In artificial neural networks, sometimes non-smooth functions are used instead for efficiency these are known as hard sigmoids. The van Genuchten–Gupta model is based on an inverted S-curve and applied to the response of crop yield to soil salinity.Įxamples of the application of the logistic S-curve to the response of crop yield (wheat) to both the soil salinity and depth to water table in the soil are shown in modeling crop response in agriculture. When a specific mathematical model is lacking, a sigmoid function is often used. Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. Inverted logistic S-curve to model the relation between wheat yield and soil salinity A sigmoid function is a mathematical function having a characteristic 'S'-shaped curve or sigmoid curve.Ī common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: S ( x ) = 1 1 + e − x = e x e x + 1 = 1 − S ( − x ).Ī sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0.