mlsanityData to 7 Oct 2026

On the effectiveness of neural priors in modeling dynamical systems

arXiv 2303.05728 ↗First posted 10 Mar 2023cs.LG eess.SPcited by 4

Not on the map. Why?

Abstract (arXiv)

Modelling dynamical systems is an integral component for understanding the natural world. To this end, neural networks are becoming an increasingly popular candidate owing to their ability to learn complex functions from large amounts of data. Despite this recent progress, there has not been an adequate discussion on the architectural regularization that neural networks offer when learning such systems, hindering their efficient usage. In this paper, we initiate a discussion in this direction using coordinate networks as a test bed. We interpret dynamical systems and coordinate networks from a signal processing lens, and show that simple coordinate networks with few layers can be used to solve multiple problems in modelling dynamical systems, without any explicit regularizers.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 16 of its 69 references that are in the map. First posted on arXiv 10 Mar 2023.

Builds on

16 of 69 references.

References · 16

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  5. 2018On the Spectral Bias of Neural Networkscited by 1,321
  6. 2019Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representationscited by 864
  7. 2020Learning Continuous Image Representation with Local Implicit Image Functioncited by 550
  8. 2020Adversarial Generation of Continuous Imagescited by 135
  9. 2021Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPscited by 134
  10. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  11. 20213D Neural Scene Representations for Visuomotor Controlcited by 110
  12. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 94
4 more
  1. 2020Global Convergence of Deep Networks with One Wide Layer Followed by Pyramidal Topologycited by 66
  2. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  3. 2015Synthesis of recurrent neural networks for dynamical system simulationcited by 16
  4. 2022Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modelingcited by 9

Built on by

Cited by year

Citing papers per year: 2024: 1; 2025: 3.

4 papers.

  1. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  2. 2024From Activation to Initialization: Scaling Insights for Optimizing Neural Fieldscited by 11
  3. 2025Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systemscited by 1
  4. 2025From Tables to Signals: Revealing Spectral Adaptivity in TabPFNcited by 1