In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity but often ignore the variability from the differentiation method itself. We show that this choice systematically introduces uncertainty, affecting both equation form and parameter estimates. Our study indicates that high-resolution schemes can magnify measurement noise, while heavily regularized methods may mask real physical variations, which leads to method-dependent findings. By evaluating six differentiation techniques on various partial differential equations under diverse noise levels using SINDy and EPDE frameworks, we consistently notice methodological biases in the determined models. This underscores the importance of selecting differentiation methods as a key modeling choice and highlights a path to enhance ensemble-based discovery by diversifying methodologies.

翻译：在微分方程发现算法中，数值微分通常是一个固定的预处理步骤。现有方法通过数据子采样和稀疏性提高了鲁棒性，但往往忽略了微分方法本身带来的变异性。我们证明，该方法选择会系统地引入不确定性，影响方程形式和参数估计。我们的研究表明，高分辨率格式可能放大测量噪声，而强正则化方法可能掩盖真实的物理变化，从而导致方法依赖性的发现。通过使用SINDy和EPDE框架，在不同噪声水平下对多种偏微分方程评估六种微分技术，我们一致观察到所确定模型中的方法学偏差。这强调了选择微分方法作为关键建模决策的重要性，并指出了通过方法多样化来增强基于集成的发现路径。