The following folders have Jupyter notebook files that are used to obtain the results we present in Section I.1, I.2, III.B, III.C, IV.A and IV.B and Appendix C and D and Figures 9, 10, 11, 13. To calculate the graphical corrections we extensively use the Python package ``restflow'' (https://github.com/us-itp4/restflow). Each folder has one subfolder with figures used in the notebooks.

Description of supplementary files

1) tutorials: A folder which illustrates with examples how to use the package ``restflow''. It includes:

• model_b_simple.ipynb: A pedagogical tutorial to use restflow for the graphical corrections of the Model B (for the classic case with shifted field)

• ckpz.ipynb: A pedagogical tutorial to use restflow for the graphical corrections of the cKPZ

• neural.ipynb: A pedagogical tutorial to use restflow for the graphical corrections of a neural field model. It also analyzes the flow equations with the fixed points and plots Fig.11

2) analysis: A folder which is used for the analysis of the Active Model B+ and the Model B with the extra cubic term. It includes:

• model_b_noshift.ipynb: calculates the graphical corrections for the Model B without shifting the field (with the b model parameter) (Appendix C). It is used to plot Fig.13

• amb+_graphs.ipynb: calculates the graphical corrections of the Active Model B+ (Appendix D). It also calculates the graphical corrections leading to higher-order terms (Section III.C)

• amb+_noshift.ipynb: calculates the flow equations  for the Active Model B+ without shifting the field. It also analyzes its fixed points and applies stability analysis (Section III.D.1). It optionally plots the flow equations (figure not shown in manuscript)

• amb+_shift.ipynb: calculates the flow equations for the Active Model B+ with shifting the field. It also analyzes its fixed points and applies stability analysis (Section III.D.2). It optionally plots the flow equations (figure not shown in manuscript)

3) simulations: A folder which is used for the flow equations of the modified cKPZ and for the numerical simulations of the stochastic partial differential equation using py-pde. It includes:

• modified_ckpz.ipynb: calculates the graphical corrections and analyzes the flow equations for the modified cKPZ of Section IV.A. It plots Fig.9 and simulates the stochastic partial differential equation using py-pde and plots Fig.10

• 3d_4000: A folder of the data of the modified cKPZ using py-pde. It is used for the modified_ckpz.ipynb