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We create and test a neural network which quantifies uncertainty errors in the Poisson equation generated by an uncertain source term. The neural networks performance is compared to a Monte Carlo approximation and analytically derived bounds. We find that with a suitable dataset the neural network can learn this task well enough to be considered as an alternative for Monte Carlo and analytical methods.

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Using Neural Networks to Approximate Distance of Possible Solutions of Uncertain Poisson Equation

  • 会议论文

  • 发表日期：

    2025年

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  • Vilho Halonen,
  • Ilkka Pölönen,
  • Monika Wolfmayr

摘要

We create and test a neural network which quantifies uncertainty errors in the Poisson equation generated by an uncertain source term. The neural networks performance is compared to a Monte Carlo approximation and analytically derived bounds. We find that with a suitable dataset the neural network can learn this task well enough to be considered as an alternative for Monte Carlo and analytical methods.