DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations

Understand

We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations.

• The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods.
• Exploiting the spectral bias, DeepONet-based components are harnessed to address low-frequency error components, while conventional iterative methods are employed to mitigate high-frequency error components.
• Our preconditioning framework comprises two distinct hybridization approaches: direct preconditioning (DP) and trunk basis (TB) approaches.