Dmitry I. Kabanov

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• PhD in Applied Mathematics and Computational Sciences
• Research Software Engineer at University of Münster

MaRDI Open Interfaces is a software project aimed at improving reuse and interoperability in Scientific Computing by alleviating the difficulties of crossing boundaries between different programming languages, in which numerical packages are usually implemented, and of switching between multiple implementations of the same mathematical problem. The...

These are the slides from my talk at the PDESoft conference held in Cambridge, United Kingdom, on 1-3 July 2024. I was presenting our work on Open Interfaces, which is the project that aims to alleviate two problems that computational scientists often face while conducting computational experiments: different programming languages used for numeric...

In recent years, neural networks have been increasingly used to solve scientific problems. Particularly, physics-informed neural networks—networks augmented with the knowledge of physical constraints—have been applied to problems in mechanics to reconstruct fields of state variables with higher accuracy, than purely data-driven neural networks can...

We apply neural networks to the problem of estimating divergence-free velocity flows from given sparse observations. Following the modern trend of combining data and models in physics-informed neural networks, we reconstruct the velocity flow by training a neural network in such a manner that the network not only matches the observations but also a...

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L² projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions...

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis...

We apply neural networks to the problem of estimating wind flow from given sparse observations. We assume that the wind speed is low, hence, the flow is incompressible, namely, divergence-free. Following modern trend of combining data and models together to obtain physics-informed neural networks, we reconstruct the flow by training a neural networ...

We consider parameter estimation of the partial differential equations from the given observations. Parameter estimation, in general, includes multiple solves of the partial differential equations. Here, we replace these solves with a surrogate based on a feedforward neural network, which is trained to approximately satisfy the equation in addition...

We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using...

We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using...

Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled with the equations describing thermodynamic and chemical properties of the fluid. Mathematically, these governing equations admit steady-state travelling-wave solutions consisting of a leading shock wave followed by...

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard...

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard...

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard...

We propose a method to study linear stability of detonations by linearizing equations about steady-state, solving them numerically and then postprocessing using dynamic mode decomposition. We compare our results for the one-step model with the results obtained using normal-mode analysis. Besides, we show that our method is easily extensible to more...