Phase Field Modeling with Neural Operators
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The solution of phase field models, which describe a wide range of phenomena including phase transitions [1], material interfaces [2], and multiphase flow [3], typically requires the numerical solution of complex partial differential equations (PDEs). Traditional methods such as finite difference, finite element, and spectral methods can be computationally expensive, especially when dealing with high-dimensional problems or multiple scales. In this talk, we explore the use of Neural Operators (NOs) [4], a class of deep learning models, to efficiently solve phase field problems. By exploiting the ability of NOs to learn mappings from one function space to another, we show how these models can effectively approximate the solution operators for phase field equations without the need for extensive numerical solvers. In addition, we will present results comparing the performance of NOs with conventional numerical solvers, highlighting their potential for accelerated simulations in phase field modeling. Through this work, we aim to demonstrate how NOs can contribute to the next generation of computational tools for materials science, fluid dynamics, and other fields requiring phase field modeling.