Multi-Order Monte Carlo IMEX hierarchies for uncertainty quantification in multiscale hyperbolic systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908943261892608 |
|---|---|
| author | Bertaglia, Giulia Boscheri, Walter Pareschi, Lorenzo |
| author_facet | Bertaglia, Giulia Boscheri, Walter Pareschi, Lorenzo |
| contents | We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to satisfy the asymptotic-preserving property across different discretization orders of accuracy. In contrast to traditional Multi-Level Monte Carlo methods, which require costly hierarchical re-meshing, our method constructs a multi-order hierarchy by varying both spatial and temporal discretization orders within the Monte Carlo framework. This enables efficient variance reduction while naturally adapting to the multiple scales inherent in the problem ensuring asymptotic consistency. The proposed method is particularly well-suited for hyperbolic systems with stiff relaxation, kinetic equations, and low Mach number flows, where standard Multi-Level Monte Carlo techniques often encounter computational challenges. Numerical experiments demonstrate that the novel Multi-Order Monte Carlo approach achieves substantial reduction of both error and variance while maintaining asymptotic consistency in the asymptotic limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Order Monte Carlo IMEX hierarchies for uncertainty quantification in multiscale hyperbolic systems Bertaglia, Giulia Boscheri, Walter Pareschi, Lorenzo Numerical Analysis 65C05, 65L04, 65L06, 65C30, 35L65, 35B40 We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to satisfy the asymptotic-preserving property across different discretization orders of accuracy. In contrast to traditional Multi-Level Monte Carlo methods, which require costly hierarchical re-meshing, our method constructs a multi-order hierarchy by varying both spatial and temporal discretization orders within the Monte Carlo framework. This enables efficient variance reduction while naturally adapting to the multiple scales inherent in the problem ensuring asymptotic consistency. The proposed method is particularly well-suited for hyperbolic systems with stiff relaxation, kinetic equations, and low Mach number flows, where standard Multi-Level Monte Carlo techniques often encounter computational challenges. Numerical experiments demonstrate that the novel Multi-Order Monte Carlo approach achieves substantial reduction of both error and variance while maintaining asymptotic consistency in the asymptotic limit. |
| title | Multi-Order Monte Carlo IMEX hierarchies for uncertainty quantification in multiscale hyperbolic systems |
| topic | Numerical Analysis 65C05, 65L04, 65L06, 65C30, 35L65, 35B40 |
| url | https://arxiv.org/abs/2508.20187 |