On Nonintrusive Uncertainty Quantification and Surrogate Model Construction in Particle Accelerator Modeling

Abstract

Using a cyclotron based model problem, we demonstrate for the first time the applicability and usefulness of an uncertainty quantification (UQ) approach in order to construct surrogate models. The surrogate model quantities for example emittance, energy spread, or the halo parameter, can be used to construct a global sensitivity model along with error propagation and error analysis. The model problem is chosen such that it represents a template for general high-intensity particle accelerator modelling tasks. The usefulness and applicability of the presented UQ approach is then demonstrated on an ongoing research project, aiming at the design of a compact high-intensity cyclotron. The proposed UQ approach is based on polynomial chaos expansions and relies on a well defined number of high fidelity particle accelerator simulations. Important uncertainty sources are identified using Sobol' indices within the global sensitivity analysis.

Machine learning for orders of magnitude speedup in multiobjective optimization of particle accelerator systems

“…However, one downside of using a simple NN model is that it does not inherently give an estimate of prediction uncertainty and model sensitivity without additional analysis. In contrast, the PCE model has the benefit of providing straightforward estimates of prediction uncertainty and sensitivity via the Sobol' indices [25,39]. The PCE model also has fewer hyperparameters to tune (i.e., polynomial order, type of polynomial used).…”

“…Details on the datasets, training procedures, implementations of the ML models and the GA, and the details of the physics simulations can be found in the Appendix. We first focus on artificial neural networks (NNs) to demonstrate the technique, and later briefly compare the results with those obtained from polynomial chaos expansion (PCE) [25,37] and support vector regression (SVR) models. The randomly varied inputs include the injector rf phase ϕ 1 and accelerating gradient G 1 , the linac cavity rf phase ϕ 2 and accelerating gradient G 2 , and two solenoid strengths K 1 and K 2 .…”

“…We have used ML models in several previous instances to create fast-executing surrogates for computationally intensive accelerator simulations [21][22][23][24][25]. Here, we build on those works and take a substantial step forward by evaluating such models for use in optimization (and multiobjective optimization in particular).…”

Polynomial Chaos Expansion method as a tool to evaluate and quantify field homogeneities of a novel waveguide RF Wien filter

“…When K equals the cardinality of the design of experiment N , the validation method is called the leave-one-out cross-validation (LOOCV). The implemented algorithm selects a single instance ξ k from 4 Any expansion implemented on a computer is actually truncated. the input set and computes the meta-model of the remaining set, i.e., M ξ − {ξ k } = Y k .…”

“…Surrogate modeling is one possible solution that is feasible and which provides a reliable method to quantify uncertainties and provides a sensitivity analysis at zero additional cost. The PCE method has been used in many engineering applications, such as modeling uncertainties in electric motors [3], and also in accelerator science [4].…”