Active Subspace is a supervised learning dimension reduction technique used to approximate a scalar quantity of interest (defined in m input dimensions) in n (<m) dimensions. This technique assumes that the function is continuous over the domain and hence its gradient information is available at each point in the domain. The gradient information is used to find the direction of maximum variation in function which is called as ‘active subspace’ and other orthogonal directions are called as ‘inactive subspace’. The process to find the active subspace is illustrated in figure below as well as in the animation file presented adjacent to the figure.