Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers
A verifier-guided (VG) workflow built around ODEFormer enables reliable transfer of pretrained symbolic transformers from synthetic ODE trajectories to high-dimensional physical data The VG method uses dynamical and physical-admissibility criteria to select candidate equations from a multi-trajectory pool, outperforming the original ODEFormer on Van der Pol oscillators across held-out initial conditions Applied to vortex shedding at fixed and varying Reynolds numbers, VG discovers reduced-order
Analysis
TL;DR
- A verifier-guided (VG) workflow built around ODEFormer enables reliable transfer of pretrained symbolic transformers from synthetic ODE trajectories to high-dimensional physical data
- The VG method uses dynamical and physical-admissibility criteria to select candidate equations from a multi-trajectory pool, outperforming the original ODEFormer on Van der Pol oscillators across held-out initial conditions
- Applied to vortex shedding at fixed and varying Reynolds numbers, VG discovers reduced-order equations capturing fundamental shedding oscillators and higher harmonics without a wake-specific candidate library or prescribed Navier-Stokes structure
- Cross-parameter generalization was achieved, with the model successfully transferring to withheld Reynolds number regimes
- Reconstruction fidelity alone does not guarantee symbolic discoverability; compatibility between latent dynamics and the backbone's pretraining distribution is the critical factor
Why It Matters
This work bridges the gap between opaque machine-learning surrogates and interpretable symbolic models for physical forecasting, addressing a critical need in scientific AI where both accuracy and auditability matter. By enabling pretrained symbolic transformers to generalize to real-world high-dimensional systems without system-specific equation knowledge, it offers a scalable path toward physically auditable forecasting tools for atmospheric, plasma, and engineering applications.
Technical Details
- Backbone architecture: ODEFormer, a pretrained transformer that maps synthetic ODE trajectories to symbolic equations, serving as the symbolic discovery engine
- Verifier-guided selection: A multi-stage filtering pipeline applies dynamical consistency checks and physical-admissibility criteria to rank and select candidate equations from a pool generated across multiple trajectories
- Van der Pol validation: Benchmark testing on canonical nonlinear oscillators demonstrates superior generalization across held-out initial conditions compared to the original ODEFormer workflow
- Vortex shedding application: Coordinate reduction combined with symbolic discovery at fixed and varying Reynolds numbers recovers reduced-order equations capturing the fundamental shedding frequency and higher harmonics, without relying on a pre-specified Navier-Stokes structure or wake-specific candidate library
- Key finding on generalization: Cross-parameter transfer to withheld Reynolds number regimes succeeded, revealing that latent-dynamics-to-pretraining-distribution compatibility, not mere reconstruction fidelity, determines symbolic discoverability
Industry Insight
- The verifier-guided paradigm establishes a reusable template for neural-to-symbolic discovery that can be adapted to other physical domains (climate modeling, plasma physics, structural dynamics) where interpretable surrogates are valued over black-box predictions
- Practitioners should prioritize alignment between the pretraining distribution of symbolic backbones and the latent dynamics of target systems, rather than optimizing solely for reconstruction error, when deploying transferable equation-discovery pipelines
- The success at varying Reynolds numbers without regime-specific retraining suggests that pretrained symbolic transformers, when paired with appropriate verifiers, could reduce the cost and expertise barrier for scientific model discovery across parameter sweeps in engineering and natural sciences
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