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Continuous analogue to iterative optimization for PDE-constrained inverse problems [PDF]

Inverse Problems in Science and Engineering, 2018
The parameters of many physical processes are unknown and have to be inferred from experimental data. The corresponding parameter estimation problem is often solved using iterative methods such as steepest descent methods combined with trust regions. For a few problem classes also continuous analogues of iterative methods are available.
Boiger, R., Fiedler, A., Hasenauer, J., Kaltenbacher, B.   +3 more
openaire   +3 more sources

The General Fractional Derivative and Related Fractional Differential Equations

Mathematics, 2020
In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
doaj   +1 more source

A Second-Order Network Structure Based on Gradient-Enhanced Physics-Informed Neural Networks for Solving Parabolic Partial Differential Equations

Entropy, 2023
Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has ...
Kuo Sun, Xinlong Feng
doaj   +1 more source

Are physiological oscillations physiological?

The Journal of Physiology, EarlyView., 2023
Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
wiley   +1 more source

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

International Journal of Mathematics and Mathematical Sciences, 2014
Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction
Nemat Dalir
doaj   +1 more source

Neural networks as smooth priors for inverse problems for PDEs

Journal of Computational Mathematics and Data Science, 2021
Abstract In this paper we discuss the potential of using artificial neural networks as smooth priors in classical methods for inverse problems for PDEs. Exploring that neural networks are global and smooth function approximators, the idea is that neural networks could act as attractive priors for the coefficients to be estimated from noisy data.
Jens Berg, Kaj Nyström
openaire   +2 more sources

The RBF-FD and RBF-FDTD Methods for Solving Time-Domain Electrical Transient Problems in Power Systems

International Transactions on Electrical Energy Systems, 2023
In this paper, the development and application of the radial basis function-finite difference (RBF-FD) method and the RBF-finite difference time domain (RBF-FDTD) method for solving electrical transient problems in power systems that are defined by the ...
Duc-Quang Vu, Nhat-Nam Nguyen, Phan-Tu Vu   +2 more
doaj   +1 more source

Consensus ADMM for Inverse Problems Governed by Multiple PDE Models

, 2021
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these large-scale inverse problems into smaller, simpler sub-problems, for which computationally efficient solvers are available ...
Lozenski, Luke, Villa, Umberto
openaire   +2 more sources

Gradient Statistics-Based Multi-Objective Optimization in Physics-Informed Neural Networks

Sensors, 2023
Modeling and simulation of complex non-linear systems are essential in physics, engineering, and signal processing. Neural networks are widely regarded for such tasks due to their ability to learn complex representations from data.
Sai Karthikeya Vemuri, Joachim Denzler
doaj   +1 more source

Accelerated Variational PDEs for Efficient Solution of Regularized Inversion Problems

Journal of Mathematical Imaging and Vision, 2019
We further develop a new framework, called PDE acceleration, by applying it to calculus of variation problems defined for general functions on ℝ n , obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDEs. While the resulting family of PDEs
Benyamin, Minas, Calder, Jeff, Sundaramoorthi, Ganesh, Yezzi, Anthony   +3 more
openaire   +4 more sources