Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real-world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. We present a novel deterministic mixed-integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics-based constraints on the first and second derivatives.

中文翻译：

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具有导数信息的确定性符号回归：一般方法和在状态方程中的应用

符号回归方法通过生成表达式树同时确定模型函数形式和回归参数值。符号回归可以捕捉现实世界现象的复杂性，但由于现有公式搜索空间的复杂性，符号回归的确定性优化的使用受到限制。我们提出了一种用于符号回归的新确定性混合整数非线性规划公式，该公式通过辅助表达式树结合了导数约束。通过将链式法则应用于数学运算，二叉表达式树能够表示一阶和二阶导数的计算。我们将此公式应用于使用衍生信息的说明性示例，以显示增加的模型辨别能力。此外，