16 citations · 17 across the 6 of their papers we have counts for
6 papers
Hyb-Adam-UM: hybrid ultrametric-aware mtDNA phylogeny reconstruction
Dmitrii Chaikovskii, Weilai Qu, Boris Melnikov +2
Motivation: mtDNA distance matrices are standard inputs for distance-based phylogeny, but computing all pairwise alignments is costly. Missing entries can degrade inferred topology…
Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations
Qiao Zhu, Dmitrii Chaikovskii, Bangti Jin +1
Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep…
Internal layer solutions and coefficient recovery in time-periodic reaction-diffusion-advection equations
Dmitrii Chaikovskii, Ye Zhang, Aleksei Liubavin
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a non…
Asymptotic expansion regularization for inverse source problems in two-dimensional singularly perturbed nonlinear parabolic PDEs
Dmitrii Chaikovskii, Aleksei Liubavin, Ye Zhang
In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partia…
Solving forward and inverse problems in a non-linear 3D PDE via an asymptotic expansion based approach
Dmitrii Chaikovskii, Ye Zhang
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--d…
Convergence analysis for forward and inverse problems in singularly perturbed time-dependent reaction-advection-diffusion equations
Dmitrii Chaikovskii, Ye Zhang
In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed parti…