The authors introduce Dynamical Physics-Modeled Neural Networks (DynPMNNs), where each hidden layer is the solution of an ordinary differential equation (ODE) instead of a static activation function. They ground the framework in Reproducing Kernel Banach Spaces, implement it using the FitzHugh–Nagumo neuronal model with Euler-type ODE solvers embedded in the computational graph, and train both network weights and dynamical parameters jointly. On the California Housing dataset, DynPMNNs achieve competitive performance with fewer trainable parameters than Neural ODEs and Closed-form Continuous-Time Networks.
Main takeaways:
- Each hidden layer is defined as the time-evolving solution of an ODE, replacing static activations with dynamical systems inspired by biology/physics.
- The framework is formalized using Reproducing Kernel Banach Spaces, connecting it rigorously to standard neural network theory.
- A concrete implementation uses the FitzHugh–Nagumo model (a classic neuronal activation model) with numerical ODE solvers embedded in the training graph.
- On California Housing, DynPMNNs match or beat Neural ODEs and CfCs despite using fewer parameters.