SPUDS Seminar

Abstract: A new meshfree geometric multigrid (MGM) method is presented for solving linear systems that arise from discretizing elliptic PDEs on unstructured grids and point clouds.  The method uses a Poisson disk sampling-type technique for coarsening the vertices of an unstructured grid or the nodes of a point cloud, and new meshfree restriction/interpolation operators based on polyharmonic splines for transferring information between the coarsened levels. These components are then combined with standard smoothing and operator coarsening methods in a V-cycle iteration.  We demonstrate the applicability of the method as a solver and preconditioner for several problems discretized with finite element, discontinuous Galerkin, and radial basis function finite differences.  We also perform a side-by-side comparison to algebraic multigrid (AMG) methods for solving the same systems.

Abstract: Data-driven methods have gained increasing attention in computational mechanics and design. This study investigates a two-scale data-driven design for thermal metamaterials with various functionalities. To address the complexity of multiscale design, the design variables are chosen as the components of the homogenized thermal conductivity matrix originating from the lower scale unit cells. Multiple macroscopic functionalities including thermal cloak, thermal concentrator, thermal rotator/inverter, and their combinations, are achieved using the developed approach. Sensitivity analysis is performed to determine the effect of each design variable on the desired functionalities, which is then incorporated into topology optimization. Geometric extraction demonstrates an excellent matching between the optimized homogenized conductivity and the extraction from the constructed database containing both architecture and property information. The designed heterostructures exhibit multiple thermal meta-functionalities that can be applied to a wide range of heat transfer fields from personal computers to aerospace engineering.

Abstract: Discrete-time survival models (DTSMs) are an alternative to the classic Cox proportional hazards models used widely in survival analyses. DTSMs have an (arguably) simpler set of assumptions, and fit many applications without loss of information, in comparison with continuous Cox models—though perhaps at the cost of increased computational complexity. This talk introduces survival analysis in general, DTSMs and their construction in particular, and lastly presents a recent retrospective case study using DTSMs to measure the effect of crowded hospitals on Covid-19 inpatient mortality in Colorado.

Abstract: Acquired in 2014 by Idaho National Laboratory (INL), Falcon was the world’s 97th fastest supercomputer. Falcon processors were later upgraded and 4 additional racks of nodes added, bringing it to its current computing capacity of 932 nodes with 33,553 cores capable of more than 1 PetaFLOPS. In 2022, the management and use of Falcon was transferred by INL to the three Idaho universities through the “C3Plus3”. Now, university faculty, staff, and students can freely access Falcon for their research and training needs. Planning is underway for future INL supercomputer transfers to C3Plus3. 

In this talk, I’ll demonstrate how to obtain a Falcon Account, easily access Falcon for running research jobs, and give a quick tutorial. If anyone wants to work along with me on Falcon - they can request an account here. 

Abstract: With its protein content making up roughly 3.5% of its weight, milk is an important source of protein for human nutrition. Whey and casein, the two main forms of milk proteins, each has its special qualities and advantages. Whereas casein proteins have been connected to slower digestion and higher levels of muscle protein synthesis, whey proteins have been linked to decreased blood pressure, and muscular growth. Nonetheless, milk adulteration is still a serious issue because it could have negative impacts on one’s health. Water, urea, melamine, and other non-milk components are examples of adulterants in milk that can drastically change the nutritional value and safety of milk. Several analytical techniques have been developed to identify these adulterants, including chemometric techniques as well as more traditional techniques like physical characteristics, spectroscopy, and high-performance liquid chromatography (HPLC). Chemometrics enhances the detection of milk adulteration and enables the analysis of big datasets.

The application of chemometrics has substantially enhanced the study of milk proteins by enhancing both qualitative and quantitative assessments. It provides the rapid and precise assessment of protein content in dairy products, hence contributing in the confirmation of product labeling claims. The quality control of milk and dairy products has been substantially enhanced as a result of these chemometrics improvements, to the benefit of both producers and consumers. In this study, we present the qualitative and quantitative analysis of adulterants in milk using chemometrics. Also, we evaluated four chemometric models, including partial least squares, support vector regression (SVR), ridge, and logistic regression to accurately predict the concentrations of β-lactoglobulin and α-lactalbumin in milk.

Abstract: Inverse problems arise when the cause of a given effect cannot be directly measured, but the effect can. If the system is well represented by a known mathematical model characterized by a set of parameters, we can use inverse methods to infer the parameters from observed data. Locating abrupt changes in parameters is an important problem across several scientific disciplines. Parameter discontinuities can represent a wide array of important things such as tumor boundaries, changes in salinity, or fractures in a structure.  Because inverse problems are typically ill-posed, parameter estimates are often unstable under data perturbation, so regularization is often used to stabilize the solution. Total variation (TV) regularization was developed to preserve sharp parameter changes while removing noise. Iteratively Re-weighted Least Squares (IRLS) is one algorithm for producing TV regularized parameter estimates. This algorithm produces parameter estimates by solving a series of weighted least squares problems that converge to the TV regularized parameter estimate. Typically, the weighting matrix is discarded at the end of the estimation process, but this matrix contains information which indicates the location of parameter discontinuities. In this talk, I will give a brief overview of inverse problems, regularization, and the IRLS algorithm before explaining how the IRLS weighting matrix can be used to locate parameter discontinuities.

Abstract: On January 15th, 2022 around 04:05UTC, the undersea volcano Hunga Tonga-Hunga Ha’apai located near the south pacific island of Tonga erupted, releasing a large amount of energy into the atmosphere. The atmospheric disturbances generated by this event were detected by equipment all around the world. Analysis of the data later revealed that some of these  disturbances were Lamb waves generated by the volcanic eruption. Previous works have successfully modeled these types of waves through shallow water approximations. In this talk I will present a numerical simulation using high resolution finite volume methods and adaptive mesh refinement for the shallow water approximation of the Lamb wave generated by the Hunga Tonga-Hunga Ha’apai eruption.

Abstract: Overland flooding represents a significant environmental challenge that demands advanced computational modeling to accurately capture its complex hydrodynamic processes and the requirement for high-resolution data. This research is dedicated to improving the computational performance of simulating such phenomena by leveraging the acceleration capabilities of GPUs (Graphics Processing Units), a strategy that has gained recognition for its ability to expedite complex computations across several scientific fields. The core goal of this study is to enhance the computational speed of CPU (Central Processing Unit) patch-based Riemann solvers utilized in the GeoFlood code by integrating CUDA (Compute Unified Device Architecture) acceleration. By focusing on overcoming the existing limitations in scalability and computational duration of the current software, this endeavor seeks to facilitate more precise and time-efficient simulation outcomes. Early findings indicate an acceleration of 6–10 times on a standard home GPU setup.

Abstract: Data assimilation and inverse methods for ill-posed problems find optimal estimates of states or parameters. Methods for both combine observations with a model, which here we assume is a partial differential equation (PDE). Finding a compromise between observations and model is challenging because the actual observations often have values significantly different than the corresponding PDE estimates. Neither the observations nor the PDE exactly characterize the state because each has error, and in the case of the PDE, this can be due to unknown forcings, initial or boundary conditions.

State estimates from data assimilation can vary significantly depending on specified errors in the PDE. In this work we estimate PDE errors by developing a common framework between variational data assimilation and regularization for ill-posed problems. This framework arises when weakly constrained variational data assimilation is viewed as regularizing the severely underdetermined data fitting problem in data assimilation. Within this framework we derive error estimates for data assimilation using regularization parameter selection methods including the L-curve, Generalized Cross Validation (GCV) and the Chi-squared method. Data assimilation results will be shown from a one dimensional transport model with simulated data, where the resulting state estimates can be viewed as air quality estimates.