Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals
Journal:
arXiv
Published Date:
Jul 8, 2025
Abstract
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.
