A Scalable Framework for Learning the Geometry-Dependent Solution Operators of Partial Differential Equations

Mathematics, Information Science, Computer Science, Artificial Intelligence,
partial differential equations   geometric mapping   neural operator   artificial intelligence   computational efficiency  

Introduction In recent years, solving partial differential equations (PDEs) using numerical methods has played a significant role in various fields such as engineering and medicine. These methods have shown remarkable effectiveness in applications like topology and design optimization as well as clinical prognostication. However, the high computati...

Migrant Resettlement by Evolutionary Multiobjective Optimization

Mathematics, Engineering, Information Science, Computer Science, Artificial Intelligence,
migrant resettlement   multiobjective optimization   evolutionary algorithms   greedy algorithm   submodular optimization   humanitarianism   employment rate  

A Research Report on a New Framework for Solving Migrant Resettlement Using Multiobjective Evolutionary Optimization Against the backdrop of accelerated globalization and evolving socio-economic conditions, migration has become an undeniable global trend. From the perspective of humanitarian relief or the sustainable development of a globalized eco...

New Results on Finite-Time Stability and Instability Theorems for Stochastic Nonlinear Time-Varying Systems

Mathematics, Engineering, Information Science, Electronic Information, Computer Science,
stochastic systems   nonlinear dynamics   finite-time stability   stability theorems   nonlinear systems   time-varying systems   Lyapunov method  

New Results on Finite-Time Stability and Instability Theorems for Stochastic Nonlinear Time-Varying Systems 1. Research Background and Significance Stability theory is a central topic in systems theory and engineering applications, serving as the fundamental consideration in system analysis and synthesis. In stability theory, the two most commonly ...

Comparative Numerical Analysis of Astigmatism Tolerance in Bifocal, Extended Depth-of-Focus, and Trifocal Intraocular Lenses

Mathematics, Physics, Optics, Medicine, Ophthalmology, Medical Imaging,
bifocal intraocular lenses   astigmatism tolerance   extended depth of focus   trifocal lenses   visual function   full-wave analysis   postoperative prediction  

Numerical Analysis Enhances Postoperative Visual Assessment and Optimization for Multifocal Intraocular Lenses (IOLs) Introduction and Research Background One of the main goals of cataract surgery is to achieve spectacle-free vision for patients. However, this goal is limited by two major challenges: loss of accommodative function and postoperative...

Event-Triggered Fuzzy Adaptive Stabilization of Parabolic PDE–ODE Systems

Mathematics, Engineering, Electrical Engineering, Information Science, Automation, Artificial Intelligence,
Event-Triggered Control   Fuzzy Logic Systems   Parabolic PDE-ODE Systems   Stabilization Control   Adaptive Backstepping  

Scientific Report: On “Event-Triggered Fuzzy Adaptive Stabilization of Parabolic PDE–ODE Systems” Research Background and Significance In modern engineering systems, such as flexible manipulators, heat transfer devices, and reactor controllers, many complex systems must be modeled using partial differential equations (PDEs). Due to their unique rea...