Research map / Probabilistic and scientific modeling / Causal discovery
Marrying Causal Representation Learning with Dynamical Systems for Science
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Connects causal representation learning identifiability results to parameter estimation in dynamical systems and builds an identifiable "mechanistic identifier" (multiview CRL + mechanistic neural networks) evaluated on simulated wind and real sea-surface temperature data.
Problem
Parameter estimation in dynamical systems lacks identifiability guarantees, while causal representation learning has identifiability theory but few real-world applications; the paper asks whether time-invariant trajectory-specific physical parameters can be identified from real time series while kee
Approach
Cast trajectory-specific ODE parameters as latent variables in CRL, reuse multiview CRL alignment-plus-sufficiency objectives with a differentiable mechanistic neural network solver as decoder, so the learned encoder partially identifies shared parameters while forecasting efficiently.
Key results
- On the SST-V2 climate-zone task, the mechanistic identifier reaches 0.902 ID accuracy and 0.824 OOD accuracy, versus 0.468 for Ada-GVAE and 0.697 for TI-MNN (contrastive identifier: 0.904 ID, 0.861 OOD).
- On SST-V2 forecasting, the mechanistic identifier achieves forecasting error 0.007 versus 0.043 for Ada-GVAE and 0.024 for TI-MNN.
- On wind simulation, the layer-thickness parameter is isolated in one 4-dimensional partition (accuracy approximately 1) for contrastive and mechanistic identifiers, while Ada-GVAE and TI-MNN average about 60%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the mechanistic solver instead of a vanilla decoder | Mechanistic identifier versus Ada-GVAE · SST-V2 | forecast error: 0.043 ± 0.044 -> 0.007 ± 0.003 | Helped |
| Add multiview CRL to the time-invariant MNN | Mechanistic identifier versus TI-MNN · SST-V2 | ID accuracy: 0.697 ± 0.049 -> 0.902 ± 0.005 | Helped |
| Add multiview CRL to the time-invariant MNN | Mechanistic identifier versus TI-MNN · SST-V2 | OOD accuracy: 0.668 ± 0.074 -> 0.824 ± 0.016 | Helped |
| Use a mechanistic decoder instead of no decoder | Mechanistic identifier versus Contrastive identifier · SST-V2 | forecast error | Mixed |
| Use the mechanistic identifier instead of the contrastive identifier | SST-V2 climate-zone classification · SST-V2 | ID accuracy: 0.904 ± 0.011 -> 0.902 ± 0.005 | Mixed |
| Use the mechanistic identifier instead of the contrastive identifier | SST-V2 climate-zone classification · SST-V2 | OOD accuracy: 0.861 ± 0.022 -> 0.824 ± 0.016 | Hurt |
| Use multiview CRL with the mechanistic solver rather than TI-MNN | Wind simulation · Wind simulation layer-thickness classification | accuracy: average acc. of 60% | Helped |
| Use multiview CRL rather than a vanilla decoder | Wind simulation · Wind simulation layer-thickness classification | accuracy: acc≈1 | Helped |
Surprising findings
- The paper argues that a generic unknown-form ODE is in general non-identifiable, so identifiability requires weak supervision such as multiview data.
Limitations
- Theory requires deterministic dynamics and excludes stochastic differential equations.
- Assumes direct observation of the state without measurement noise.
- Identifiability analysis is limited to the infinite-data regime.
Experimental setup
Datasets: SpeedyWeather.jl wind simulation SST-V2 ODEBench
Benchmarks: ODEBench SST-V2 climate-zone classification SpeedyWeather wind layer-thickness classification
Metrics: RMSE accuracy (ID/OOD) forecasting error ATE estimate trend
Baselines: Ada-GVAE TI-MNN Contrastive identifier
Builds on: mechanistic neural networks multiview causal representation learning Ada-GVAE SINDy
Closest papers by meaning
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.89)
- CausalDynamics: A large‐scale benchmark for structural discovery of dynamical causal models (NeurIPS 2025 · similarity 0.88)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.88)
- Causal Representation Learning Made Identifiable by Grouping of Observational Variables (ICML 2024 · similarity 0.88)
- Causal Climate Emulation with Bayesian Filtering (NeurIPS 2025 · similarity 0.87)
- Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts (NeurIPS 2026 · similarity 0.87)
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