Ji Qiang

Hengrui Luo, Xiaoye S. Li, Yang Liu et al.

Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to optimistically narrow posterior intervals and biased decisions. We study GP regression under input measurement uncertainty by representing each noisy input as a probability measure and defining covariance through Wasserstein distances between these measures. Building on this perspective, we instantiate a deterministic projected Wasserstein ARD (PWA) kernel whose one-dimensional components admit closed-form expressions and whose product structure yields a scalable, positive-definite kernel on distributions. Unlike latent-input GP models, PWA-based GPs (\PWAGPs) handle input noise without introducing unobserved covariates or Monte Carlo projections, making uncertainty quantification more transparent and robust.

Hao Zhang, Jack Hirschman, Randy Lemons et al.

Structured optical waveforms are emerging as powerful control fields for the next generation of complex photonic and electromagnetic systems, where the temporal structure of light can determine the ultimate performance of scientific instruments. However, identifying optimal optical drive fields in strongly nonlinear regimes remains challenging because the mapping between optical inputs and system response is high-dimensional and typically accessible only through computationally expensive simulations. Here, we present a physics-guided deep learning framework for the inverse design of optical temporal waveforms. By training a light-weighted surrogate model on simulations, the method enables gradient-based synthesis of optical profiles that compensate nonlinear field distortions in driven particle-field systems. As a representative application, we apply the approach to the generation of electron beams used in advanced photon and particle sources. The learned optical waveform actively suppresses extrinsic emittance growth by more than 52% compared with conventional Gaussian operation and by approximately 9% relative to the theoretical flattop limit in simulation. We further demonstrate experimental feasibility by synthesizing the predicted waveform using a programmable pulse-shaping platform; incorporating the measured optical profile into beamline simulations yields a 31% reduction in the extrinsic emittance contribution. Beyond accelerator applications, this work establishes a general way for physics-guided inverse design of optical control fields, enabling structured light to approach fundamental performance limits in nonlinear photonic and high-frequency electromagnetic systems.