transport (DOAT) problem with acceleration cost, decomposes it into SOAT couplings and cubic minimum-cost single-particle paths, approximates unknown velocities iteratively, and regresses the acceleration field and initial velocity with flow matching; lineage barcodes enter via a penalized cost matrix.

Key results

• On the 2D simulation, TracingFlow reaches W1 0.3748 and W2 0.5180, versus 0.5270 and 0.5922 for OT-CFM (best baseline in that column group).
• On EB 5D held-out time points, TracingFlow achieves W1 4.4974 vs 4.5602 for SF2M, the best baseline.
• On 3D Sim-Lineage, TracingFlow achieves lineage-weighted W1 0.4538 vs 1.5255 for SF2M; on Hematopoiesis it gives 14.0470 vs 15.2165 for CAF.

Surprising findings

• The Cite 100D results show OT-CFM (10.55 W1) outperforming TracingFlow only on none; TracingFlow is best there at 8.07 W1, but SF2M and 3MSBM show wide variance across datasets.

Limitations

• SOAT pre-computation is computationally intensive for large datasets, mitigated only by minibatch OT.
• Velocity distribution is approximated by its conditional expectation, a deterministic approximation.
• The acceleration action functional lacks a clear physical interpretation.

Experimental setup

Datasets: 2D simulation Cite 5D Cite 100D EB 5D 3D Simulation Lineage Hematopoiesis

Benchmarks: 2D Simulation Cite 5D Cite 100D EB 5D 3D Sim-Lineage Hematopoiesis

Metrics: W1 distance W2 distance lineage-weighted W1 lineage-weighted W2

Baselines: OT-CFM SF2M 3MSBM MMFM HRF CAF

Builds on: OT-CFM 3MSBM Schrödinger bridge flow matching (SF2M)

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