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Page 12 of 25 Wang et al. J. Mater. Inf. 2026, 6, 16

One important strategy is transfer learning between simulation tiers or between simulations and
experiments. A common paradigm involves pretraining a deep neural network (DNN) on abundant LF data,
followed by fine-tuning selected layers using limited HF data, sometimes with physics-informed
constraints [87-89] . For example, Chakraborty proposed a MF physics-informed deep neural network
(MF-PIDNN) that encodes approximate physical laws at the LF level and is subsequently updated using
scarce HF data, demonstrating reliable predictions in reliability analysis where experiments are limited but
governing physics is known . In materials applications, this approach has been used for mechanical
[88]
property inference from small punch tests, polymer property prediction using heterogeneous data sources,
and formation energy prediction, where DFT pretraining accelerates learning on scarce experimental labels
[Figure 4B] [35,43,57] . Similar paradigms have been applied to fatigue life prediction with small datasets and
[90]
even cross-domain transfer from inorganic datasets to metal-organic frameworks, where pretraining on one
materials domain accelerates discovery in another . The latter study provides concrete validation of the
[55]
generalization capability of MF transfer learning, demonstrating that latent representations learned from one
class of materials can be reused in chemically distinct domains. Such transfer substantially reduces HF data
requirements when exploring new materials families and highlights the robustness of MF representations
beyond narrowly defined training distributions.

While transfer learning leverages sequential training, an alternative approach is to integrate multiple fidelities
simultaneously within a composite neural network . Islam et al. demonstrated this concept for molecular
[91]
[49]
dynamics, where coarse time-step data serve as LF inputs and fine time-step results provide HF corrections,
yielding accurate pressure predictions with reduced computational time cost. To assess not only accuracy but
also reliability, the authors evaluated model stability under repeated training. For each training-set size, the
networks were retrained multiple times using different random selections of HF data while keeping the LF
dataset fixed (10,000 samples for E* or 100,000 samples for σ ). The error bars in Figure 4C report the
y
standard deviation of the resulting mean absolute percentage error (MAPE) across these repeated trainings,
thereby quantifying variability in generalization performance. The substantially narrower error bars observed
for MF models indicate more stable predictions and higher reliability under changes in the HF training
subset. This example illustrates that, beyond improving mean accuracy, MF learning can significantly
enhance robustness and reduce sensitivity to data selection . Similar frameworks have been applied to
[30]
predict the residual strength of graded composites and to recover stress-strain fields from digital image
correlation in welds, all by coupling simulated and experimental data within a unified deep network [36,92] .
These studies show how composite neural networks exploit correlations between fidelities to deliver robust
surrogates that outperform HF-only training at much lower cost.

A related approach is correction learning, where a network is trained directly on the discrepancy between LF
and HF predictions. In band-gap benchmark studies, this strategy achieved lower errors than both transfer
learning and composite neural networks, as the model concentrates its capacity on systematic LF bias .
[93]
However, correction learning requires nested LF/HF pairs for training and typically demands an LF
evaluation for every new query, which can limit its applicability when LF evaluations are computationally
expensive.

Building on these approaches, the most ambitious efforts extend deep learning into MF GNNs. Chen et al.
incorporated fidelity tags into the Materials Graph Network (MEGNet) to learn across band-gap datasets
ranging from the PBE (LF) functional to the HSE hybrid functional and experimental measurements (HF) .
[29]
By embedding fidelity as a global state, their model integrates heterogeneous datasets and captures
correlations across fidelity levels. As shown in Figure 4D, MF GNNs consistently outperform SF and stacking
models. Performance is evaluated on randomly segmented test sets (80%-10%-10% split for
training-validation-test sets, repeating 6 runs), where the error bars show one standard deviation across runs