Results 51 to 60 of about 37,100 (232)

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

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking

, 2010
We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter $\lambda$.
Bogdanov L, Bogdanov L, Dunajski M, Dunajski M Tod K P, Guil F, Kadomtsev B B, Kodama Y, Konopelchenko B, Manakov S V, Manakov S V, Manakov S V, Manakov S V Santini P M, Neyzi F, P M Santini, S V Manakov, Takasaki K Takebe T, Takasaki K Takebe T, Timman R Oswatitsch K, Zakharov V E, Zakharov V E, Zakharov V E, Zobolotskaya E A   +21 more
core   +1 more source

The Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: The Adaptive Explicit Inverse Preconditioning Approach

Modelling and Simulation in Engineering, 2019
Critical comments on the complexity of computational systems and the basic singularly perturbed (SP) concepts are given. A class of several complex SP nonlinear elliptic equations arising in various branches of science, technology, and engineering is ...
Anastasia-Dimitra Lipitakis
doaj   +1 more source

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

, 2004
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation ...
Agranovsky M, Agranovsky M, Andersson L-E, Bers L, Courant R, Denisjuk A, Ehrenpreis L, Fawcett J A, Finch D, Flatto L, Gelfand I, Gelfand I, Gindikin S, Helgason S, Hörmander L, John F, Kruger R A, Kuchment P, Louis A K, Natterer F, Natterer F, Nilsson S, Norton S J, Norton S J, Palamodov V P, Patch S K, Quinto E T, Quinto E T, Spivak M, Xu Y, Ya V, Zobin N   +31 more
core   +2 more sources

On numerical simulation of liquid polymer moulding

Mathematical Modelling and Analysis, 2003
In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is ...
R. Čiegis, O. Iliev
doaj   +1 more source

Neural network augmented inverse problems for PDEs

, 2017
In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function approximators and as such they do not require explicit regularization of the error functional to recover smooth ...
Berg, Jens, Nyström, Kaj
openaire   +2 more sources

Transient modeling of extraction columns: Parameter estimation, uncertainty analysis, and operation optimization

AIChE Journal, EarlyView.
Abstract Despite extensive modeling efforts in extraction research, transient column models are rarely applied in industry due to concerns regarding parameter identifiability and model reliability. To address this, we analyzed uncertainty propagation from estimated parameters in a previously introduced column model and assessed identifiability via ill ...
Andreas Palmtag, Jannik Dohmen, Andreas Jupke   +2 more
wiley   +1 more source

Causality-Aware Training of Physics-Informed Neural Networks for Solving Inverse Problems

Mathematics
Inverse Physics-Informed Neural Networks (inverse PINNs) offer a robust framework for solving inverse problems governed by partial differential equations (PDEs), particularly in scenarios with limited or noisy data. However, conventional inverse PINNs do
Jaeseung Kim, Hwijae Son
doaj   +1 more source

Partially integrable systems in multidimensions by a variant of the dressing method. 1

, 2006
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially integrable''.
A I Zenchuk, Ablowitz M J, Ablowitz M J, Beals R Coifman R R, Bogdanov L V, Calogero F, Drinfeld V G, Konopelchenko B, Manakov S V Santini P M, P M Santini, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zenchuk A   +16 more
core   +1 more source

Toward Knowledge‐Guided AI for Inverse Design in Manufacturing: A Perspective on Domain, Physics, and Human–AI Synergy

Advanced Intelligent Discovery, EarlyView.
This perspective highlights how knowledge‐guided artificial intelligence can address key challenges in manufacturing inverse design, including high‐dimensional search spaces, limited data, and process constraints. It focused on three complementary pillars—expert‐guided problem definition, physics‐informed machine learning, and large language model ...
Hugon Lee, Hyeonbin Moon, Junhyeong Lee, Seunghwa Ryu   +3 more
wiley   +1 more source