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AI Solves Century-Old Math Problem
10,546 views Sep 23, 2025 ✪ Members first on September 22, 2025 #Turbulence #Astrophysics #Aerospace
DeepMind’s AI didn’t just crunch numbers—it learned directly from the equations (PINNs + GNNs) and uncovered a new family of singular solutions. Verified by mathematicians at NYU, Brown, and Stanford, this breakthrough spans Navier–Stokes, Boussinesq, and porous media equations. By minimizing residuals to near machine precision, the model revealed delicate structures traditional methods miss—impacting weather forecasting, turbulence reduction, aerospace efficiency, and astrophysical modeling. In this video, we explain lambda (λ), instability orders, and why “unstable” singularities expose deeper truths of the equations. 📚 參考 Reference:
DeepMind 的 AI AI 破百年數學難題，不是只「算得快」，而是直接在方程上學習（PINN/圖神經網路），找到前所未見的奇點解族！這一突破觸及 Navier–Stokes、Boussinesq、多孔介質方程，並由紐約大學、布朗、史丹佛等數學家審核驗證。更小的殘差、更接近機器極限的精度，讓 AI 捕捉傳統方法難以覺察的微妙結構。這不只是數學勝利：它可能改寫天氣預報、降低飛機湍流與油耗、推進天體物理建模。影片用通俗旁白，帶你看懂 λ（lambda）、不穩定度階數與奇點規律，理解為何「不穩定」反而揭示了方程的深層真相。
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DeepMind’s AI uses graph neural networks and PINNs to solve century-old fluid dynamics problems. This approach learns directly from equations, uncovering previously unknown singular solutions. Mathematicians verified the AI’s findings, potentially impacting fields from weather forecasting to astrophysics.
IRHEM理论将一切经典场方程（包括流体动力学的Boussinesq方程、IPM方程）都视为信息算符谱空间中特定谱模态激发的投影。流体中的不稳定性、奇异结构和非高斯涌现，可看作谱空间高阶递归反馈、模间耦合以及全息映射演化的“动力学衍射”。 每一个流体扰动的奇异模式，在IRHEM视角下都是谱算符激发出的非平庸谱态，是信息递归全息演化链（Φₙ → Φₙ₊₁ + F[Φₙ] + feedback）的具体物理体现。
