AI 中文总结
该研究提出利用非线性PT对称系统的原位伴随协议，实现无需反向传播的精确梯度评估，可自主发现参数配置以实现时空功能，为构建自优化非线性机器提供了新途径。
AI 中文摘要
伴随方法为基于梯度的优化提供了强大途径，但在一般非线性系统中，其物理实现受到阻碍，因为伴随动力学需要反向时间演化、雅可比转置和终端值约束。本文表明，非线性宇称-时间（$\boldsymbol{\textit{PT}}$）对称系统可克服这一阻碍。利用一类非线性非厄米谐振器网络，我们建立了对称关系，将形式上的伴随动力学映射到可实验获取的正向时间演化，并辅以受控注入。这种构造无需显式反向传播或矩阵转置，即可实现伴随梯度的精确原位评估。我们在非线性$\boldsymbol{\textit{PT}}$对称谐振器链中演示了该方法，所得优化协议可自主发现参数配置，以实现规定的时空功能，包括均匀能量再分布和在预定义时间窗口内的定向波传输。我们的结果表明，$\boldsymbol{\textit{PT}}$对称是在物理系统内实现计算灵敏度的一种资源，并为自优化非线性机器开辟了一条途径。
英文摘要
Adjoint methods provide a powerful route for gradient-based optimization, but their physical implementation is obstructed in generic nonlinear systems because the adjoint dynamics requires backward-time evolution, Jacobian transposition, and terminal-value constraints. Here we show that nonlinear parity-time ($\mathcal{PT}$)-symmetric systems overcome this obstruction. Using a class of nonlinear non-Hermitian resonator networks, we establish symmetry relations that map the formal adjoint dynamics onto experimentally accessible forward-time evolutions supplemented by controlled injections. This construction enables exact in-situ evaluation of adjoint gradients without requiring explicit backward propagation or matrix transposition. We demonstrate the approach in nonlinear $\mathcal{PT}$-symmetric resonator chains, where the resulting optimization protocol autonomously discovers parameter configurations that realize prescribed spatio-temporal functionalities, including uniform energy redistribution and targeted wave transport at predefined time windows. Our results identify $\mathcal{PT}$ symmetry as a resource for implementing computational sensitivities within physical systems and establish a route toward self-optimizing nonlinear machines.
Comments12 pages, 4 figures
