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Wang et al. J. Mater. Inf. 2026, 6, 16 Page 17 of 25

Table 2. Comparison of multi-fidelity strategies across advantages, limitations, bias-variance focus, and data requirements
Strategy Advantages Limitations Bias/Variance Data requirements

Statistical weighting Simple, interpretable Limited expressiveness Variance Non-nested, flexible
Direct ML with fidelity Flexible, leverages features May underperform with Bias Works with non-nested
features sparse HF data
Correction-based (e.g., Captures correlations, Needs nested data, heavy Both Best with nested
co-kriging) uncertainty quantification compute
Needs large datasets, less Non-nested, but
Deep learning frameworks Captures complex relations Bias
interpretable data-hungry
Active learning / adaptive Sample-efficient, reduces cost Complex acquisition design Both Few samples; can create
sampling nested adaptively
In this review, we use the terms nested and non-nested to describe whether the same inputs are observed at multiple fidelity levels. This is
sometimes referred to as co-located vs. non-co-located in the literature; both describe the same concept of overlapping vs. non-overlapping input
sets. HF: High fidelity; ML: machine learning.

CROSS-CUTTING THEMES
Bias vs. variance
Compared with HF data, LF sources typically exhibit larger errors, which can be decomposed into bias and
variance. Bias refers to systematic deviations introduced by differences in data-generation pipelines, such as
experiments vs. simulations, simplified physical models, alternative algorithms (e.g., HSE vs. PBE), or choices
of simulation hyperparameters [29,32-34,52,82,91,95,98,99] . Variance, by contrast, reflects random measurement noise
and is generally lower in HF data. Examples include measurements made under the same protocol but
carried out by novice vs. experienced researchers, or using worn vs. newly calibrated instruments .
[100]

The relative contributions of bias and variance strongly influence the choice of MF methodology, as shown
in Table 2. When systematic bias dominates, correction-based methods are particularly effective because they
explicitly model cross-fidelity discrepancies. Deep learning approaches or models with explicit fidelity
indicators (e.g., one-hot encoding) can play a similar role by learning fidelity-specific corrections. When
variance is the primary concern, statistical approaches with heteroscedastic modeling or inverse-variance
weighting provide a principled treatment. In practice, especially in experimental materials data, bias and
variance almost always coexist [101] . In such mixed settings, kriging-based methods (e.g., co-kriging), which
simultaneously capture cross-fidelity correlations and account for heteroscedastic errors, are attractive
options . Active learning strategies also provide robust solutions, as they can adaptively downweight LF
[48]
inputs in non-critical regions without requiring explicit assumptions about error type.

Overall, recognizing whether bias, variance, or both dominate a MF dataset is essential for selecting an
appropriate strategy, and remains a central cross-cutting theme in the design of effective materials
informatics workflows.

Data requirements: nested vs. non-nested
In addition to error characteristics, the feasibility of MF methods is strongly influenced by their data
requirements, particularly the distinction between nested and non-nested designs. In a nested design, the
same input x is observed at multiple fidelity levels, allowing direct comparison and correction between low-
and HF outputs. By contrast, in a non-nested design, most inputs are observed at only one fidelity level,
leaving little or no overlap across fidelities.

Correction-based methods such as co-kriging are especially sensitive to this distinction, as they typically
assume a nested structure to learn systematic deviations between fidelities. In practice, however, materials
datasets are often non-nested, arising from disparate sources such as separate DFT databases, experimental