Machine learning has permeated material optimization, providing high value. Nevertheless, its re- liance on a high number of samples limits its applicability to relatively explored material families. In this paper we extend the applicability of machine learning to novel and understudied materials through the PYTHIA (Probabilistic Yet Transferable Hierarchical Interaction Architecture) framework. Pythia utilizes two of the most powerful machine learning concepts, foundational models and transfer learning. We employ a complex foundational model trained on a large dataset of chemically similar molecules, on a target that is physically close to our prediction target. Then, we freeze the weights and perform subspace alignment with the use of a transformer layer and add uncertainty quantification with gaussian processes. These two layers can be trained on a limited dataset yet allow us to leverage the gained knowl- edge and the studied materials and complex architectures. The resulting model is used as a surrogate for a Bayesian Optimization scheme. To showcase the robustness of the framework, we applied it to the investigation of adsorption and defect optimization of two distinct systems. Not only were we able to correctly and efficiently identify the optimal adsorption sites of even complex a

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