Results 31 to 40 of about 2,057 (240)
Mathematics, 2023 Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws.
Zhixiang Liu +4 more
doaj +1 more source
Introduction to inverse problems for differential equations [PDF]
, 2017 This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed
Hasanov Hasanoğlu, Alemdar +3 more
core +1 more source
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
Consensus ADMM for Inverse Problems Governed by Multiple PDE Models
CoRR, 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 ...
Luke Lozenski, Umberto Villa
openaire +2 more sources
Initial and boundary value problems in two and three dimensions [PDF]
, 2010 This thesis: (a) presents the solution of several boundary value problems (BVPs) for the Laplace and the modified Helmholtz equations in the interior of an equilateral triangle; (b) presents the solution of the heat equation in the interior of an ...
core +2 more sources
Solving Inverse Source Problems for linear PDEs using Sparse Sensor Measurements [PDF]
, 2016 Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting its cause/source, using some ...
Pier Luigi Dragotti +3 more
core +1 more source
Computational Inverse Problems for Partial Differential Equations (hybrid meeting) [PDF]
, 2020 Inverse problems in partial differential equations (PDEs) consist in reconstructing some part of a PDE such as a coefficient, a boundary condition, an initial condition, the shape of a domain, or a singularity from partial knowledge of solutions to the
core +4 more sources
PDEs in the Inverse Problem of Dynamics [PDF]
, 2003 The basic equations are exposed for the following version of the inverse problem of dynamics: determine the two-dimensional potential compatible with a given family of orbits, traced by a material point. If the potential is known in advance, a nonlinear equation is satisfied by the function representing the family of orbits.
openaire +1 more source
Probabilistic numerical methods for PDE-constrained Bayesian inverse problems [PDF]
AIP Conference Proceedings, 2017 This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem.
Jon Cockayne +3 more
openaire +2 more sources
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 +2 more
doaj +1 more source