arXiv subjects

Christopher R. Wentland

Publications and source records attributed to Christopher R. Wentland.

4 recordsLinked to original sources

arXiv2025

Conditional pathways-based climate attribution

Attribution of climate impacts to natural and anthropogenic source forcings is essential for understanding and addressing climate effects. While standard methods like optimal fingerprinting have been effective for long-term changes, they often struggle in low signal-to-noise regimes typical of short-term forcings or with climate variables loosely related to the forcing. Single-step approaches fail to leverage additional climate information to enhance attribution certainty. To overcome these limitations, we propose a formal statistical framework that incorporates hypothesized physical pathways linking source forcings to downstream impacts. By establishing relationships based on scalar features and simple forcing response models, we create a series of conditional probabilities that describe the likelihood of the final impact. This method captures both primary and secondary processes by which the downstream impact evolves. Through hypothesis testing in a likelihood ratio framework, we demonstrate improved attribution confidence for source magnitudes in low signal-to-noise scenarios. Using the 1991 eruption of Mt. Pinatubo as a case study, we show that incorporating near-surface temperature and stratospheric radiative flux measurements enhances attribution certainty compared to analyses based solely on temperature, even at seasonal and regional scales. This framework holds promise for improving climate attribution assessments for unknown source magnitudes and low signal-to-noise impacts, where traditional methods may falter. Additionally, the formal inclusion of pathways allows for a deeper exploration of complex, multivariate relationships influencing source attribution.

stat.AP↗

arXiv2024

The role of interface boundary conditions and sampling strategies for Schwarz-based coupling of projection-based reduced order models

This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a given problem of interest is posed. In this approach, the solution on the full domain is obtained via an iterative process in which a sequence of subdomain-local problems are solved, with information propagating between subdomains through transmission boundary conditions (BCs). We explore several new directions involving the Schwarz alternating method aimed at maximizing the method's efficiency and flexibility, and demonstrate it on three challenging two-dimensional nonlinear hyperbolic problems: the shallow water equations, Burgers' equation, and the compressible Euler equations. We demonstrate that, for a cell-centered finite volume discretization and a non-overlapping DD, it is possible to obtain a stable and accurate coupled model utilizing Dirichlet-Dirichlet (rather than Robin-Robin or alternating Dirichlet-Neumann) transmission BCs on the subdomain boundaries. We additionally explore the impact of boundary sampling when utilizing the Schwarz alternating method to couple subdomain-local hyper-reduced PROMs. Our numerical results suggest that the proposed methodology has the potential to improve PROM accuracy by enabling the spatial localization of these models via domain decomposition, and achieve up to two orders of magnitude speedup over equivalent coupled full order model solutions and moderate speedups over analogous monolithic solutions.

math.NA↗

arXiv2022

Reduced models with nonlinear approximations of latent dynamics for model premixed flame problems

Efficiently reducing models of chemically reacting flows is often challenging because their characteristic features such as sharp gradients in the flow fields and couplings over various time and length scales lead to dynamics that evolve in high-dimensional spaces. In this work, we show that online adaptive reduced models that construct nonlinear approximations by adapting low-dimensional subspaces over time can predict well latent dynamics with properties similar to those found in chemically reacting flows. The adaptation of the subspaces is driven by the online adaptive empirical interpolation method, which takes sparse residual evaluations of the full model to compute low-rank basis updates of the subspaces. Numerical experiments with a premixed flame model problem show that reduced models based on online adaptive empirical interpolation accurately predict flame dynamics far outside of the training regime and in regimes where traditional static reduced models, which keep reduced spaces fixed over time and so provide only linear approximations of latent dynamics, fail to make meaningful predictions.

math.NA↗

arXiv2021

Model Reduction for Multi-Scale Transport Problems using Model-form Preserving Least-Squares Projections with Variable Transformation

A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the structure of the governing equations. Least-squares-based minimization is leveraged to guarantee symmetrization and discrete consistency with the full-order model (FOM). Two levels of scaling are used to achieve the conditioning required to effectively handle problems with extremely disparate physical phenomena, characterized by extreme stiffness in the system of equations. The formulation -- referred to as model-form preserving least-squares with variable transformation (MP-LSVT) -- provides global stabilization for both implicit and explicit time integration schemes. To achieve computational efficiency, a pivoted QR decomposition is used with oversampling, and adapted to the MP-LSVT method. The framework is demonstrated in representative two- and three-dimensional reacting flow problems, and the MP-LSVT is shown to exhibit improved stability and accuracy over standard projection-based ROM techniques. Physical realizability and local stability are promoted by enforcing limiters in both temperature and species mass fractions. These limiters are demonstrated to be important in eliminating regions of spurious burning, thus enabling the ROMs to provide accurate representations of the heat release rate and flame propagation speed. In the 3D application, it is shown that more than two orders of magnitude acceleration in computational efficiency can be achieved, while also providing reasonable future-state predictions. A key contribution of this work is the development and demonstration of a comprehensive ROM formulation that targets highly challenging multi-scale transport-dominated problems.

physics.comp-ph↗