Uncertainty quantification of laser pulse shapes using Student-T processes with input noise

Focused Energy is developing a direct-drive laser fusion pilot plant (FPP) using a diode-pumped, solid-state laser to compress deuterium-tritium fuel. Achieving ignition requires precise shaping of the nanosecond laser pulse, but inherent uncertainties in the system's physics and operating conditions make deterministic analysis insufficient. This necessitates a stochastic uncertainty quantification (UQ) approach.

While Gaussian process (GP) models are common for UQ, their light-tailed distributions assign low probability to extreme events, and their posterior variance depends only on input locations, not observed responses. These are significant drawbacks for modeling the complex physics of laser-plasma interactions. We therefore propose a more robust UQ model: the Student-T process (STP) with input uncertainty. The STP’s adjustable degrees-of-freedom parameter (kurtosis) allows for heavier-tailed distributions, better capturing the likelihood of outliers. By more realistically accounting for physical variance and extreme events, the STP provides a more reliable framework for FPP design and optimization.

This talk will detail the STP formulation and its application to modeling laser pulse delivery uncertainty. We will demonstrate how this model enables the design of robust, high-performance implosions by properly accounting for operational uncertainties.