Hybrid nonlinear preconditioning approach for phase-field model with double-obstacle potential

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In recent years, LLMs have shown significant improvements in their overall performance. When they first became mainstream a couple of years before, they were already impressive with their seemingly human-like conversation abilities, but their reasoning always lacked. They were able to describe any sorting algorithm in the style of your favorite author; on the other hand, they weren't able to consistently perform addition. However, they improved significantly, and it's more and more difficult to find examples where they fail to reason. This created the belief that with enough scaling, LLMs will be able to learn general reasoning.

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