When a neural surrogate cannot accelerate a solver: runtime share, closed-loop drift, and the economics of uncertainty gating in a stiff coupled simulation
研究探讨了神经网络代理在加速复杂物理模拟中的局限性，通过分析运行时间占比、闭环漂移及不确定性门控的经济性问题。
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An asymptotic rigidity property from the realizability of chirotope extensions
This paper addresses the oriented affine rigidity of point configurations: if two finite point sets $P$ and $Q$ induce chirotopes with identical realizability across all finite generic extensions, must $P$ and $Q$ be orientation-preserving affinely equivalent? Method: The authors establish a quantitative link between chirotope extension realizability and geometric rigidity, leveraging tools from oriented matroid theory, real algebraic geometry, genericity analysis, and affine approximation. Contribution/Results: They prove that this combinatorial condition precisely characterizes orientation-preserving affine equivalence classes of point configurations. Furthermore, they formulate and prove an $varepsilon$-rigidity theorem: for any $varepsilon > 0$, there exists a finite generic extension $widehat{P}$ such that any configuration $Q$ realizing the chirotope of $widehat{P}$ admits an orientation-preserving affine transformation mapping each point of $Q$ into the $varepsilon$-neighborhood of the corresponding point in $P$. This result provides a robust, quantitative foundation for combinatorial rigidity in affine geometry.
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When a neural surrogate cannot accelerate a solver: runtime share, closed-loop drift, and the economics of uncertainty gating in a stiff coupled simulation
研究探讨了神经网络代理在加速复杂物理模拟中的局限性，通过分析运行时间占比、闭环漂移及不确定性门控的经济性问题。
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An asymptotic rigidity property from the realizability of chirotope extensions
This paper addresses the oriented affine rigidity of point configurations: if two finite point sets $P$ and $Q$ induce chirotopes with identical realizability across all finite generic extensions, must $P$ and $Q$ be orientation-preserving affinely equivalent? Method: The authors establish a quantitative link between chirotope extension realizability and geometric rigidity, leveraging tools from oriented matroid theory, real algebraic geometry, genericity analysis, and affine approximation. Contribution/Results: They prove that this combinatorial condition precisely characterizes orientation-preserving affine equivalence classes of point configurations. Furthermore, they formulate and prove an $varepsilon$-rigidity theorem: for any $varepsilon > 0$, there exists a finite generic extension $widehat{P}$ such that any configuration $Q$ realizing the chirotope of $widehat{P}$ admits an orientation-preserving affine transformation mapping each point of $Q$ into the $varepsilon$-neighborhood of the corresponding point in $P$. This result provides a robust, quantitative foundation for combinatorial rigidity in affine geometry.
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