Low-rank variance reduction for uncertain radiative transfer with control variates
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918038547202048 |
|---|---|
| author | Patwardhan, Chinmay Stammer, Pia Løvbak, Emil Kusch, Jonas Krumscheid, Sebastian |
| author_facet | Patwardhan, Chinmay Stammer, Pia Løvbak, Emil Kusch, Jonas Krumscheid, Sebastian |
| contents | The radiative transfer equation models various physical processes ranging from plasma simulations to radiation therapy. In practice, these phenomena are often subject to uncertainties. Modeling and propagating these uncertainties requires accurate and efficient solvers for the radiative transfer equations. Due to the equation's high-dimensional phase space, fine-grid solutions of the radiative transfer equation are computationally expensive and memory-intensive. In recent years, dynamical low-rank approximation has become a popular method for solving kinetic equations due to the development of computationally inexpensive, memory-efficient and robust algorithms like the augmented basis update \& Galerkin integrator. In this work, we propose a low-rank Monte Carlo estimator and combine it with a control variate strategy based on multi-fidelity low-rank approximations for variance reduction. We investigate the error analytically and numerically and find that a joint approach to balance rank and grid size is necessary. Numerical experiments further show that the efficiency of estimators can be improved using dynamical low-rank approximation, especially in the context of control variates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-rank variance reduction for uncertain radiative transfer with control variates Patwardhan, Chinmay Stammer, Pia Løvbak, Emil Kusch, Jonas Krumscheid, Sebastian Numerical Analysis 65M75, 65C05, 35Q49 The radiative transfer equation models various physical processes ranging from plasma simulations to radiation therapy. In practice, these phenomena are often subject to uncertainties. Modeling and propagating these uncertainties requires accurate and efficient solvers for the radiative transfer equations. Due to the equation's high-dimensional phase space, fine-grid solutions of the radiative transfer equation are computationally expensive and memory-intensive. In recent years, dynamical low-rank approximation has become a popular method for solving kinetic equations due to the development of computationally inexpensive, memory-efficient and robust algorithms like the augmented basis update \& Galerkin integrator. In this work, we propose a low-rank Monte Carlo estimator and combine it with a control variate strategy based on multi-fidelity low-rank approximations for variance reduction. We investigate the error analytically and numerically and find that a joint approach to balance rank and grid size is necessary. Numerical experiments further show that the efficiency of estimators can be improved using dynamical low-rank approximation, especially in the context of control variates. |
| title | Low-rank variance reduction for uncertain radiative transfer with control variates |
| topic | Numerical Analysis 65M75, 65C05, 35Q49 |
| url | https://arxiv.org/abs/2501.06125 |