用神经网络拟合突变信号，精准估计非自治微分方程参数
Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals
- 用神经网络将突变信号平滑逼近，再用于参数估计
- 在昼夜节律与酵母交配响应中实现高精度参数还原
- 适合处理含突发外部刺激的生物系统建模
非自治微分方程对受外部信号影响的系统建模至关重要，但当信号发生突变时，模型拟合尤为困难。为此，我们提出一种基于人工神经网络的功能逼近参数估计方法——称为基于神经网络的不连续外信号谐波逼近（HADES-NN）。该方法分两步迭代进行：第一步，用神经网络将不连续信号近似为光滑函数；第二步，利用此平滑近似信号进行模型参数估计。HADES-NN在多种应用中均实现高精度、高鲁棒性参数估计，包括通过可穿戴设备测量的光照调控的昼夜节律系统，以及酵母对环境信息素信号的交配响应。该方法显著拓展了真实世界数据下模型拟合的适用范围。
原文摘要 · Abstract (English)
Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a novel parameter estimation method utilizing functional approximations with artificial neural networks. Our approach, termed Harmonic Approximation of Discontinuous External Signals using Neural Networks (HADES-NN), operates in two iterated stages. In the first stage, the algorithm employs a neural network to approximate the discontinuous signal with a smooth function. In the second stage, it uses this smooth approximate signal to estimate model parameters. HADES-NN gives highly accurate and precise parameter estimates across various applications, including circadian clock systems regulated by external light inputs measured via wearable devices and the mating response of yeast to external pheromone signals. HADES-NN greatly extends the range of model systems that can be fit to real-world measurements.
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