Learning Parameterized ODEs From Data

In contemporary research, neural networks are being used to derive Ordinary Differential Equations (ODEs) from observations. However, parameterized ODEs pose a more significant challenge than non-parameterized since the required understand roles of parameters, i.e., structure equations. This paper proposes novel approach by combining Symbolic Neural Network (S-Net) with ODE Solver solve this issue. First, S-Net learns and then predicts dynamics based on new parameters initial states. To assess its performance, we compare our widely (O-Net) that directly ODEs. Our numerical experiments demonstrate outperforms O-Net when applied Lotka-Volterra Lorenz