Neural Sequence Transformation
Neural Sequence Transformation
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DOI：
10.1111/cgf.14407
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发表时间：
2021-10
影响因子：
2.5
通讯作者：
S. Mukherjee;S. Mukherjee;Binh-Son Hua;Nobuyuki Umetani;D. Meister
中科院分区：
文献类型：
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作者：
S. Mukherjee;S. Mukherjee;Binh-Son Hua;Nobuyuki Umetani;D. Meister
蒙特卡罗积分是一种通过随机抽样被积函数来对定积分进行数值估计的技术。这些样本可以被平均以作出改进的估计，并且累进估计形成一个序列，该序列收敛于极限上的整数值。不幸的是，蒙特卡罗估计序列以O()的速度收敛，其中n表示样本计数，随着样本的抽取，有效地减慢了速度。为了克服这一点，我们可以应用序列转换，它将一个收敛序列转换为另一个序列，目标是加快收敛速度。然而，由于序列的随机性和被积函数的复杂性，解析地为蒙特卡罗估计找到这样的变换可能是具有挑战性的。在这篇文章中，我们建议利用神经网络来学习序列变换，以改善蒙特卡罗积分的渐进估计的收敛。我们在几个典型的一维积分问题上证明了该方法的有效性，并在光传输模拟中得到了应用。
Monte Carlo integration is a technique for numerically estimating a definite integral by stochastically sampling its integrand. These samples can be averaged to make an improved estimate, and the progressive estimates form a sequence that converges to the integral value on the limit. Unfortunately, the sequence of Monte Carlo estimates converges at a rate of O(), where n denotes the sample count, effectively slowing down as more samples are drawn. To overcome this, we can apply sequence transformation, which transforms one converging sequence into another with the goal of accelerating the rate of convergence. However, analytically finding such a transformation for Monte Carlo estimates can be challenging, due to both the stochastic nature of the sequence, and the complexity of the integrand. In this paper, we propose to leverage neural networks to learn sequence transformations that improve the convergence of the progressive estimates of Monte Carlo integration. We demonstrate the effectiveness of our method on several canonical 1D integration problems as well as applications in light transport simulation.