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Model reduction by manifold boundaries. [PDF]
Phys Rev Lett, 2014 Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce "black boxes" disconnected from the microscopic physics.
Transtrum MK, Qiu P.
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Nonlinear methods for model reduction [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2021 Typical model reduction methods for parametric partial differential equations construct a linear space Vn which approximates well the solution manifold M consisting of all solutions u(y) with y the vector of parameters. In many problems of numerical computation, nonlinear methods such as adaptive approximation, n-term approximation, and certain tree ...
Bonito, Andrea +5 more
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A statistical model for melody reduction [PDF]
Future Directions of Music Cognition, 2021 5 pages, 1 figure. Proceeding and presentation available at Future Directions of Music Cognition but the conference has not yet officially published until summer 2021. http://org.osu.edu/mascats/march-6-talks/
Tianxue Hu, Claire Arthur
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Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport
Mathematics, 2021 Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework.
Vasiliy V. Grigoriev +1 more
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Finite Element Simulation of Thermo-Mechanical Model with Phase Change
Computation, 2021 In this work, we consider a mathematical model and finite element implementation of heat transfer and mechanics of soils with phase change. We present the construction of the simplified mathematical model based on the definition of water and ice fraction
Maria Vasilyeva +2 more
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Mathematics, 2021 In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards
Denis Spiridonov +3 more
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DG-GMsFEM for Problems in Perforated Domains with Non-Homogeneous Boundary Conditions
Computation, 2021 Problems in perforated media are complex and require high resolution grid construction to capture complex irregular perforation boundaries leading to the large discrete system of equations. In this paper, we develop a multiscale model reduction technique
Valentin Alekseev +3 more
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Combining Model Reductions [PDF]
Electronic Notes in Theoretical Computer Science, 2010 Molecular biological models usually suffer from a large combinatorial explosion. Indeed, proteins form complexes and modify each others, which leads to the formation of a huge number of distinct chemical species (i.e. non-isomorphic connected components of proteins).
Camporesi, Ferdinanda +3 more
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An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing
Mathematics, 2020 In this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains.
Vasily Vasil’ev, Maria Vasilyeva
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Fluids, 2021 In this paper, we consider the poroelasticity problem in fractured and heterogeneous media. The mathematical model contains a coupled system of equations for fluid pressures and displacements in heterogeneous media.
Aleksei Tyrylgin +4 more
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