Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals

TL;DR

This paper introduces HADES-NN, a neural network-based method for estimating parameters in non-autonomous differential equations with discontinuous external signals, improving accuracy and applicability to real-world systems.

Contribution

The paper presents a novel two-stage neural network approach for parameter estimation in systems with discontinuous external signals, extending modeling capabilities.

Findings

HADES-NN achieves high accuracy in diverse applications.

The method effectively approximates discontinuous signals with smooth functions.

It broadens the range of systems that can be modeled from real-world data.

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.