Physics-Modeled Neural Networks

• URL: http://arxiv.org/abs/2605.08176v1
• Date: Tue, 05 May 2026 07:29:48 GMT
• Title: Physics-Modeled Neural Networks
• Abstract summary: We introduce emphDynamical Physics-Modeled Neural Networks (DynPMNNs)<n>DynPMNNs are a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

Related papers

• Momentum-Conserving Graph Neural Networks for Deformable Objects [64.91655405516482]
  We propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction.<n>Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses.<n>We show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role.
  arXiv  Detail & Related papers  (2026-04-28T20:19:33Z)
• Fractional Spike Differential Equations Neural Network with Efficient Adjoint Parameters Training [63.3991315762955]
  Spiking Neural Networks (SNNs) draw inspiration from biological neurons to create realistic models for brain-like computation.<n>Most existing SNNs assume a single time constant for neuronal membrane voltage dynamics, modeled by first-order ordinary differential equations (ODEs) with Markovian characteristics.<n>We propose the Fractional SPIKE Differential Equation neural network (fspikeDE), which captures long-term dependencies in membrane voltage and spike trains through fractional-order dynamics.
  arXiv  Detail & Related papers  (2025-07-22T18:20:56Z)
• A Low-complexity Structured Neural Network to Realize States of Dynamical Systems [0.0]
  This paper stems from data-driven learning to advance states of dynamical systems utilizing a structured neural network (StNN)<n>We present numerical simulations to solve dynamical systems utilizing the StNN based on the Hankel operator.<n>We show that the proposed StNN paves way for realizing state-space dynamical systems with a low-complexity learning enabling prediction and understanding of future states.
  arXiv  Detail & Related papers  (2025-03-31T03:52:38Z)
• Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks [21.117540483724603]
  We develop compositional learning algorithms for coupled dynamical systems, with a particular focus on electrical networks.<n>We introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parameterize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE.<n>We show that the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons.
  arXiv  Detail & Related papers  (2024-12-15T15:13:11Z)
• Recurrent convolutional neural networks for modeling non-adiabatic dynamics of quantum-classical systems [1.23088383881821]
  We present a RNN model based on convolution neural networks for modeling the non-adiabatic dynamics of hybrid quantum-classical systems.<n>We demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.
  arXiv  Detail & Related papers  (2024-12-09T16:23:25Z)
• An Attempt to Devise a Pairwise Ising-Type Maximum Entropy Model Integrated Cost Function for Optimizing SNN Deployment [0.0]
  Spiking Neural Networks (SNNs) emulate the spiking behavior of biological neurons and are typically deployed on distributed-memory neuromorphic hardware.<n>We model SNN dynamics using an Ising-type pairwise interaction framework, bridging microscopic neuron interactions with macroscopic network behavior.<n>We evaluate our approach on two SNNs deployed on the sPyNNaker neuromorphic platform.
  arXiv  Detail & Related papers  (2024-07-09T16:33:43Z)
• SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases [66.61789780666727]
  We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states. Our model yields a significant improvement over the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-08-25T07:15:58Z)
• How neural networks learn to classify chaotic time series [77.34726150561087]
  We study the inner workings of neural networks trained to classify regular-versus-chaotic time series. We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
  arXiv  Detail & Related papers  (2023-06-04T08:53:27Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models [13.637931956861758]
  We show how we can approximate missing ordinary differential equations with known ODEs using a neural network approximation. Results indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation.
  arXiv  Detail & Related papers  (2021-10-12T15:38:13Z)
• Accelerating Neural ODEs Using Model Order Reduction [0.0]
  We show that mathematical model order reduction methods can be used for compressing and accelerating Neural ODEs. We implement our novel compression method by developing Neural ODEs that integrate the necessary subspace-projection and operations as layers of the neural network.
  arXiv  Detail & Related papers  (2021-05-28T19:27:09Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.