arXiv:2608.02662cs.LGcs.AI2026-08

用验证器引导符号模型,从物理数据中自动发现可解释的动力学方程。

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

论文配图:Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers
图 1 · 摘自论文原文
  • 通过动态与物理合理性筛选候选方程,提升符号模型在真实物理数据上的迁移能力。
  • 在范德波尔振子和涡脱现象中均实现高精度建模,且跨雷诺数泛化成功。
  • 不依赖特定流场库或纳维-斯托克斯结构,适合科学发现与工程预测场景。

可靠的非线性物理系统预测支撑科学发现与工程决策。然而高保真模拟成本高昂,机器学习代理模型常缺乏可解释性且隐含系统动力学假设,限制泛化能力。预训练的变换器将合成常微分方程轨迹映射为方程,提供可解释替代方案,有望实现无需系统特有方程知识的迁移。但将其可靠迁移到高维物理数据仍是挑战。本文围绕符号骨干ODEFormer构建验证器引导(VG)工作流,利用动力学与物理合理性准则从多轨迹候选方程池中筛选,实现有效迁移。在经典范德波尔振子上,VG在保留初始条件下的表现优于原ODEFormer流程。随后针对大气与等离子体中具有社会意义的涡脱现象,通过坐标降维与符号发现,在固定与变化雷诺数下进行探索。VG发现的固定参数降阶方程成功恢复基频涡脱振荡器及高次谐波,无需特定尾流候选库或预设纳维-斯托克斯结构;跨参数模型亦能泛化至未见参数区间。重建保真度并非决定符号可发现性的关键,凸显潜在动力学与骨干预训练分布间的兼容性至关重要。本研究建立了一种验证器引导的神经到符号方法,为自然科学中的可解释、可审计预测提供了新范式。

原文摘要 · Abstract (English)

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.

符号回归物理建模可解释AI动力系统

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