# Physics-Modeled Neural Networks

**Authors:** Raul Felipe-Sosa, Angel Martin del Rey, Maria Flores Ceballos  
**arXiv:** [2605.08176](https://arxiv.org/abs/2605.08176)  
**Date:** 2026-05-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2605.08176v1/

## Key points

- DynPMNNs are a novel continuous-time deep learning architecture that incorporates ODEs in each hidden layer
- Unlike traditional feed-forward networks, DynPMNNs utilize time-evolving dynamical systems for hidden-layer behavior
- The framework is rooted in RKBSs, allowing DynPMNNs to be viewed as finite-dimensional solutions of an abstract training problem
- Implementing the DynPMNN framework using biophysical neuron models like the FitzHugh–Nagumo system shows competitive performance with fewer trainable parameters compared to NODEs and CfCs

## Summary

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In this study, we introduce DynPMNNs, a novel continuous-time deep learning architecture that incorporates ODEs in each hidden layer. Unlike traditional feed-forward networks with static activation functions, DynPMNNs utilize time-evolving dynamical systems, offering a biologically inspired perspective on hidden-layer behavior and enabling the integration of physically meaningful models. The framework is rooted in RKBSs, allowing DynPMNNs to be viewed as finite-dimensional solutions of an abstract training problem and revealing structural connections with conventional neural networks. Our work demonstrates how physics-modeled neural architectures can be interpreted as finite-dimensional realizations derived from infinite-dimensional variational formulations within RKBSs. This sheds light on the relationship between classical fully connected networks and DynPMNNs, emphasizing how replacing static activation functions with solution maps of initial value problems represents a genuine extension of standard neural architectures. We implement the DynPMNN framework using biophysical neuron models, specifically focusing on the FitzHugh–Nagumo system. By integrating an explicit Euler scheme into the forward pass, we create an Euler block that corresponds to the number of integration steps and naturally induces residual connections within the network structure. Through numerical experiments conducted on datasets such as the California Housing dataset, we compare DynPMNNs with Neural ODEs (NODEs) and Closed-form Continuous-Time Networks (CfCs). Despite utilizing fewer trainable parameters, DynPMNNs exhibit competitive performance. Overall, our results position DynPMNNs as a principled bridge between dynamical systems and deep learning research.