Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909109134032896 |
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| author | Jnini, Anas Vella, Flavio Zeinhofer, Marius |
| author_facet | Jnini, Anas Vella, Flavio Zeinhofer, Marius |
| contents | We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function space dynamics. Our computational results demonstrate close to single-precision accuracy measured in relative $L^2$ norm on a number of benchmark problems. To the best of our knowledge, this constitutes the first contribution in the PINN literature that solves the Navier-Stokes equations to this degree of accuracy. Finally, we show that given a suitable integral discretization, the proposed optimization algorithm agrees with Gauss-Newton's method in parameter space. This allows a matrix-free formulation enabling efficient scalability to large network sizes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics Jnini, Anas Vella, Flavio Zeinhofer, Marius Optimization and Control Computational Physics We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function space dynamics. Our computational results demonstrate close to single-precision accuracy measured in relative $L^2$ norm on a number of benchmark problems. To the best of our knowledge, this constitutes the first contribution in the PINN literature that solves the Navier-Stokes equations to this degree of accuracy. Finally, we show that given a suitable integral discretization, the proposed optimization algorithm agrees with Gauss-Newton's method in parameter space. This allows a matrix-free formulation enabling efficient scalability to large network sizes. |
| title | Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics |
| topic | Optimization and Control Computational Physics |
| url | https://arxiv.org/abs/2402.10680 |