Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Abstract

This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples.

Sinc Collocation Method to Simulate the Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel

“…In [26], the Adomian decomposition method and homotopy perturbation method are given to approximate the solution of the time FPIEs. Liu et al [27][28][29][30][31] used the multigrid method and homotopy method to solve practical problems in the fractional flow formulation of the two-phase porous media flow equations and Biot elastic models.…”

Positive Solutions for Periodic Boundary Value Problems of Fractional Differential Equations with Sign-Changing Nonlinearity and Green’s Function

“…BVPs with positive solutions have played a very important role in the study of mathematical physics problems; see [16][17][18][19]. There are some very recent interesting results on this topic; see [16,[20][21][22][23][24][25], and the references therein.…”

An Efficient Convolutional Neural Network with Supervised Contrastive Learning for Multi-Target DOA Estimation in Low SNR

“…Numerous algorithms have been invented to tackle the DOA estimation problem, and among them, the subspace-based estimation algorithms are well known for their capacity to give a high-resolution estimation. These include MUSIC (Multiple SIgnal Classification), ES-PRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), Root-MUSIC (R-MUSIC) [1][2][3], homotopy method [4,5], multigrid method [6,7], and multigrid-homotopy method [8]. However, in low signal-to-noise ratio (SNR) environments, they suffer from significant biases.…”