A Parameterised Family of NeuralODEs Optimally Fitting Steady-State Data

This paper presents a parameterised family of neural ordinary differential equations (neuralODEs) that fit the steady-state system response in a least-squares sense. The family of neuralODEs is cast in the form of recurrent equilibrium networks (NodeRENs). One of the main advantages of the proposed approach is that it uses only linear least-squares optimisation tools. As such, the solution to the steady-state fitting problem is given in a closed-form expression. Furthermore, the NodeREN family leaves a subset of parameters free. This is useful for enforcing robustness or for fitting transient data in addition to steady-state data.