Results 51 to 60 of about 2,057 (240)

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

Inverse problems for PDEs: Models, computations and applications [PDF]

SCIENTIA SINICA Mathematica, 2018
Inverse problems for partial differential equations (PDEs) are of great importance in the areas of applied mathematics, whichcover different mathematical branches including PDEs, functional analysis, nonlinear analysis,optimizations, regularization and numerical analysis.
Cheng Jin, Liu Jijun, Zhang Bo
openaire   +1 more source

Learning to Solve PDE-constrained Inverse Problems with Graph Networks

CoRR, 2022
Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering, however, we are not only interested in a forward simulation but also in solving inverse problems with constraints defined
Qingqing Zhao, David B. Lindell, Gordon Wetzstein   +2 more
openaire   +3 more sources

Topology and Material Optimization in Ultra‐Soft Magneto‐Active Structures: Making Advantage of Residual Anisotropies

Advanced Materials, EarlyView.
Residual magnetization induces pronounced mechanical anisotropy in ultra‐soft magnetorheological elastomers, shaping deformation and actuation even without external magnetic fields. This study introduces a computational‐experimental framework integrating magneto‐mechanical coupling into topology optimization for designing soft magnetic actuators with ...
Carlos Perez‐Garcia, Rogelio Ortigosa, Jesús Martínez‐Frutos, Daniel Garcia‐Gonzalez   +3 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

Families of Orbits Produced by Three-Dimensional Central and Polynomial Potentials: An Application to the 3D Harmonic Oscillator

Axioms, 2023
We study three-dimensional potentials of the form V=U(xp+yp+zp), where U is an arbitrary function of C2-class, and p∈Z, which produces a preassigned two-parametric family of spatial regular orbits given in the solved form f(x,y,z) = c1, g(x,y,z) = c2 (c1,
Thomas Kotoulas
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
Minas Benyamin, Jeff Calder, Ganesh Sundaramoorthi, Anthony J. Yezzi   +3 more
openaire   +4 more sources

Pattern‐Aware Intelligence Enables Nondestructive, Rapid Quantification of High‐Aspect‐Ratio Silicon Etching

Advanced Science, EarlyView.
Pattern‐dependent etching is converted into a physical prior for intelligent reconstruction of high‐aspect‐ratio silicon structures. Combining YOLO‐Pose feature extraction with a topography network, the framework retrieves depth, sidewall angle, and scallop texture from minimal destructive observations, enabling accurate cross‐scale metrology and near ...
Shuyan He, Lang Chen, Bo Wen, Yufeng Jin, Wei Wang   +4 more
wiley   +1 more source

Graph Neural Regularizers for PDE Inverse Problems

CoRR
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme that alternates between FEM-based inversion and learned graph neural regularization.
William Lauga, James Rowbottom, Alexander Denker, Zeljko Kereta, Moshe Eliasof, Carola-Bibiane Schönlieb   +5 more
openaire   +2 more sources

Dictionary‐based weak‐form training for noise‐robust series hybrid models with multiplicative unknowns

AIChE Journal, EarlyView.
ABSTRACT Hybrid modeling combines first‐principles equations with a data‐driven subcomponent. Training for the data‐driven part is sensitive to measurement noise when training targets are constructed using pointwise time derivatives. Beyond differentiation errors, hybrid models involve solving an inverse problem to estimate the data‐driven term, which ...
Hangjun Cho, Akshay Kudva, Parth Shah, Dongheon Lee, Joseph Sang‐Il Kwon   +4 more
wiley   +1 more source