Deep Gaussian Process-based Cost-Aware Batch Bayesian Optimization forComplex Materials Design Campaigns

Abstract The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast, nonlinear design spaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surro-gates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations acrossmultiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost intoan upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes smallbatches of candidates in parallel, balancing exploration of under-characterized regions with exploitation ofhigh-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.