**5. Conclusions**

Calibrating complex material models using experimental tests and simulations is a critical task in computational engineering. When done in combination with statistical inference, this process can yield accurate values for the unknown material parameters plus additional information about its scatter and intervals of confidence. For example, Gaussian processes provide a natural and powerful framework to combine physical and numerical tests to obtain probability distributions of the material parameters. To fully exploit the potential of this kind of analysis, however, a large number of data points is required, and the latter can be most effectively obtained by employing a meta-model.

In this work, we described an effective framework for calibrating complex material models based on the combination of meta-models built on top of anisotropic Radial Basis Functions, Global Sensitivity Analysis, and Gaussian processes. The integration of these techniques results in a robust and efficient workflow.

We have employed the framework described for the calibration of three extremely common, although complex material models. These are the Johnson–Cook, the Zerilli–Armstrong, and Arrhenius-type models, and are typically employed for the characterization of the elasto-visco-plastic response of metals under high strain rates, and possibly high temperature as well. The outcome of our analysis is two-fold. First, we are able, for each material model, to rank the sensitivity of an impact simulation with respect to each of the parameters involved. Second, the framework produces a probability distribution for all the calibrated parameters as a function of the available or generated data, tapping into previously built and extremely fast statistical tools to obtain them. Such a characterization is more complete than simple point estimates, often employed when fitting material models.

Let us conclude by noting that the procedures described in this work have applicability beyond materials calibration to, in principle, problems where model evaluations and experimental setups are costly.

**Author Contributions:** Conceptualization, I.R.; methodology, E.M. and I.R.; software, J.L.d.P., E.M., and I.R.; validation, J.L.d.P. and E.M.; data curation, J.L.d.P. and E.M.; writing—original draft preparation, J.L.d.P. and E.M.; writing—review and editing, I.R.; visualization, J.L.d.P. and E.M.; supervision, I.R.; funding acquisition, I.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** JdP has been partially funded by the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme (Call Reference No: JTI-CS2-2017-CfP07-ENG-03-22) under grant agreement No 821044. IR would also like to acknowledge the funding received from the Spanish Ministry of Science, Innovation and Universities through project HEXAGB (RTI2018-098245-B- C21).

**Acknowledgments:** JdP has been partially funded by the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme (Call Reference No: JTI-CS2-2017-CfP07-ENG-03-22) under grant agreement No 821044. IR would also like to acknowledge the funding received from the Spanish Ministry of Science, Innovation and Universities through project HEXAGB (RTI2018-098245-B- C21).

**Conflicts of Interest:** The authors declare no conflict of interest.
