Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while…

Galerkin reduced-order models (ROMs) approximate computational fluid simulations by reducing snapshot data to a basis of proper orthogonal decomposition (POD) modes and solving for modal coefficients with ordinary differential equations. Galerkin ROMs reduce computational cost and can approximate flows with alternate Reynolds numbers, while parametric reduced order models allow adjustment of other system parameters. However,…

Given the inability to directly observe the conditions of a fault line, inversion of parameters describing them has been a subject of practical interest for the past couple of decades. To resolve this under a linear elasticity forward model, we consider Bayesian inference in the infinite dimensional setting given some surface displacement measurements, resulting in…

If you are interested in learning more about applied math research from your fellow students, or you want a friendly and constructive environment to practice presenting your own applied math research, AMGSS is for you! This is an informational and sign-up meeting, so come to learn more about AMGSS and/or to sign up to present…

In this talk we develop a method for efficient computation of reduced-order nonlinear solutions (RONS). RONS is a framework to create reduced-order models for time-dependent partial differential equations (PDEs) where the reduced-order solution has nonlinear dependence on time-varying parameters. With RONS we obtain an explicit set of ordinary differential equations (ODEs) to evolve the parameters.…

We consider sensitivity analysis of Bayesian inverse problems with respect to modeling uncertainties. To this end, we consider sensitivity analysis of the information gain, as measured by the Kullback-Leibler divergence from the posterior to the prior. This choice provides a principled approach that leverages key structures within the Bayesian inverse problem. Also, the information gain…

Extreme events are events that have an extremely low probability of occurring, but often have immense consequences. For this presentation, we focus on extreme events in climate change and wildfires. In the context of climate change, we examine the avoidance of so-called climate tipping points, which are climate regimes where small changes significantly alter the…

Zombies are popularly presented in media as resulting from an infectious outbreak. Various modeling assumptions for zombification as an infectious disease are discussed. Populations during the outbreak are then modeled with infectious disease compartment models accounting for various effects such as latent infectious populations, quarantining, etc. Equilibrium and stability conditions for these dynamics are determined,…

Talk 1: Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling - Abstract 1: Sensitivity analysis for computational fluid dynamics (CFD) simulations is a complicated procedure, which still relies, in many cases, on engineering judgment and factors of safety. This is, in part, because the computational cost of quantifying the simulation's sensitivity to all…

- Presenter: William Anderson - Title: Fast and Scalable Computation of Reduced-Order Nonlinear Solutions for PDEs - Abstract: We develop a method for fast and scalable computation of reduced-order nonlinear solutions (RONS). RONS is a framework to build reduced-order models for time-dependent partial differential equations (PDEs), where the reduced-order solution depends nonlinearly on time-varying parameters. With…

Of primary importance in computational science and applications is quantification and improvement of predictive capabilities of large-scale parameterized models, which often require the use of multi-query techniques that are intractable for computationally expensive models. This research focuses on three primary thrusts: sensitivity analysis, reduced-order modeling, and uncertainty quantification and algorithm and implementation choices that scale favorably…

Determining the sensitivity of model outputs to input parameters is an important precursor to developing informative parameter studies, building surrogate models, and performing rigorous uncertainty quantification. Determining parameter sensitivities over a range of parameter values, termed global sensitivity analysis, requires many model evaluations sampled over the parameter space, which is intractable for many large-scale computational…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of…

Inverse problems are an expanding field with many practical applications in scientific computing and engineering. Their Bayesian enhancement encodes prior knowledge and data uncertainties into a posterior. This is an important tool in uncertainty quantification. However, performing uncertainty quantification tasks on top of this posterior is difficult to formulate and often computationally intractable. Hence, for…

Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…

The purpose of this project is to develop, test, and document performance of dual-domain clustering algorithms for spatiotemporal datasets, tailored to pandemic preparedness and endgame challenges. Dual-domain clustering refers to the unsupervised learning clustering method performed on data with both application-specific attributes (e.g., number of infectious) and geographic information (e.g., latitude and longitude of data…

Two of the most popular approaches to supervised learning are kernels and artificial neural networks (ANN).The ability to emulate complicated nonlinear behavior makes them powerful tools for function approximation.Randomization schemes, which have been successfully deployed to improve efficiency for many algorithms, havealso been developed for kernel methods and ANNs. These are random weight neural networks…

If you are interested in learning more about applied math research from your fellow students, or you want a friendly and constructive environment to practice presenting your own research, AMGSS is for you! This is an informational and sign-up meeting, so come to learn more about AMGSS and/or to sign up to present your research.

Dense linear systems in large-scale kernel approximation in machine learning, discretization of boundary integral equations in mathematical physics, and low-rank approximation of Schur complements in large sparse matrix factorization often employ a multilevel structure of low-rank off-diagonal blocks. To solve such systems efficiently, we present a GPU-based parallel recursive skeletonization solver that utilizes batched dense…

PyOED is a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers…