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The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…
Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the…
We use parsimonious diffusion maps (PDMs) to discover the latent dynamics of high-fidelity Navier-Stokes simulations with a focus on the 2D fluidic pinball problem. By varying the Reynolds number, different flow regimes emerge, ranging from…
In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow…
The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to solve the load flow problem. It guarantees finding the correct solution when it exists, and identifying when a solution does not exist. The method, however, is…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…
In this paper, partition-based distributed state estimation of general linear systems is considered. A distributed moving horizon state estimation scheme is developed via decomposing the entire system model into subsystem models and…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the electromagnetic and hydrodynamic variables, especially for high…
Space plasma simulations have seen an increase in the use of magnetohydrodynamic (MHD) with embedded Particle-in-Cell (PIC) models. This combined MHD-EPIC algorithm simulates some regions of interest using the kinetic PIC method while…
Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark-gluon plasma in heavy-ion collisions to matters in supernovas, compact…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and…
Predicting the behavior of turbulent flows using large-eddy simulation requires modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with…
Real-time visual analysis tasks, like tracking and recognition, require swift execution of computationally intensive algorithms. Visual sensor networks can be enabled to perform such tasks by augmenting the sensor network with processing…
Online data assimilation in time series models over a large spatial extent is an important problem in both geosciences and robotics. Such models are intrinsically high-dimensional, rendering traditional particle filter algorithms…