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→维度平均的EI
<math>
<math>
\Delta \mathcal{J}\equiv \frac{\mathcal{J_F}}{N}-\frac{\mathcal{J_f}}{n}\approx \frac{N}{n}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln\frac{\left|\det\left(\frac{\partial_\mathbf{x} f(\mathbf{x})}{\Sigma^{1/2}}\right)\right|^2}{\left|\det\left(\frac{\partial_\mathbf{X} F(\mathbf{X})}{\Sigma_N^{1/2}}\right)\right|^2} d\mathbf{x}
\Delta \mathcal{J}\equiv \mathcal{J_F}-\mathcal{J_f}=\frac{\mathcal{EI_F}}{N}-\frac{\mathcal{EI_f}}{n}\approx \frac{N}{n}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln\frac{\left|\det\left(\frac{\partial_\mathbf{x} f(\mathbf{x})}{\Sigma^{1/2}}\right)\right|^2}{\left|\det\left(\frac{\partial_\mathbf{X} F(\mathbf{X})}{\Sigma_N^{1/2}}\right)\right|^2} d\mathbf{x}
</math>
</math>