Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals
This method addresses the problem of parameter estimation for researchers modeling systems with discontinuous external signals, such as in biology, but it appears incremental as it builds on existing neural network and functional approximation techniques.
The paper tackles the challenge of fitting non-autonomous differential equations to data with abrupt external signals by proposing HADES-NN, a method that uses neural networks to approximate discontinuous signals and estimate parameters, achieving highly accurate and precise estimates in applications like circadian clock systems and yeast mating responses.
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.