Hybrid biasing approaches for global variance reduction.

Area of Science:

• Computational physics
• Nuclear engineering
• Applied mathematics

Background:

• Monte Carlo (MC) simulations are crucial for complex systems but computationally intensive.
• Variance reduction techniques are essential to accelerate MC convergence.
• Existing methods like Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) have limitations.

Purpose of the Study:

• To introduce a new hybrid variance reduction approach based on Gaussian process theory.
• To accelerate the convergence of Monte Carlo simulations.
• To compare the new Gaussian process approach with the FW-CADIS method.

Main Methods:

• Developed a Gaussian process (GP) approach treating responses as random processes.
• Utilized deterministic adjoint models for particle importance maps and weight window biasing.
• Employed a covariance matrix to identify response correlations and reduce computational overhead.
• Determined the effective rank of the covariance matrix for biasing simulated particles.

Main Results:

• The Gaussian process approach identifies subspaces capturing dominant statistical response variations.
• It effectively reduces computational overhead for global variance reduction (GVR).
• Numerical experiments demonstrated the GP approach's potential for reducing the standard deviation of estimated responses.

Conclusions:

• The Gaussian process approach offers an effective alternative for variance reduction in MC simulations.
• It improves computational efficiency by leveraging response correlations.
• This method shows promise for accelerating convergence in complex simulations.