Abstract
We present a neural network framework for the simulation of independent random variables from arbitrary distributions. The framework includes two neural networks that are trained simultaneously using a target function, rather than a target dataset. One is a generative model that maps samples from a joint normal distribution to samples in the target space. The second network estimates the probability density of these samples, trained with targets obtained via kernel density estimation. The effectiveness of the approach is illustrated with various examples from rare-event simulation. The generator was able to learn all the 1-dimensional distribution examples well enough to pass the Kolmogorov–Smirnov test. However, estimates of higher-dimensional probability densities were limited by the kernel density estimation. Refining the density estimates of the generated samples is a clear way to improve the accuracy of the method when learning more complex higher dimensional distributions.
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Notes
- 1.
Actually, in the code the density network output activation function is the identity function, but the output is interpreted as the log-density.
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Gibson, L.J., Kroese, D.P. (2022). Rare-Event Simulation via Neural Networks. In: Botev, Z., Keller, A., Lemieux, C., Tuffin, B. (eds) Advances in Modeling and Simulation. Springer, Cham. https://doi.org/10.1007/978-3-031-10193-9_8
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