# Function-on-function kriging, with applications to 3D printing of aortic tissues

arXiv: https://arxiv.org/abs/1910.01754 · HTML: https://mlsanity.com/paper/1910.01754/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2019.

## Built on by (most cited first, 9 of 9)

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- [Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recovery](https://mlsanity.com/paper/2302.00755/) (2023)
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- [Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters](https://mlsanity.com/paper/2403.03816/) (2024)
- [Gaussian Process Subspace Regression for Model Reduction](https://mlsanity.com/paper/2107.04668/) (2021)
- [Rational Kriging](https://mlsanity.com/paper/2312.05372/) (2023)
- [Function-on-Function Bayesian Optimization](https://mlsanity.com/paper/2511.12783/) (2025)
- [P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution](https://mlsanity.com/paper/2606.19303/) (2026)

## Abstract (arXiv)

3D-printed medical prototypes, which use synthetic metamaterials to mimic biological tissue, are becoming increasingly important in urgent surgical applications. However, the mimicking of tissue mechanical properties via 3D-printed metamaterial can be difficult and time-consuming, due to the functional nature of both inputs (metamaterial structure) and outputs (mechanical response curve). To deal with this, we propose a novel function-on-function kriging model for efficient emulation and tissue-mimicking optimization. For functional inputs, a key novelty of our model is the spectral-distance (SpeD) correlation function, which captures important spectral differences between two functional inputs. Dependencies for functional outputs are then modeled via a co-kriging framework. We further adopt shrinkage priors on both the input spectra and the output co-kriging covariance matrix, which allows the emulator to learn and incorporate important physics (e.g., dominant input frequencies, output curve properties). Finally, we demonstrate the effectiveness of the proposed SpeD emulator in a real-world study on mimicking human aortic tissue, and show that it can provide quicker and more accurate tissue-mimicking performance compared to existing methods in the medical literature.