DEEP OPERATOR NETWORKS FOR THERMAL ENERGY STORAGE: LEARNING TEMPERATURE AND LIQUID-FRACTION DYNAMICS IN PHASE CHANGE MATERIALS

Abstract

Predicting transient thermal transport and phase transition in Phase Change Materials (PCMs) subjected to varying boundary heating conditions typically requires repeatedly evaluating heat conduction models coupled with an effective heat capacity framework that accounts for latent heat absorption and release. To bypass this computational burden, we implement Deep Operator Networks (DeepONets) to learn the functional mapping from arbitrary wall heat-flux inputs to interior temperature distributions T(x, z, t) within a PCM domain. The local liquid-fraction field φ(x, z, t) is directly recovered during post-processing via the analytical solidus–liquidus temperature dependency. Furthermore, we outline a Physics-Informed DeepONet (PI-DeepONet) conceptual framework incorporating momentum, mass, and energy residuals for the complete Navier–Stokes system with enthalpy-porosity and Carman–Kozeny drag terms; this conceptual extension serves theoretical completeness and is not numerically evaluated in this manuscript. We establish an error bound associated with input sensor interpolation and evaluate its algorithmic impact. Numerical experiments covering 1D thermal diffusion, nonlinear dynamical systems, and 2D PCM melting indicate that an unstacked, normalized DeepONet reaches a relative L² temperature field error of 3.2 × 10⁻⁴ averaged over time trajectories (10 saved time steps) and 3.5 × 10⁻⁴ at the final temporal snapshot, while recovering the liquid-fraction interface with a relative L² deviation of 7.2%. Independent execution benchmarks yield an average FDM solve time of 6.90 ± 0.02 s compared to an average DeepONet forward-pass execution time of 8.18 ± 0.85 ms across 10,000 evaluation points. This corresponds to an approximate 844× speedup relative to our non-vectorized Python finite-difference benchmark (vectorizing the FDM code lowers this acceleration ratio to ∼100×). Finally, key physical and methodological constraints are analyzed — including pure conduction assumptions, single-material/geometry evaluations, the absence of an empirical PI-DeepONet baseline, preliminary convergence metrics, single random-seed evaluations, and a lack of alternative operator baselines like FNOs.