Papers for

machine learning developers for physics simulations

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Physics informed neural networks improve accuracy in fluid flow simulation

Hard Constraint Projection in a Physics Informed Neural Network (Burgers)

Abstract: Physics 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. [Journal of Computational Physics, 445, 110624, 2021] from a linear partial differential equation (PDE) to a nonlinear PDE: the 1D Burgers' equation. To strictly impose a discrete approximation of the governing equation, the Burgers' equation is first locally discretised (using a finite difference stencil) then decomposed into a constraint matrix and a prediction matrix. Using tools from linear algebra, the constraint matrix is used to construct a projection matrix. A physics informed neural network (PINN) [Raissi et al. Journal of Computational Physics, 378, 686, 2019] is used to predict the velocity, and a final unlearnable layer projects the velocity prediction to the hyperplane of exact solutions to a discretised form of the Burgers' equation. Our initial results indicate that the HCP-PINN initially trains similarly to an equivalent PINN, and as the PINN loss plateaus, the HCP-PINN loss continues to decline. When tested on a previously unseen uniform grid of points covering the domain, the HCP-PINN exhibits higher accuracy, converging to a data error approximately an order of magnitude lower than the comparable PINN. We also observe that the inclusion of the HCP layer results in better observance of the governing PDE. Our findings suggest that the HCP-PINN can be more robust to the selection of physics collocation points, and less dependent on collocation point quantity.

Fri 30 OctMachine Learning
The gist
Simulating how fluids move is usually very slow and complicated. This paper shows a way to use AI that follows the exact math rules of fluid flow more strictly, making the AI's guesses more accurate. They tested this on a simple fluid flow problem called Burgers' equation and found their method reduces errors much more than usual AI-based approaches. This method also works well even when they use fewer sample points.
Open → 2610.42106v1