做动力系统建模或算子逼近的研究者，可以用这个算法自动调激活函数，省去手动试错的成本，建议直接看论文里的实验对比。
RaNNDy 是一种随机神经网络架构，用于数据驱动地逼近复杂动力系统的传递算子。其隐藏层权重和偏置随机初始化并固定，仅训练输出层，具有闭式解和低训练成本的优势。但该架构受限于初始随机参数决定的基函数质量，而基函数由激活函数决定。本文提出一种算法，在保持随机网络权重和偏置固定的前提下，优化激活函数本身，从而提供更合适的字典。通过随机微分方程和图随机游走等基准问题验证了该方法的有效性。
Optimization of randomized neural networks for transfer operator approximation
RaNNDy is a randomized neural network architecture for the data-driven approximation of transfer operators associated with complex dynamical systems. The weights and biases of the hidden layers of the network are randomly initialized and kept fixed, only the output layer is trained. This has several advantages over fully optimized neural networks, notably a closed-form solution for the output layer and significantly lower training costs. Despite these advantages, RaNNDy is restricted to the initial selection of weights and biases that parametrize the basis functions required for the operator approximation. Since the basis functions are determined by the activation function, choosing an appropriate activation function for the hidden layers is crucial. In this work, we propose an algorithm that optimizes the activation function itself, while keeping the weights and biases in the randomized neural network fixed, providing a more suitable dictionary. We illustrate the efficacy of the approach using various benchmark problems, including stochastic differential equations and random walks on graphons.