Greg Brockman· @gdb · X·· 3 小时前精选AI 评分66
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Greg Brockman 引用 @scottnarmstrong 的评论称,OpenAI 这篇论文在技术层面令人难以置信,可能超出人类能想到的范围,但仍在人类理解之内。被引评论认为该构造与凸积分(convex integration)关系更大,其做法是让流体不稳定性自行产生振荡、由雷诺应力形成使光滑涡坍缩的力,这种组合在既有文献中没有先例;已有多个 PDE 专家团队表示大致读懂了论文,预计很快会有解读。该评论还称,认为这一结果并不令人意外的人是在胡说。
推荐理由
引用数学界人士对 OpenAI 一篇偏微分方程论文的技术拆解,呈现该结果与凸积分方法的关联及学界反应。
正文 · 原文
“On a technical level, the paper is unbelievable, maybe beyond what a human could have come up with but not beyond human understanding”
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!在 X 查看被引用的帖子
来源:Greg Brockman · x.com