| Abstract: |
| Many problems in computational science and engineering require solving nonlinear systems of equations arising from partial differential equations. The commonly used methods include Newton's methods and Picard's iteration methods. However, the standard Newton's method is sensitive to the initial guess and may exhibit slow convergence or even stagnation due to unbalanced nonlinearities. To address this issue, nonlinear preconditioning techniques have been developed to improve the nonlinear convergence. Constructing an efficient preconditioner can be challenging. In addition to traditional numerical approaches, a promising direction is to leverage machine learning techniques, especially given the rapid development in the field of scientific machine learning. In this talk, we will explore how neural networks can be employed to build efficient preconditioners that accelerate the convergence of Newton's methods. |
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