Results 81 to 90 of about 37,100 (232)

Sparse Reconstructions for Inverse PDE Problems

, 2009
We are concerned with the numerical solution of linear parameter identification problems for parabolic PDE, written as an operator equation $Ku=f$. The target object $u$ is assumed to have a sparse expansion with respect to a wavelet system $Psi={psi_lambda}$ in space-time, being equivalent to a priori information on the regularity of $u=mathbf u ...
openaire   +3 more sources

Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics
Mohamed E. M. Alngar, Khaled A. Gepreel, Reham M. A. Shohib, Yakup Yildirim   +3 more
wiley   +1 more source

An Adaptive Sampling Algorithm with Dynamic Iterative Probability Adjustment Incorporating Positional Information

Entropy
Physics-informed neural networks (PINNs) have garnered widespread use for solving a variety of complex partial differential equations (PDEs). Nevertheless, when addressing certain specific problem types, traditional sampling algorithms still reveal ...
Yanbing Liu, Liping Chen, Yu Chen, Jianwan Ding   +3 more
doaj   +1 more source

Accelerated PDE's for efficient solution of regularized inversion problems

, 2018
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDE's.
Benyamin, Minas, Calder, Jeff, Sundaramoorthi, Ganesh, Yezzi, Anthony   +3 more
openaire   +2 more sources

Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo, Delfina Gómez, Maria‐Eugenia Pérez‐Martínez   +2 more
wiley   +1 more source

Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems [PDF]

, 2022
Giovanni S. Alberti
openalex   +2 more sources

Ellipsoid‐Based Interval‐Type Uncertainty Model Updating Based on Riemannian Manifold and Gaussian Process Model

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT Modern engineering systems require advanced uncertainty‐aware model updating methods that address parameter correlations beyond conventional interval analysis. This paper proposes a novel framework integrating Riemannian manifold theory with Gaussian Process Regression (GPR) for systems governed by Symmetric Positive‐Definite (SPD) matrix ...
Yanhe Tao, Qintao Guo, Jin Zhou, Cheng Yi   +3 more
wiley   +1 more source

Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems Using Transfer Learning

Applied Sciences
Physics-Informed Neural Network (PINN) is a data-driven solver for partial and ordinary differential equations (ODEs/PDEs). It provides a unified framework to address both forward and inverse problems.
Abdul Hannan Mustajab, Hao Lyu, Zarghaam Rizvi, Frank Wuttke   +3 more
doaj   +1 more source

Physics‐Driven Deep Neural Networks for Solving the Optimal Transport Problem Associated With the Monge–Ampère Equation

CAAI Transactions on Intelligence Technology, EarlyView.
ABSTRACT Monge–Ampère equations (MAEs) are fully nonlinear second‐order partial differential equations (PDEs), which are closely related to various fields including optimal transport (OT) theory, geometrical optics and affine geometry. Despite their significance, MAEs are extremely challenging to solve.
Xinghua Pan, Zexin Feng, Kang Yang
wiley   +1 more source

Pharmacological and Mechanistic Interventions for Cognitive Impairment Associated With Schizophrenia: A Review of Registered Clinical Trials

Acta Psychiatrica Scandinavica, EarlyView.
ABSTRACT Background Schizophrenia is characterized by positive, negative, and cognitive symptoms. Current pharmacological treatments often fail to address cognitive deficits. In this review of clinical trials, we aim to identify studies that explore neurobiological (non‐psychological) strategies to address Cognitive Impairment Associated with ...
Bahareh Peyrovian, Lena Palaniyappan, Theodore T. Kolivakis, Howard C. Margolese   +3 more
wiley   +1 more source