用神经网络生成多种最优参数，解决等离子体激光融合中的不稳定性问题。
Generative Neural Reparameterization for Differentiable PDE-constrained Optimization
- 将优化参数重参数化为神经网络输出，实现分布化优化。
- 在激光聚变场景中生成多个高性能且多样化的最优解。
- 适合需要多组优质解的物理仿真与工程设计场景。
偏微分方程（PDE）约束优化是求解由PDE governing系统最优参数的经典方法，但通常仅能获得一组最优参数。若具备可微的PDE求解器，可将自由参数重参数化为神经网络的输出，训练该网络以学习从概率分布到最优参数分布的映射。当PDE存在多个表现良好的局部极小值时，此方法尤为有效。本文将其应用于激光聚变中激光-等离子体不稳定性最小化的优化任务，证明神经网络能够生成多个性能优异且多样化的最优参数解。
原文摘要 · Abstract (English)
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per optimization. Given a differentiable PDE solver, if the free parameters are reparameterized as the output of a neural network, that neural network can be trained to learn a map from a probability distribution to the distribution of optimal parameters. This proves useful in the case where there are many well performing local minima for the PDE. We apply this technique to train a neural network that generates optimal parameters that minimize laser-plasma instabilities relevant to laser fusion and show that the neural network generates many well performing and diverse minima.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。