Results 121 to 130 of about 2,057 (240)

Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics [PDF]

, 2012
The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized.
Manzoni, Andrea
core   +1 more source

Fault Geometry Invariance and Differentiable Ensemble Solutions for Simultaneous Fault and Slip Inversion in Heterogeneous Crustal Structures

Journal of Geophysical Research: Machine Learning and Computation, Volume 3, Issue 4, August 2026.
Abstract Fault slip inversions based on geodetic observations deepen our understanding of earthquake source processes. Previous attempts to simultaneously estimate the fault geometry and slip distribution have typically assumed a homogeneous half‐space owing to the prohibitively high computational costs of conventional numerical approaches.
Tomohisa Okazaki, Ryoichiro Agata, Masayuki Kano, Takeo Ito, Kazuro Hirahara, Naonori Ueda   +5 more
wiley   +1 more source

A rational deferred correction approach to parabolic optimal control problems [PDF]

, 2016
The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved.
Stefan Güttel, John W Pearson, Pearson, John W., Güttel, Stefan, Güttel, Stefan; id_orcid, Pearson, John W   +5 more
core   +1 more source

Latent Twins

Machine Learning: Science and Technology
Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems.
Matthias Chung, Deepanshu Verma, Max Collins, Amit N Subrahmanya, Varuni Katti Sastry, Vishwas Rao   +5 more
doaj   +1 more source

LocRes–PINN: A Physics–Informed Neural Network with Local Awareness and Residual Learning

Computation
Physics–Informed Neural Networks (PINNs) have demonstrated efficacy in solving both forward and inverse problems for nonlinear partial differential equations (PDEs).
Tangying Lv, Wenming Yin, Hengkai Yao, Qingliang Liu, Yitong Sun, Kuan Zhao, Shanliang Zhu   +6 more
doaj   +1 more source

Self‐improving property for certain degenerate functionals with generalized Orlicz growth

Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.
Abstract We investigate a self‐improving property of variational integrals in a weighted framework under generalized Orlicz growth conditions. Assuming that the weight belongs to an appropriate Muckenhoupt class and the growth function satisfies standard structural conditions, we prove that the gradient of any local quasi‐minimizer has local higher ...
Vertti Hietanen, Mikyoung Lee
wiley   +1 more source

Numerical approximation of inverse problems for PDEs via neural network augmentation [PDF]

, 2020
LAUREA MAGISTRALEN/AIn this thesis, we consider the numerical approximation of inverse problems for linear and nonlinear elliptic PDEs by augmenting them with a neural network to predict unknown or uncertain model coefficients.
MONTAG, DILLON VICTOR PAUL
core  

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

Mathematics
This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet,
Prashant K. Jha
doaj   +1 more source

Deep Energy Method for Large Deformation Analysis of Isotropic and Inhomogeneous Hyperelastic Ellipsoidal Pressurized Structures

International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.
ABSTRACT The accurate prediction of displacement and stress fields in pressure vessels is essential for the safe and reliable design of these structures, particularly when dealing with nonlinear behavior such as that of hyperelastic functionally graded materials (FGMs).
Nasser Firouzi, Shaofan Li, Timon Rabczuk   +2 more
wiley   +1 more source

One-Dimensional Elastic and Viscoelastic Full-Waveform Inversion in Heterogeneous Media Using Physics-Informed Neural Networks

IEEE Access
In this study, we discuss a mathematical framework to handle the inverse problem for the applications of partial differential equations (PDEs). In particular, we focus on wave equations and attempt to identify the wave parameters such as wave velocity ...
Alireza Pakravan
doaj   +1 more source