Let $K\subset\mathbb{R}^n$ be a convex body, let $X$ and $Y$ be independent uniform points of $K$, and set $R_K=(|K|/\omega_n)^{1/n}$. We consider the distribution function \[ D_K(\rho)=\mathbb P\{|X-Y|/R_K<\rho\}, \] and its homogeneous counterpart \begin{equation*} \mathcal J_\rho(K)=\iint_{K\times K}\mathbf{1}_{\{|x...
The Neural Harmonic Measure Operator is introduced, a neural solver for elliptic PDE problems on variable-shape domains that improves over four prior baselines on the MCB-B 3D variable-shape Poisson benchmark across all five categories, and is competitive with major neural-operator baselines on a controlled 2D testbed.
Jin-Jin He, Si-Nan Wang, Yu-Chen Sun et al.· 0 citations
GPUPhysBench brings physical simulation workloads to coding-agent evaluation, testing both the ability to implement numerical methods correctly and the ability to make them run efficiently.
Yu-Chen Sun, Jin-Jin He, Si-Nan Wang et al.· 0 citations
We present the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator for amortized incompressible density transport. Given a new source-target density pair, VIOT predicts a divergence-free velocity field and generates the full transport trajectory by feed-forward inference, replacin...
Jin-Jin He, Shenyifan Lu, Si-Nan Wang et al.· 0 citations
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