Results 81 to 90 of about 2,810 (199)

Accurate and Efficient Data‐Driven Partitioned Scheme for Coupled Heterogeneous Numerical Models

Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.
ABSTRACT Heterogeneous numerical models (HNMs) combine conventional discretization modules such as finite elements with nonconventional data‐driven and reduced‐order modules. HNMs can improve computational efficiency and enable simulations of multi‐physics systems in which one or more constituent components lack first‐principles descriptions and must ...
Edward Huynh, Justin Owen, Paul Kuberry, Pavel Bochev   +3 more
wiley   +1 more source

A Posteriori Estimates For A Coupled Piezoelectric Model With Uncertain Data

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.
ABSTRACT The paper is concerned with a coupled piezo‐electric problem with incompletely known coefficients of the elasticity tensor and two other tensors that define electric properties of the media. Due to this uncertainty, the problem possesses a set (cloud) of equally probable solutions instead of a unique solution.
S. Repin, T. Samrowski
wiley   +1 more source

Journal of Mathematical Analysis and Applications / Optimal control of a singular PDE modeling transient MEMS with control or state constraints

, 2014
A particular feature of certain microelectromechanical systems (MEMS) is the appearance of a so-called "pull-in" instability, corresponding to a singularity in the underlying PDE model. We here consider a transient MEMS model and its optimal control via the dielectric properties of the membrane and/or the applied voltage. In contrast to the static case,
Clason, Christian, Kaltenbacher, Barbara
openaire   +2 more sources

Toward Robust Optimal Control of Chromatographic Separation Processes With Controlled Flow Reversal

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.
ABSTRACT Column liquid chromatography is an important technique applied in the production of biopharmaceuticals, specifically for the separation of biological macromolecules such as proteins. When setting up process conditions, it is crucial that the purity of the product is sufficiently high, even in the presence of perturbations in the process ...
Dominik H. Cebulla, Christian Kirches, Andreas Potschka   +2 more
wiley   +1 more source

Learning variable-order time fractional diffusion equations using Physics-Informed Neural Networks. [PDF]

PLoS One
Ren L, Jin S.
europepmc   +1 more source

Model Predictive Control of Gas Networks Based on Port‐Hamiltonian Formulations

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.
ABSTRACT To efficiently compute optimal compressor actions in gas networks, we investigate port‐Hamiltonian models consisting of linear and a nonlinear model assumptions. The control actions are derived via adjoint‐based gradients that incorporate the constraints of the underlying optimization problem. We then present results from the implementation of
Andres Ortegón‐Villacorte, Jan Rohleff   +1 more
wiley   +1 more source

Data-driven, ML-assisted approaches to problem well-posedness. [PDF]

PNAS Nexus
Bertalan T, Kevrekidis GA, Koronaki ED, Mishra S, Rebrova E, Kevrekidis IG.   +5 more
europepmc   +1 more source

Adaptive Matrix‐Free Simulations of Fluid‐Filled Phase‐Field Fractures With Fixed‐Stress Coupling and Fracture‐Width Computation

International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.
ABSTRACT Fluid‐filled phase‐field fracture simulations require robust, scalable solvers that can handle strongly nonlinear, non‐smooth mechanics and tightly coupled flow on locally refined meshes. In this work, we develop an adaptive finite element framework for quasi‐static, fluid‐filled phase‐field fractures that combines semi‐smooth Newton methods ...
Leon M. Kolditz, Viktor Kosin, Sanghyun Lee, Thomas Wick   +3 more
wiley   +1 more source

A novel shifted Vieta-Lucas spectral collocation approach for multidimensional generalized Benjamin-Bona-Mahony-Burgers equations. [PDF]

Sci Rep
Hafez RM, Ahmed HM, Alburaikan A, Alrajeh MAA, Khalifa HAE.   +4 more
europepmc   +1 more source

Inductive Differential Constraint Method: Symbolic Regression‐Based Partial Differential Equation Regularization for Fatigue Crack Growth Prediction

International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.
ABSTRACT This study introduces the inductive differential constraint method (IDCM), a data‐informed structural regularization framework that enhances neural network predictions under data‐scarce regimes by enforcing invariant differential structures extracted from simulation data.
Rekisei Ozawa, Yoshitaka Wada
wiley   +1 more source