Prior knowledge meets neural odes: a two stage training method for improved explainability

Abstract

Neural Ordinary Differential Equations (ODEs) have been used extensively to model physical systems because they represent a continuous-time function that can make predictions over the entire time domain. However, most of the time, the parameters of these physical systems are subject to strict laws/constraints. But there is no guarantee that the Neural ODE model satisfies these constraints. Therefore, we propose a two-stage training for Neural ODE. The first stage aims at find ing feasible parameters by minimizing a loss function defined by the constraints violation. The second stage aims at improving the feasible solution by minimiz ing the distance between the predicted and ground-truth values. By training the Neural ODE in two stages, we ensure that the governing laws of the system are satisfied and the model fits the data.