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Implementing physics-informed neural networks with deep learning for differential equations.

Frank Emmert-Streib1,2, Shailesh Tripathi3, Amer Farea1

  • 1Predictive Society and Data Analytics Lab, Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, Finland.

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View abstract on PubMed

Summary
This summary is machine-generated.

Physics-informed neural networks (PINNs) offer a novel approach to solving ordinary differential equations (ODEs). This study demonstrates PINN implementation for ODEs, addressing forward and inverse problems with practical case studies.

Keywords:
data-driven scientific machine learningforward probleminverse problemordinary differential equationphysics-aware machine learningphysics-informed neural network

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Area of Science:

  • Computational Physics
  • Machine Learning

Background:

  • Physics-aware machine learning, particularly physics-informed neural networks (PINNs), integrates physical laws into machine learning models.
  • PINNs enable interpretable and physically consistent solutions but face practical implementation challenges.

Purpose of the Study:

  • To demonstrate the implementation of PINNs for systems of ordinary differential equations (ODEs).
  • To address the forward problem (solving ODEs) and the inverse problem (parameter estimation) for ODEs using PINNs.
  • To provide practical insights and identify future research directions for PINN frameworks.

Main Methods:

  • Implementation of PINNs for systems of ODEs.
  • Utilized a Python-based framework, DeepXDE, for practical case studies.
  • Investigated both forward and inverse problem formulations within the ODE context.

Main Results:

  • Successfully demonstrated PINN implementation for ODE systems, covering both forward and inverse problems.
  • Presented two case studies offering practical insights into the application of PINNs for ODEs.
  • Highlighted key challenges and potential future research avenues in PINN frameworks.

Conclusions:

  • PINNs offer a viable and powerful tool for addressing ODEs, an area less explored than PDEs in the physics community.
  • Practical implementation through frameworks like DeepXDE facilitates the application of PINNs.
  • Further research is needed to overcome current challenges and expand the utility of PINNs for ODEs.