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A bstract Previous work has explored the connections between three concepts — operator size, complexity, and the bulk radial momentum of an infalling object — in the context of JT gravity and the SYK model. In this paper we investigate the higher dimensional generalizations of these connections. We use a toy model to study the growth of an operator when perturbing the vacuum of a CFT. From circuit analysis we relate the operator growth to the rate of increase of complexity and check it by complexity-volume duality. We further give an empirical formula relating complexity and the bulk radial momentum that works from the time that the perturbation just comes in from the cutoff boundary, to after the scrambling time.

Uncertainty quantification (UQ) in metal additive manufacturing (AM) has attracted tremendous interest in order to dramatically improve product reliability. Model-based UQ, which relies on the validity of a computational model, has been widely explored as a potential substitute for the time-consuming and expensive UQ solely based on experiments. However, its adoption in the practical AM process requires overcoming two main challenges: (1) the inaccurate knowledge of uncertainty sources and (2) the intrinsic uncertainty associated with the computational model. Here, we propose a data-driven framework to tackle these two challenges by combining high throughput physical/surrogate model simulations and the AM-Bench experimental data from the National Institute of Standards and Technology (NIST). We first construct a surrogate model, based on high throughput physical simulations, for predicting the three-dimensional (3D) melt pool geometry and its uncertainty with respect to AM parameters and uncertainty sources. We then employ a sequential Bayesian calibration method to perform experimental parameter calibration and model correction to significantly improve the validity of the 3D melt pool surrogate model. The application of the calibrated melt pool model to UQ of the porosity level, an important quality factor, of AM parts, demonstrates its potential use in AM quality control. Themore »proposed UQ framework can be generally applicable to different AM processes, representing a significant advance toward physics-based quality control of AM products.

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