A filter-based neural ODE approach for modelling natural systems with prior knowledge constraints

Abstract

Neural Ordinary Differential Equations (Neural ODEs) have been used to model natural systems because of their continuous dynamics. However, for meaningful predictions, it is critical to accurately extract from the data the underlying rules or laws governing these systems. To overcome the limitations of commonly used penalty methods, we propose a filter-based approach for Neural ODEs that uses a filter methodology to ensure convergence to a feasible and optimal solution for constrained natural systems. The proposed filter methodology prioritises feasible solutions followed by infeasible and non-dominated solutions. The proposed algorithm provides explicit control over the parameter optimisation process, increases the interpretability of the model, and improves the overall performance. We validate the proposed filter-based Neural ODE approach by modelling two different constrained natural systems. Experimental results show that the models trained by our method provide robust generalisation and satisfy the imposed constraints. Our findings indicate that the proposed method represents a promising approach for incorporating prior knowledge constraints into Neural ODE models.