A Unified Multiscale Auxiliary PINN Framework for Generalized Phonon Transport

TL;DR

This paper introduces MTNet, a multiscale auxiliary PINN framework that efficiently solves the generalized phonon radiative transfer equation, capturing complex nanoscale thermal transport phenomena.

Contribution

The work presents a novel mesh-free, fully differential PINN approach with auxiliary formulation, enabling scalable, accurate simulations of phonon transport and inverse problems.

Findings

Successfully simulates ballistic-diffusive regimes in silicon thin films.

Captures boundary slip effects under large temperature gradients.

Retrieves unknown slab thickness from interface temperature data.

Abstract

Nanoscale thermal transport is governed by the phonon Boltzmann transport equation (BTE). However, simulating the sub-continuum dynamics remains computationally prohibitive due to the high dimensionality of the phase space and the intrinsic nonlinearity of the scattering collision operator. Traditional numerical solvers and standard physics-informed neural networks (PINNs) inherently struggle with these integro-differential equations due to deterministic quadrature limitations, artificial thermalization introduced by the relaxation time approximation (RTA), and multiscale spectral bias. This work introduces a multiscale auxiliary physics-informed neural network (MTNet) to solve the generalized equation of phonon radiative transfer (GEPRT). By leveraging an auxiliary formulation, this mesh-free framework recasts the GEPRT into a fully differential system, enabling the analytical evaluation of scattering operators via automatic differentiation and facilitating scalable multi-GPU parallelization. To circumvent optimization stiffness, the architecture employs a decoupled, shallow neural network explicitly constrained by radiative equilibrium. MTNet is validated by simulating steady-state cross-plane transport in a silicon thin film, successfully capturing ballistic-diffusive regimes and characteristic boundary slips across extreme temperature gradients ($\Delta T = 100$ K) beyond the standard linearization approach. Furthermore, we show that our framework successfully solves a geometric inverse problem in a slab geometry, retrieving the unknown slab thickness based only on interface temperature constraints in the mesoscopic regime. Ultimately, MTNet establishes a robust, fully differentiable foundation for predicting high-fidelity kinetic transport and extracting material properties in next-generation nanostructures.