Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal (2408.07847v2)

Abstract: Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high performance physics-based simulators for predicting behavior in a charged particle beam are computationally expensive, limiting their utility for solving inverse problems online. The problem of estimating upstream six-dimensional phase space given downstream measurements of charged particles in an accelerator is an inverse problem of growing importance. This paper introduces a reverse Latent Evolution Model (rLEM) designed for temporal inversion of forward beam dynamics. In this two-step self-supervised deep learning framework, we utilize a Conditional Variational Autoencoder (CVAE) to project 6D phase space projections of a charged particle beam into a lower-dimensional latent distribution. Subsequently, we autoregressively learn the inverse temporal dynamics in the latent space using a Long Short-Term Memory (LSTM) network. The coupled CVAE-LSTM framework can predict 6D phase space projections across all upstream accelerating sections based on single or multiple downstream phase space measurements as inputs. The proposed model also captures the aleatoric uncertainty of the high-dimensional input data within the latent space. This uncertainty, which reflects potential uncertain measurements at a given module, is propagated through the LSTM to estimate uncertainty bounds for all upstream predictions, demonstrating the robustness of the LSTM against in-distribution variations in the input data.

• The paper introduces a novel rLEM that reverses beam dynamics using a CVAE-LSTM framework to accurately reconstruct upstream 6D phase space from downstream data.
• Numerical simulations with LANSCE data yield high accuracy with MSE ~5e-7 and SSIM ~0.998, validating the model's computational efficiency.
• The framework effectively quantifies uncertainty from input variability, enhancing online diagnostics and control in particle accelerators.

An Essay on "Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal"

The paper "Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal" by Mahindra Rautela, Alan Williams, and Alexander Scheinker presents a notable advance in accelerating the solution of inverse problems in beam dynamics using machine learning techniques. The proposed reverse Latent Evolution Model (rLEM) is meticulously designed for temporal inversion of forward beam dynamics in particle accelerators, offering computational efficiency and robustness in the face of high-dimensional and uncertain data.

Methodological Framework

The research introduces a two-step self-supervised deep learning framework to address the inverse problem inherent in charged particle dynamics. The challenge is to estimate the upstream six-dimensional (6D) phase space from downstream measurements in a particle accelerator. The dynamics of the charged particles evolve within the phase space $\mathbf{(x, y, z, p_x, p_y, p_z)}$ and are influenced by various electromagnetic fields and temporal variations.

The crux of this framework is the employment of a Conditional Variational Autoencoder (CVAE) to encode the high-dimensional phase space projections into a lower-dimensional latent space. This enables the efficient capture of spatial correlations while significantly reducing dimensionality. The subsequent step involves training a Long Short-Term Memory (LSTM) network to learn the reverse temporal dynamics within this latent space autoregressively. This coupled CVAE-LSTM architecture allows the rLEM to predict upstream phase space projections based on downstream measurements, effectively addressing the inverse problem with high accuracy and computational efficiency.

Numerical Results and Observations

Extensive simulations were performed using High Performance Simulator (HPSim), an advanced tool developed at Los Alamos National Laboratory, to generate the dataset used for training and evaluation. The dataset encompasses 15 unique 2D projections of phase space across 48 modules of the LANSCE accelerator, constituting a total size of 1400×48×15×256×256.

The visualization of the latent space achieved through Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) highlights the model's ability to learn and represent the spatial correlations effectively. The training and validation results demonstrate a strong capability of the rLEM to generate accurate predictions of beam dynamics in upstream modules. The mean squared error (MSE) and structural similarity index (SSIM) values underscore the high precision of the model, achieving overall MSE and SSIM of approximately 5e-7, 0.998 (training set) and 1e-6, 0.976 (test set).

Uncertainty Quantification

An essential feature of the rLEM is its ability to capture and propagate aleatoric uncertainty, which stems from the inherent variability in input data measurements. The CVAE encodes this uncertainty in the latent space by minimizing the negative log-likelihood of data, assuming a Gaussian distribution. This encoded uncertainty is then translated through the LSTM network. The paper demonstrates that the LSTM exhibits robust performance even under input data variations, maintaining the consistency of predictions within the uncertainty bounds.

Practical and Theoretical Implications

The practical implications of this research are substantial. By offering a highly efficient method for predicting upstream beam dynamics, the rLEM can significantly enhance online diagnostics and control in particle accelerators. This model is particularly advantageous for facilities such as LANSCE, where rapid adjustments and accurate predictions are critical for minimizing beam losses and optimizing accelerator performance.

Theoretically, the approach opens avenues for further research in the application of deep learning models to complex physical systems involving spatiotemporal dynamics. The model's design paradigms can be extended beyond particle accelerators to other domains requiring temporal inversion of spatially complex data. Future work could involve augmenting the framework to incorporate epistemic uncertainty, employing techniques like Bayesian neural networks (BNNs) or Monte Carlo dropout.

Conclusion

This paper presents a comprehensive and methodologically sophisticated solution to the inverse problem in beam dynamics, leveraging the strengths of modern deep learning techniques. The reverse Latent Evolution Model (rLEM) stands out for its ability to perform precise, efficient, and uncertainty-aware predictions of particle beam dynamics, setting a benchmark for future developments in accelerator physics and related fields. With its promising results and broad implications, this research marks a significant contribution to the field, facilitating improved performance and control in particle accelerators.