A Self-Adaptive Penalty Method for Integrating Prior Knowledge Constraints into Neural ODEs
This work addresses the need for interpretable and constrained models in scientific domains like population dynamics and physics, though it appears incremental as it builds on existing penalty methods for Neural ODEs.
The authors tackled the problem of integrating prior knowledge constraints into Neural ODEs for modeling natural systems, proposing a self-adaptive penalty method that dynamically adjusts parameters and demonstrated its effectiveness in three case studies, showing more accurate and robust predictions compared to other approaches.
The continuous dynamics of natural systems has been effectively modelled using Neural Ordinary Differential Equations (Neural ODEs). However, for accurate and meaningful predictions, it is crucial that the models follow the underlying rules or laws that govern these systems. In this work, we propose a self-adaptive penalty algorithm for Neural ODEs to enable modelling of constrained natural systems. The proposed self-adaptive penalty function can dynamically adjust the penalty parameters. The explicit introduction of prior knowledge helps to increase the interpretability of Neural ODE -based models. We validate the proposed approach by modelling three natural systems with prior knowledge constraints: population growth, chemical reaction evolution, and damped harmonic oscillator motion. The numerical experiments and a comparison with other penalty Neural ODE approaches and \emph{vanilla} Neural ODE, demonstrate the effectiveness of the proposed self-adaptive penalty algorithm for Neural ODEs in modelling constrained natural systems. Moreover, the self-adaptive penalty approach provides more accurate and robust models with reliable and meaningful predictions.