Fig. 1

A Equivalent input–output network of the conventional Patlak plot with the nonlinear transformations \(\Psi_{{\text{X}}}\) and \(\Psi_{{\text{Y}}}\) in closed-form expressions. B \(\Psi_{{\text{X}}}\) and \(\Psi_{{\text{Y}}}\) are replaced with neural networks in the proposed Deep Patlak model.