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Greg Brockman· @gdb · X·· 4 小时前AI 评分60
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Greg Brockman 引用数学家 Scott Armstrong 的分析称,OpenAI 关于流体方程爆破解的论文在技术层面难以置信,也许超出人类能想出的范围,但并未超出人类理解范围。Armstrong 指出该构造与凸积分关系最大,用物理不稳定性让流动自身产生振荡,Reynolds stress 成为制造坍缩光滑涡旋的力,这种手法此前文献中没有先例;多个 PDE 专家小组正在消化该论文,预计很快会有解读,并称认为这一结果不令人意外的说法站不住脚。

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“On a technical level, the paper is unbelievable, maybe beyond what a human could have come up with but not beyond human understanding”

引用Scott Armstrong@scottnarmstrong
Since I'm now blocked by bluey from replying to this thread, I answer here by quote tweet the openAI construction has more to do with convex integration than anything else. In convex integration, the oscillations are typically built by hand and the iteration procedure creates wild weak solutions. The non-uniqueness construction of Albritton–Brué–Colombo used an unstable vortex to split solutions apart. The Córdoba–Martínez-Zoroa singularities amplify vorticity across scales by strain. In the openAI paper, a fluid instability is clever made so that the flow itself generates the oscillations: they grow by drawing energy from the background shear. The Reynolds stress then becomes the force that creates the collapsing smooth vortex. Using a physical instability to create the stress in this way has no precedent, and it is what produces a smooth force rather than a merely rough one. Some on these ideas are in the literature (e.g. Leibovich-Stewartson 1983) but the way they are combined is definitely insane and definitely nowhere in the literature previously. I also don't know of anyone suggesting that convex integration would play a role in the creation of a blow-up solution like this. On a technical level, the paper is unbelievable, maybe beyond what a human could have come up with but not beyond human understanding: there are several different groups of pde experts working on understanding it who say that they more or less understand now. I expect digestions soon td;lr: anyone saying that this OAI result is unsurprising is bullshitting sorry!
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来源:Greg Brockman · x.com