Evolution of the envelope mass as computed with the solved equations of the internal structure (red lines) and with our DNN (blue lines). We also show the comparison with what would be obtained using the approach of I00 (grey areas), and B15 (green areas) for different choices of the envelope opacity (see text). The evolution of the core mass is shown by the red dashed line. Each figure has different scales for the time and the envelope mass. Upper left: with the BL94 opacity for a planet at 5 AU that accretes with Ṁ_core = 10⁻⁶ M_⊕ yr⁻¹. Upper right: with the BL94 opacity for a planet at 5 AU that accretes with Ṁ_core = 5 × 10⁻⁷ M_⊕ yr⁻¹. Lower left: with a reduced opacity for a planet at 10 AU that accretes with Ṁ_core = 10⁻⁶ M_⊕ yr⁻¹. Lower right: with a reduced opacity for a planet at 5 AU that accrete with Ṁ_core = 10⁻⁶ M_⊕ yr⁻¹, but assuming a disc temperature equal to 50 K (150 K in all other cases). The kink in the green areas is due to the rapid runaway accretion of gas when the planet reaches the cross-over mass (mass of accreted gas equal to the mass of accreted solids; see B15).