Surrogate Models studies for laser-plasma accelerator electron source design through numerical optimisation

TL;DR

Laser wakefield accelerators offer high gradients but present complex, nonlinear injector design challenges. The authors build and compare surrogate models—MLP, Gaussian Processes, and XGBoost—trained on over $3000$ PIC simulations to map LPI input configurations to beam outputs, achieving near-$R^2$ values around $0.97$ for the best models. These surrogates enable rapid optimization, including single- and multi-objective Bayesian approaches, to locate stable working points with targeted $E_{med}$, $Q$, $\delta E_{mad}$, and $\epsilon_y$, while reducing computational cost by about $10^7$ times relative to PIC. The work demonstrates potential for integrating surrogates into start-to-end laser-plasma accelerator design and highlights the importance of data distribution, paving the way for real-time, data-driven control and multi-fidelity frameworks with experiments.

Abstract

Designing a high-quality plasma injector electron source driven by a laser beam relies on numerical parametric studies using particle-in-cell codes. The common input parameters to explore are laser characteristics, plasma species and density profiles produced by computational fluid dynamic studies. We demonstrate the construction of surrogate models using machine learning techniques for a laser-plasma injector (LPI) based on more than $3000$ particle-in-cell simulations of laser wakefield acceleration performed for sparsely spaced input parameters published by Drobniak [Phys. Rev. Accel. Beams, 26, 091302, (2023)]. Surrogate models are relevant for LPI design and optimisation, as they are approximately $10^7$ times faster than PIC simulations. Their speed enables more efficient design studies by allowing extensive exploration of the input-output relationship without significant computational cost. We develop and compare the performance of three surrogate models, namely, multilayer perceptron (MLP), decision trees (DT) and Gaussian processes (GP). We show that using a simple and frugal MLP-based model trained on a reasonable-size random scan data set of 500 particles in cell simulations, we can predict beam parameters with a coefficient determination score $R^2=0.93$ . The best surrogate model is used to quickly find optimal working points and stability regions and get targeted electron beam energy, charge, energy spread and emittance using different methods, namely random search, Bayesian optimisation and multi-objective Bayesian optimisation. This simple approach can serve more global design study of an LPI in a start-to-end linear laser-driven accelerator.on beam energy, charge and energy spread using different methods, namely random search, Bayesian optimisation and multi-objective Bayesian optimisation

Figures (14)

• Figure 1: Surrogate models and injection prediction-based LPI design optimisation studies flowchart. The dashed line represents the potential optimisation loop update of the input $x^{(i)}$.
• Figure 2: Distribution of the input parameters for the $9846$ training data simulations (blue) and the $3536$ test data simulations (orange).
• Figure 3: Injection model tested on randomly generated points. The dark-blue curve is $2.5 \cdot p_c$, with $p_c$ the critical pressure necessary for self-focusing.
• Figure 4: Scatter plot showing the relationship between the density of input data configuration points and MSE for every test point for the MLP model. The blue points represent the different configurations.
• Figure 5: coefficient of determination $R^2$ as a function of the training size in log scale, for all the SM trained on SET2 and tested on SET1. $R^2$ was taken as the average over 10 training sessions, with the vertical bars representing the standard deviation