In one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system's parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which can be a cumbersome task and is code-specific. To propose an adjoint solver that is not code-specific, we develop a data-driven strategy. We demonstrate its application on the computation of gradients of long-time averages of chaotic flows. First, we deploy a parameter-aware echo state network (ESN) to accurately forecast and simulate the dynamics of a dynamical system for a range of system's parameters. Second, we derive the adjoint of the parameter-aware ESN. Finally, we combine the parameter-aware ESN with its adjoint version to compute the sensitivities to the system parameters. We showcase the method on a prototypical chaotic system. Because adjoint sensitivities in chaotic regimes diverge for long integration times, we analyse the application of ensemble adjoint method to the ESN. We find that the adjoint sensitivities obtained from the ESN match closely with the original system. This work opens possibilities for sensitivity analysis without code-specific adjoint solvers.

翻译：在一次计算中，伴随敏感性分析可提供目标函数相对于所有系统参数的梯度。传统上，伴随求解器需通过微分计算模型来实现，这一过程既繁琐又具有代码特异性。为提出一种非代码特异性的伴随求解器，我们开发了一种数据驱动策略，并展示了其在混沌流长时间平均梯度计算中的应用。首先，我们部署一种参数感知型回声状态网络（ESN）以准确预测和模拟动态系统在参数范围内的动力学行为；其次，推导出该参数感知型ESN的伴随形式；最后，结合参数感知型ESN及其伴随版本计算对系统参数的敏感性。我们将该方法应用于典型混沌系统进行验证。由于混沌系统中的伴随敏感性在长时间积分下会发散，我们分析了集成伴随方法在ESN中的应用。结果表明，通过ESN获得的伴随敏感性与原系统高度吻合。该工作为无需代码特异性伴随求解器的敏感性分析开辟了可能性。