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Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: State-space inference for stochastic systems · 0 citations (OpenAlex)

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Proposes DYSCO, a multi-view temporal contrastive learning method that jointly recovers latent trajectories and symbolic governing dynamics (polynomial basis) from noisy nonlinear observations, with identifiability up to an affine gauge.

Problem

Recovering latent dynamical states and their governing equations from high-dimensional, noisy, nonlinear observations (Gaussian or Poisson noise) with identifiability guarantees, where prior contrastive identifiability results assume noiseless observations.

Approach

Uses multiple independent noisy views of the same latent trajectory in a temporal InfoNCE contrastive objective with a symbolic polynomial-basis dynamics model rolled out by ODE integration, so that cross-view consistency denoises the encoder; proves affine identifiability in the infinite-view limit and gives a symbolic sparsity-over-affine-orbit recovery procedure.

Key results

• Across seven simulated systems under Gaussian and Poisson noise, DYSCO averages 97.6% R^2 and 87.4% dynR^2 (Gaussian) and 98.0% R^2 and 85.4% dynR^2 (Poisson).
• On Lorenz and Stuart-Landau vs DYNCL under Poisson noise, DYSCO reaches 94.4% and 98.0% R^2 with dynR^2 82.3% and 83.1%, while DYNCL gets 0.0% dynR^2 on both.
• Ablation on Lorenz shows performance improves monotonically with number of views (1,2,4,8), and remains good up to noise sigma about 1 (SNR about 4 dB).

Surprising findings

• A single view already yields good results on the Lorenz system, attributed to dense resampling of neighboring latent states on the chaotic attractor.
• Winner-Take-All shows only average dynR^2 despite visually excellent phase portraits, suggesting the metric is affected by slow-velocity attractors.

Limitations

• Evaluated only on simulated data; real neural data not demonstrated.
• Latent dimensionality and symbolic basis are assumed known.
• Scalar potential term omitted in implementation, which may matter for non-uniform marginals; symbolic recovery is only a proof of concept with imperfect spurious terms.

Experimental setup

Datasets: simulated latent dynamical systems (Duffing, Lorenz, FitzHugh-Nagumo, Winner-Take-All, Double-Well, Stuart-Landau, Heter

Benchmarks: Duffing Lorenz FitzHugh-Nagumo Winner-Take-All Double-Well Stuart-Landau Heteroclinic

Metrics: R^2 after affine alignment dynR^2 flow-field R^2

Baselines: DYNCL

Builds on: DYNCL SINDy InfoNCE nonlinear ICA

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