Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation

• URL: http://arxiv.org/abs/2512.05976v1
• Date: Tue, 25 Nov 2025 16:25:24 GMT
• Title: Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation
• Authors: Antonio Varagnolo, Giuseppe Romano, Raphaël Pestourie,
• Abstract summary: Physics-Enhanced Deep Surrogate (PEDS)<n>Network learns geometry-dependent corrections and a mixing coefficient that interpolates between macroscopic and nano-scale behavior.<n>PEDS reduces training-data requirements by up to 70% compared with purely data-driven baselines.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Designing materials with controlled heat flow at the nano-scale is central to advances in microelectronics, thermoelectrics, and energy-conversion technologies. At these scales, phonon transport follows the Boltzmann Transport Equation (BTE), which captures non-diffusive (ballistic) effects but is too costly to solve repeatedly in inverse-design loops. Existing surrogate approaches trade speed for accuracy: fast macroscopic solvers can overestimate conductivities by hundreds of percent, while recent data-driven operator learners often require thousands of high-fidelity simulations. This creates a need for a fast, data-efficient surrogate that remains reliable across ballistic and diffusive regimes. We introduce a Physics-Enhanced Deep Surrogate (PEDS) that combines a differentiable Fourier solver with a neural generator and couples it with uncertainty-driven active learning. The Fourier solver acts as a physical inductive bias, while the network learns geometry-dependent corrections and a mixing coefficient that interpolates between macroscopic and nano-scale behavior. PEDS reduces training-data requirements by up to 70% compared with purely data-driven baselines, achieves roughly 5% fractional error with only 300 high-fidelity BTE simulations, and enables efficient design of porous geometries spanning 12-85 W m$^{-1}$ K$^{-1}$ with average design errors of 4%. The learned mixing parameter recovers the ballistic-diffusive transition and improves out of distribution robustness. These results show that embedding simple, differentiable low-fidelity physics can dramatically increase surrogate data-efficiency and interpretability, making repeated PDE-constrained optimization practical for nano-scale thermal-materials design.

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