We present a framework for constraining the automatic sequential generation of equations to obey the rules of dimensional analysis by construction. Combining this approach with reinforcement learning, we built $\Phi$-SO, a Physical Symbolic Optimization method for recovering analytical functions from physical data leveraging units constraints. Our symbolic regression algorithm achieves state-of-the-art results in contexts in which variables and constants have known physical units, outperforming all other methods on SRBench's Feynman benchmark in the presence of noise (exceeding 0.1%) and showing resilience even in the presence of significant (10%) levels of noise.

翻译：我们提出了一种框架，通过构造方法约束方程自动序列生成过程，使其严格遵循量纲分析规则。将该方法与强化学习相结合，我们构建了$\Phi$-SO——一种物理符号优化方法，利用单位约束从物理数据中恢复解析函数。在变量和常量具有已知物理单位的场景中，我们的符号回归算法取得了最先进的成果：在SRBench的费曼基准测试中，面对超过0.1%的噪声水平时，该方法在所有其他方法中表现最优，即使在10%的高噪声水平下仍展现出鲁棒性。