Fig. 5: Results of 2D in-plane phonon transport (\(\Delta T=2\) K). | npj Computational Materials

Fig. 5: Results of 2D in-plane phonon transport (\(\Delta T=2\) K).

From: Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium

Fig. 5: Results of 2D in-plane phonon transport ( $$\Delta T=2$$ Δ T = 2 K).

a Dimensionless x-directional heat flux results along the y-axis (see inset in panel (b)) in silicon films with different length scales, where \({q}_{x}^{\ast }={q}_{x}(Y)/{q}_{{\rm{bulk}}}\) and \(Y=y/L\). From bottom to top, the PINN predictions are shown as circles for L = 100 nm, 300 nm, 1 μm, 10 μm. The black solid lines represent analytical solutions by the Fuchs-Sondheimer theory. b Effective thermal conductivity normalized by the bulk thermal conductivity at different length scales. The filled circles represent the parameter points used in training, while the open circles are predicted points not included in training. The inset shows the schematic of the simulation domain and boundary conditions.

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