Abstract:In this paper, we propose Geometric Optics Approximation Sampling (GOAS), a reflector-induced transport-map framework for sampling from target measures. Once a reflecting surface is constructed, the associated transport map is explicitly determined by the physical law of reflection. As a concrete realization, we develop a supporting-hyperellipsoid construction that requires only a discrete approximation of the target measure and does not require gradient information of the target density. The formulation accommodates both density-based and sample-based target representations. A softmin smoothing technique is introduced to obtain a smooth approximate transport map from this piecewise hyperellipsoidal construction. We establish well-posedness and stability of the reflector-induced push-forward measure and derive quantitative error estimates in the maximum mean discrepancy metric, and convergence of continuous statistical observables, including fixed-order moments. Numerical experiments on an analytically tractable example, strongly non-Gaussian targets, sample-based target approximations, and Bayesian inverse problems demonstrate the accuracy and flexibility of GOAS.
From: Guang-Hui Zheng [view email]
[v1]
Mon, 4 Mar 2024 00:25:11 UTC (5,570 KB)
[v2]
Thu, 16 Oct 2025 09:04:10 UTC (780 KB)
[v3]
Thu, 3 Sep 2026 15:40:20 UTC (6,727 KB)
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