发表机构
Imperial College London（伦敦帝国学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出了一种验证器引导式（VG）工作流程，基于预训练符号 Transformer ODEFormer 实现物理动力系统的可解释预测，在范德波尔振荡器和涡旋脱落场景中展现出优于原方法的性能与泛化能力。
AI 中文摘要
非线性物理系统的可靠预测是科学发现与工程决策的基础，然而高保真模拟成本过高，而机器学习代理模型可能存在不透明性并编码了关于系统动力学的假设，限制了泛化能力。将合成常微分方程（ODE）轨迹映射为方程的预训练 Transformer 提供了可解释的替代方案，有望在无需特定系统方程知识的情况下实现迁移，但将其可靠迁移至高维物理数据仍是未解决的挑战。我们围绕 ODEFormer 作为符号主干开发了验证器引导式（VG）工作流程，利用动力学和物理可容许性准则从多轨迹候选方程池中进行选择，从而实现迁移。在经典范德波尔（Van der Pol）振荡器上，VG 在保留的初始条件下的表现优于原始 ODEFormer 工作流程。随后，我们针对与社会相关的大气和等离子体系统中发生的涡旋脱落现象，通过坐标降维以及固定和变化雷诺数下的符号发现进行研究。VG 发现了固定参数的降阶方程，能够恢复基本脱落振荡器和高次谐波，无需特定尾流的候选库或规定的纳维-斯托克斯（Navier-Stokes）结构，而跨参数模型可泛化至未见过的工况。仅重构保真度无法决定符号可发现性，凸显了潜在动力学与主干预训练分布之间兼容性的重要性。本研究建立了一种验证器引导式的神经符号转换方法，用于自然科学中可解释且可物理审计的预测。
英文摘要
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.
Comments33 pages, 13 figures, 10 tables
