NSE - Nash-Sutcliffe Efficiency

\[\text{NSE}(y, \hat{y}) = 1 - \frac{\sum_{i=0}^{N - 1} (y_i - \hat{y_i})^2}{ \sum_{i=0}^{N - 1} (y_i - mean(y))^2}\]

• Nash-Sutcliffe Efficiency (NSE): Best possible score is 1.0, bigger value is better. Range = (-inf, 1]

• Link: https://agrimetsoft.com/calculators/Nash%20Sutcliffe%20model%20Efficiency%20coefficient

Latex equation code:

\text{NSE}(y, \hat{y}) = 1 - \frac{\sum_{i=0}^{N - 1} (y_i - \hat{y_i})^2}{ \sum_{i=0}^{N - 1} (y_i - mean(y))^2}

Example to use NSE metric:

from numpy import array
from permetrics.regression import RegressionMetric

## For 1-D array
y_true = array([3, -0.5, 2, 7])
y_pred = array([2.5, 0.0, 2, 8])

evaluator = RegressionMetric(y_true, y_pred, decimal=5)
print(evaluator.nash_sutcliffe_efficiency())

## For > 1-D array
y_true = array([[0.5, 1], [-1, 1], [7, -6]])
y_pred = array([[0, 2], [-1, 2], [8, -5]])

evaluator = RegressionMetric(y_true, y_pred, decimal=5)
print(evaluator.NSE(multi_output="raw_values"))