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High-Order Sequential Simulation via Statistical Learning in Reproducing Kernel Hilbert Space.

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This study introduces a novel statistical learning framework for high-order simulation. The method accurately reproduces spatial statistics and resolves data conflicts, showing promise for real-world applications.

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Area of Science:

  • Geostatistics
  • Statistical Learning
  • Computational Science

Background:

  • Accurate spatial modeling is crucial for resource estimation and risk assessment.
  • Existing simulation methods may struggle to capture complex high-order spatial statistics.
  • Integrating diverse data sources in geostatistical modeling presents challenges.

Purpose of the Study:

  • To propose a new high-order simulation framework using statistical learning.
  • To develop a method that reproduces high-order spatial statistics from training data.
  • To address potential conflicts between training images and sample data in spatial modeling.

Main Methods:

  • A statistical learning framework is employed within a reproducing kernel Hilbert space (RKHS).
  • A spatial Legendre moment (SLM) reproducing kernel is constructed to incorporate high-order spatial statistics.
  • Target random field distributions are mapped into the SLM-RKHS, with solutions obtained via quadratic programming.

Main Results:

  • The proposed framework successfully reproduces high-order spatial statistics from available data.
  • The method effectively resolves conflicts between training images and sample data.
  • Case studies demonstrate the framework's ability to handle complex spatial attributes and its practical applicability.

Conclusions:

  • The novel statistical learning framework offers a robust approach for high-order spatial simulation.
  • The use of the SLM kernel and RKHS provides generalization capabilities for accurate modeling.
  • The method is validated through diverse case studies, including a 3D gold deposit application.