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This paper proposes and tests the first-ever reduced basis warm-start iterative method for the parametrized linear systems, exemplified by those discretizing the parametric partial differential equations. Traditional iterative methods are…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization,…
The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However,…
This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We…
Finite-temperature calculations are relevant for rationalizing material properties yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many…
In this paper, models that approximate stochastic processes from the space $Sub_\varphi(\Omega)$ with given reliability and accuracy in $L_p(T)$ are considered for some specific functions $\varphi(t)$. For processes that are decomposited in…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…
Molecular dynamics simulation is employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2-20 number of shells (55-28741 atoms). The embedded atom method was used to describe the…
We propose a systematic expansion method which is applied to freely evolving granular fluids contained in sufficiently small systems. Restricting ourselves to small systems, we show that there exists a small parameter which characterizes a…
This work presents a scalable computational framework for optimal design under uncertainty with application to multi-material insulation components of building envelopes. The forward model consists of a multi-phase thermo-mechanical model…
Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant…
The thermal response function given to a unit-step dissipation accurately characterizes the thermal system. Instead of the thermal response function the so-called structure function describing three-dimensional as the equivalent model of…
While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…
Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…
The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order…
As an aid to the development of hydrogen separation membranes, we predict the temperature dependent phase diagrams using first principles calculations combined with thermodynamic principles. Our method models the phase diagram without…
In algebraic quantum field theory the (inverse) temperature is shown to be a macroscopic \textit{order parameter} to parametrize mutually disjoint thermal \textit{sectors} arising from the \textit{broken scale invariance} under…
Approximation of the previously estimated excess specific heat C^{excess}/T^{5} of two fluoropolymers, PTFE and PCTFE, is presented using Orthonormal Polynomial Expansion Method (OPEM). The new type of weighting functions in OPEM involves…