Physics-Modeled Neural Networks
Summary
This paper introduces Dynamical Physics-Modeled Neural Networks (DynPMNNs), a continuous-time deep learning architecture where hidden layers are defined by ordinary differential equations. It presents a biologically inspired approach grounded in Reproducing Kernel Banach Spaces, demonstrating competitive performance on the California Housing dataset with fewer parameters than standard Neural ODEs.
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# Physics-Modeled Neural Networks
Source: [https://arxiv.org/abs/2605.08176](https://arxiv.org/abs/2605.08176)
[View PDF](https://arxiv.org/pdf/2605.08176)
> Abstract:We introduce \\emph\{Dynamical Physics\-Modeled Neural Networks\} \(DynPMNNs\), a continuous\-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation\. Unlike classical feed\-forward networks, this approach replaces static activation functions with time\-evolving dynamical systems, providing a biologically inspired interpretation of hidden\-layer behavior and enabling the integration of physically meaningful models\. The framework is rigorously grounded in Reproducing Kernel Banach Spaces \(RKBSs\), allowing DynPMNNs to be characterized as finite\-dimensional solutions of an abstract training problem and revealing structural connections with standard neural networks\. We present a concrete implementation based on the FitzHugh\-\-Nagumo model for neuronal activation, where numerical ODE solvers are embedded into the computational graph via Euler\-type schemes\. Both network weights and dynamical parameters are trained jointly\. Through experiments on the California Housing dataset, we compare DynPMNNs with Neural ODEs \(NODEs\) and Closed\-form Continuous\-Time Networks \(CfCs\)\. Despite using fewer trainable parameters, DynPMNNs achieve competitive performance\. These results position DynPMNNs as a principled bridge between dynamical systems and deep learning, with promising directions for further research in expressivity, stability, and physics\-based modeling\.
## Submission history
From: Raul Felipe Sosa \[[view email](https://arxiv.org/show-email/e2677981/2605.08176)\] **\[v1\]**Tue, 5 May 2026 07:29:48 UTC \(436 KB\)Similar Articles
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