Efficient Cross-Functional Learning for Atomistic Modeling of Materials

Adapting atomistic foundation models to higher-fidelity DFT functionals is limited by the scarcity and cost of target labels. In practice, models are often pre-trained on large datasets computed with lower-cost functionals such as PBE, and then fine-tuned on smaller datasets generated with higher-accuracy but more computationally expensive functionals like r2SCAN. However, there is limited understanding of how to efficiently perform such cross-functional transfer, especially how the choice of adaptation strategy interacts with target-data availability and compute constraints. In this work, we compare two cross-functional adaptation strategies for atomistic foundation models under realistic data and compute constraints: (i) a simple and lightweight delta-learning method for efficient adaptation in low-data regimes, and (ii) a multi-head fine-tuning that jointly learns multiple functionals through a shared representation. Through layer-wise probing, we show that early layers provide more transferable features for cross-functional adaptation, which helps explain the effectiveness of the simple delta-learning. Delta-learning is the most effective strategy in low-data, low-compute settings, achieving competitive performance with up to two orders of magnitude less compute. By contrast, multi-head learning enables bidirectional transfer between functionals, with higher-fidelity supervision also improving lower-fidelity predictions. These results provide a practical recipe for cross-functional adaptation under different resource constraints.