Hard Constraint Projection Extends PINN to Burgers Equation
Original title: Hard Constraint Projection in a Physics Informed Neural Network (Burgers)
HCP-PINN enforces discretized PDE constraints via projection layer, yielding order-of-magnitude accuracy gains over standard PINN.
The work extends hard constraint projection from linear to the nonlinear Burgers' equation. A finite-difference discretization creates constraint and prediction matrices; a projection matrix then enforces exact solutions in an unlearnable output layer. Experiments show HCP-PINN loss continues declining after PINN plateaus and delivers superior accuracy on unseen grids while better satisfying the governing PDE.
- HCP-PINN loss declines after PINN plateaus
- Higher accuracy on unseen uniform grid
- Order-of-magnitude lower data error
- More robust to collocation point choice
- Improved observance of discretized Burgers equation
From the original article
1 min read at arxiv.orgPhysics informed machine learning provides a framework to study and simulate fluid dynamics, potentially at a fraction of the computational cost of traditional numerical methods, with the goal of improving the explainability, accuracy and robustness of purely data driven machine learning methods. In this work, we extend the hard constraint projection (HCP) method developed by Chen et al.
By Miranda J S Horne · arxiv.org
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