Continued progress in inertial confinement fusion (ICF) requires solving inverse problems relating experimental observations to simulation input parameters, followed by design optimization. However, such high-dimensional dynamic PDE-constrained optimization problems are extremely challenging or even intractable. It has been recently shown that inverse problems can be solved by only considering certain robust features. Here we consider the ICF capsule's deuterium-tritium (DT) interface, and construct a causal, dynamic, multifidelity reduced-order surrogate that maps from a time-dependent radiation temperature drive to the interface's radius and velocity dynamics. The surrogate targets an ODE embedding of DT interface dynamics, and is constructed by learning a controller for a base analytical model using low- and high-fidelity simulation training data with respect to radiation energy group structure. After demonstrating excellent accuracy of the surrogate interface model, we use machine learning (ML) models with surrogate-generated data to solve inverse problems optimizing radiation temperature drive to reproduce observed interface dynamics. For sparse snapshots in time, the ML model further characterizes the most informative times at which to sample dynamics. Altogether we demonstrate how operator learning, causal architectures, and physical inductive bias can be integrated to accelerate discovery, design, and diagnostics in high-energy-density systems.

翻译：惯性约束聚变（ICF）的持续进展需要解决将实验观测与模拟输入参数相关联的反问题，进而完成设计优化。然而，此类高维动态偏微分方程约束优化问题极具挑战性，甚至难以求解。近期研究表明，通过仅关注特定鲁棒特征即可求解反问题。本文以ICF靶丸的氘-氚（DT）界面为研究对象，构建了一个因果性、动态、多保真度的降阶代理模型，该模型将随时间变化的辐射温度驱动映射至界面半径与速度动力学。该代理模型以DT界面动力学的常微分方程嵌入为目标，通过利用辐射能量群结构相关的低保真度与高保真度模拟训练数据，学习基础解析模型的控制器而构建。在验证代理界面模型具有优异精度后，我们采用基于代理生成数据的机器学习（ML）模型求解反问题，通过优化辐射温度驱动以复现观测到的界面动力学。针对时间稀疏快照情形，ML模型进一步刻画了动力学采样的最有效时间点。整体研究表明，算子学习、因果架构与物理归纳偏置的融合能够有效加速高能量密度系统中的科学发现、工程设计与实验诊断进程。