thermal engineers

Abstract: Multi-domain physics-informed neural networks (PINNs) flexibly model medium-specific representations to solve fluid--solid conjugate heat transfer (CHT). However, standard multi-domain PINNs enforce governing equations and interface conditions on separately sampled domain supports, which can yield plausible temperature fields but inaccurate end-to-end energy transfer and outlet temperatures. We propose Cova-PINN, a multi-domain PINN framework that aligns conservation support with thermal interaction paths in complex geometries. Cova-PINN jointly optimizes cross-domain composite control-volume balances at the local scale and paired-wall closure at the global exchanger scale. We evaluate Cova-PINN on four triply periodic minimal surface (TPMS) heat exchangers and a geometrically distinct DualMS design against CHT-specific, optimization-oriented, and complex-geometry PINN baselines under a common protocol. Relative to the closest baseline, MUSA-PINN-CHT, Cova-PINN reduces average outlet-temperature and device-level closure errors across the four TPMS topologies by $37.7\%$ and $60.2\%$, respectively, while also improving full-field and heat-duty accuracy, with consistent gains on DualMS.

Abstract: Many physical systems are driven and observed only on lower-dimensional submanifolds of a larger spatial domain, while their dynamics are governed by the ambient medium occupying that domain. Examples include laser-heated parts imaged by an infrared camera, and ground-level emissions measured on a sensor plane. Full-domain solvers, however, compute the entire volume for every new source although only the observation submanifold is needed, and black-box surrogates do not exploit that the ambient medium remains fixed. We introduce the \emph{Green's Observation Operator (GObO)}, which maps the ambient medium once to the Green's kernel of a linear PDE restricted to the source and observation submanifolds. New sources then cost one lower-dimensional integral and no network evaluation. Exponential rates in the kernel yield an exact finite streaming state with horizon-independent memory; we prove its stability and an approximation rate for the restricted heat kernel. On three-dimensional heat conduction and advection--diffusion with collocated and distinct source and observation geometries, GObO trained on static sources predicts responses to moving sources zero-shot with 4--8$\times$ lower error than black-box surrogates, at 1.4\,ms per query after a single conditioning pass. The same kernel transfers across resolutions and admits corrections for mild nonlinearities, including radiative losses and temperature-dependent conductivity, without retraining, at the cost of lower in-distribution accuracy.