The paper is interesting and provides a new line of thinking about reservoir modeling through soft margin with an interpretation in terms of cumulants and second order Green function. The work serves as a proof-of-concept that perturbation analysis of the interaction is useful in practical computational problems. Reviewers recommend acceptance, but we strongly urge the authors to address the issues raised by the reviewers and add discussions to shed more light on intricate details and provide insights. The authors' response addresses some of these issues already, and this should be integrated into the final manuscript.