Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers

• URL: http://arxiv.org/abs/2608.02662v1
• Date: Sat, 01 Aug 2026 19:03:21 GMT
• Title: Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers
• Abstract summary: We develop a verifier-guided neural-to-symbolic methodology for interpretable and physically auditable forecasting in the natural sciences.<n>This work establishes a verifier-guided neural-to-symbolic methodology for interpretable and physically auditable forecasting in the natural sciences.
• Score: 11.537633174586956
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making. Yet high-fidelity simulations are prohibitively costly, and machine-learning surrogates can be opaque and encode assumptions about system dynamics, limiting generalizability. Pretrained transformers mapping synthetic ODE trajectories to equations offer interpretable alternatives, promising transfer without system-specific equation knowledge. Transferring them reliably to high-dimensional physical data, however, remains an open challenge. We develop a verifier-guided (VG) workflow around ODEFormer as a symbolic backbone, using dynamical and physical-admissibility criteria to select from a multi-trajectory candidate equation pool, enabling transfer. On canonical Van der Pol oscillators, VG outperforms the original ODEFormer workflow across held-out initial conditions. We then address vortex shedding, a phenomenon occurring in atmospheric and plasma systems of societal relevance, through coordinate reduction and symbolic discovery at fixed and varying Reynolds numbers. VG discovers fixed-parameter reduced-order equations that recover the fundamental shedding oscillator and higher harmonics without a wake-specific candidate library or prescribed Navier-Stokes structure, while the cross-parameter model generalizes to withheld regimes. Reconstruction fidelity alone did not determine symbolic discoverability, highlighting the importance of compatibility between latent dynamics and the backbone's pretraining distribution. This work establishes a verifier-guided neural-to-symbolic methodology for interpretable and physically auditable forecasting in the natural sciences.

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