Systematic Analysis of Penalty-Optimised Illumination Design for Tomographic Volumetric Additive Manufacturing via the Extendable Framework TVAM AID Using the Core Imaging Library

Tomographic Volumetric Additive Manufacturing(TVAM) is a novel manufacturing method that allows for the fast creation of objects of complex geometry in layerless fashion. The process is based on the solidification of photopolymer that occurs when a sufficient threshold dose of light-energy is absorbed. In order to create complex shapes, an illumination plan must be designed to force solidification in some desired areas while leaving other regions liquid. Determining an illumination plan can be considered as an optimisation problem where a variety of objective functionals (penalties) can be used. This work considers a selection of penalty functions and their impact on selected printing metrics; linking the shape of penalty functions to ranges of light-energy dose levels in in-part regions that should be printed and out-of-part regions that should remain liquid. Further, the threshold parameters that are typically used to demarcate minimum light-energy for in-part regions and maximum light-energy for out-of-part regions are investigated systematically as design parameters on both existing and new methods. This enables the characterisation of their effects on some selected printing metrics as well as informed selection for default values. This work is underpinned by a reproducible and extensible framework, TVAM Adaptive Illumination Design(TVAM AID), which makes use of the open-source Core Imaging Library(CIL) that is designed for tomographic imaging with an emphasis on reconstruction. The foundation of TVAM AID which is presented here can hence be easily enhanced by existing functionality in CIL thus lowering the barrier to entry and encouraging use of strategies that already exist for reconstruction optimisation.

Fast Gaussian Processes under Monotonicity Constraints

Gaussian processes (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and can be leveraged to improve model fidelity. Incorporating such constraints into GP models enhances predictive accuracy and reduces uncertainty, but remains a computationally challenging task for high-dimensional problems. In this work, we present a novel virtual point-based framework for building constrained GP models under monotonicity constraints, based on regularized linear randomize-then-optimize (RLRTO), which enables efficient sampling from a constrained posterior distribution by means of solving randomized optimization problems. We also enhance two existing virtual point-based approaches by replacing Gibbs sampling with the No U-Turn Sampler (NUTS) for improved efficiency. A Python implementation of these methods is provided and can be easily applied to a wide range of problems. This implementation is then used to validate the approaches on approximating a range of synthetic functions, demonstrating comparable predictive performance between all considered methods and significant improvements in computational efficiency with the two NUTS methods and especially with the RLRTO method. The framework is further applied to construct surrogate models for systems of differential equations.