New Trends of Mathematical Inverse Problems and Applications: ICNTAM 2022, Béni Mellal, Morocco, May 19–21

Preface
Contents
Comparing Numerical Methods  for Inverse Source Problem in Time-Fractional Diffusion Equation
	1 Introduction
	2 Primal-Dual Method
	3 Descent-Gradient Method
	4 Numerical Results
		4.1 Primal-Dual Algorithm
		4.2 Descent-Gradient Algorithm
		4.3 Comparison
	5 Conclusion
	References
An Improvement to the Nonparametric Regression Models Using the Nonsmooth Loss Functions
	1 Introduction
	2 Setting of the Problem
	3 Smoothed Absolute Loss
	4 Numerical Algorithms
	5 Experiments
		5.1 Stability of the Algorithm
	6 Conclusion
	References
The Asymptotic Behavior of the Reynolds Equations\' Solution
	1 Introduction
	2 The Incompressible Case
		2.1 Incompressible Reynolds Equation
		2.2 Variational Inequation
		2.3 Model Eldord and Adams
	3 The Compressible Case
		3.1 Reynolds Compressible
	References
Heart Failure Prediction Using Supervised Machine Learning Algorithms
	1 Introduction
	2 Background and the Setting of the Problem
	3 Experimental Results
		3.1 Dataset Description
		3.2 Results and Discussions
		3.3 Feature Importance
	4 Conclusion
	References
Optimization Method for Estimating the Inverse Source Term in Elliptic Equation
	1 Introduction
	2 Variational Formulation and a Priori Estimates
	3 Existence of the Optimization Problem
	4 Convexity of the Optimization Problem
	5 The Proposed Algorithm
	6 Numerical Results
		6.1 Results for the One-Dimensional Case
		6.2 Results for the Two-Dimensional Case
	7 Conclusion
	References
A Mesh Free Wavelet Method to Solve the Cauchy Problem for the Helmholtz Equation
	1 Introduction
	2 Statement of the Inverse Cauchy Problem
		2.1 Brief Overview of the Helmholtz Equation
		2.2 The Inverse Problem
		2.3 Overview of the Haar Wavelet Method
		2.4 Function Approximation
		2.5 Integrals Haar Wavelets
	3 Solving Inverse Cauchy Problems Using Haar Wavelets
	4 Haar Wavelets Approximation of the Direct Problem
	5 Solving the Linear System
		5.1 Regularization and Preconditioning
	6 Numerical Computations
	7 Conclusion
	References
Meshless Methods to Noninvasively Calculate Neurocortical Potentials from Potentials Measured at the Scalp Surface
	1 Introduction
	2 Overview of the Problem
		2.1 Modeling the Geometry of the Head
		2.2 Inverse Problems
	3 Theoretical Background
		3.1 The Associated Cauchy Problem
	4 Successive Approach
		4.1 Polynomial Expansion Method
		4.2 Substitution of the Polynomial Expansions into the Laplace Equation and Boundary Conditions
		4.3 Solving the Resulting System of Linear Equations for the Expansion Coefficients
	5 Numerical Results
	6 Discussion and Conclusion
	References
Solving Geometric Inverse Problems with a Polynomial Based Meshless Method
	1 Introduction
	2 Mathematical Formulation of the Inverse Problem
	3 Decoupled Cauchy-Newton Algorithm
		3.1 Polynomial Expansion Approximation of the Cauchy Problem
		3.2 Regularization and Preconditioning
		3.3 Determining the Unknown Boundary with Newton Method
	4 Numerical Results and Discussion
	5 Noise Effect
	6 Conclusion
	References
Image Restoration Using a Coupled Reaction-Diffusion Equations
	1 Introduction
	2 The Proposed Reaction-Diffusion System
	3 Existence and Uniqueness
	4 Discretization
	5 Numerical Results
	6 Conclusion
	References
A Novel Identification Scheme of an Inverse Source Problem Based on Hilbert Reproducing Kernels
	1 Introduction
	2 Setting Problem and Formulation
		2.1 Formulation to Optimal Control Problem
	3 Existence of an Optimal Solution
		3.1 Existence and Uniqueness of the Solution of the State Problem
		3.2 Continuity of Cost Functional
	4 Numerical Reconstruction Method
		4.1 State Sensitivity Study
		4.2 Gradient Calculation
		4.3 Approximation in a Reproducing Kernel Space
		4.4 Numerical Algorithm
	5 Numerical Results
	6 Conclusion
	References