Machine-assisted methods for discovering physical laws from background theory and data have recently emerged, promising to advance our understanding of the physical world. However, training and benchmarking these systems remains challenging: real physical theories are limited in number. To address this need, we introduce SynPAT, a system for generating synthetic physical theories with accompanying data. SynPAT produces: (i) a consistent set of axioms forming a synthetic theory, (ii) a symbolic consequence of these axioms representing the discovery target, and (iii) noisy data approximating this consequence. Crucially, to mirror historically incorrect theories (e.g., Newtonian mechanics before Special Relativity), SynPAT can also generate theories whose axioms do not strictly entail, and in fact conflict with, the observed consequence, requiring a correction to the assumed axioms to bridge the gap. We detail SynPAT's methodology and benchmark several open-source symbolic regression systems on our generated theories and data.

翻译：从背景理论和数据中发现物理定律的机器辅助方法最近已经出现，有望推进我们对物理世界的理解。然而，训练和评估这些系统仍然具有挑战性：真实的物理理论在数量上是有限的。为了满足这一需求，我们引入了SynPAT，一个用于生成附带数据的合成物理理论的系统。SynPAT产生：(i) 一组构成合成理论的一致公理，(ii) 这些公理的一个符号化推论，代表发现目标，以及 (iii) 近似该推论的噪声数据。至关重要的是，为了反映历史上不正确的理论（例如，狭义相对论之前的牛顿力学），SynPAT也可以生成其公理并不严格蕴含、甚至与观察到的推论相冲突的理论，这需要对假设的公理进行修正以弥合差距。我们详细阐述了SynPAT的方法论，并在我们生成的理论和数据上对几个开源符号回归系统进行了基准测试。