Cool Graphs: Active Property Search Towards Quantum Nano-Refrigerators

Nanodevices that absorb energy from their thermal environment can act as quantum refrigerators. Finding suitable configurations, however, is a needle-in-a-haystack problem: the many-body state space scales exponentially with the size of the device, where each candidate configuration requires an expensive quantum-chemical computation. We introduce a search framework that couples a Graph Variational Autoencoder (GVAE) with an uncertainty-driven Active Learning (AL) loop to efficiently identify energy-absorbing configurations in electronic junctions with a 2D "working material" to be optimized. The GVAE maps physical parameters - site energies, coupling matrices, temperature - into a smooth latent space that distinguishes cooling from dissipative parameter regimes, achieving a classification discriminability of $0.920 \pm 0.004$ on held-out configurations and $0.895 \pm 0.010$ on unseen extrapolation topologies. An AL pipeline based on Monte Carlo dropout then targets the decision boundary, iteratively selecting the candidates where the model is least certain for simulation. Over 32 AL cycles, the uncertainty-driven strategy discovers energy absorbing systems at rates consistently exceeding the random baseline across all tested topologies (where only 1.9-8.4% of configurations exhibit the desired property), providing a data-efficient pathway for navigating a combinatorically large design space. The learned latent space organizes configurations along physically interpretable axes, that correlate with underlying microscopic model parameters. This hints at the existence of "cooling coordinates" - low-dimensional, physically interpretable quantities separating cooling from non-cooling regimes. Our framework, thus, paves a new way towards effective cooling of nanoscale electronic information processing devices, to reduce the environmental footprint of high performance computing.