Partial-differential-algebraic equations of nonlinear dynamics by Physics-Informed Neural-Network: (I) Operator splitting and framework assessment

📰 ArXiv cs.AI

Learn to solve partial-differential-algebraic equations using Physics-Informed Neural Networks (PINNs) with operator splitting and framework assessment

advanced Published 5 May 2026

Action Steps

Apply operator splitting to partial-differential-algebraic equations using PINNs
Implement the nonlinear Kirchhoff rod as a prototype for demonstration
Use the DeepXDE framework to construct and test PINN models
Resolve pathological problems encountered in the DeepXDE framework using novel methods
Assess the performance of the proposed PINN framework using benchmark examples

Who Needs to Know This

Researchers and engineers working on nonlinear dynamics and physics-informed neural networks can benefit from this article to improve their skills in solving complex equations

Key Insight

💡 PINNs with operator splitting can effectively solve complex nonlinear dynamics equations

Key Takeaways

Learn to solve partial-differential-algebraic equations using Physics-Informed Neural Networks (PINNs) with operator splitting and framework assessment

Full Article

Title: Partial-differential-algebraic equations of nonlinear dynamics by Physics-Informed Neural-Network: (I) Operator splitting and framework assessment

Abstract:
arXiv:2408.01914v4 Announce Type: replace-cross Abstract: Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype for demonstration. The open-source DeepXDE is likely the most well documented framework with many examples. Yet, we encountered some pathological problems and proposed novel methods to resolve them. Amo

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