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Computational Partial Differential Equations: From Finite Element to Deep Learning
Computational Partial Differential From Finite Elements to Deep LearningBy Medhat Ullah
This book offers a rigorous yet modern treatment of computational partial differential equations (PDEs), connecting classical numerical formulations with cutting-edge deep learning architectures for scientific computation.
Bridging the gap between finite element theory, numerical discretization, and data-driven solvers, this text provides a complete computational perspective — from variational formulations to physics-informed neural networks (PINNs).
Key Topics Mathematical foundations of elliptic, parabolic, and hyperbolic PDEs
Detailed derivations of finite difference, finite volume, and finite element methods
Implementation of solvers using Python, C++, and modern numerical libraries
Analysis of stability, convergence, and error propagation
Integration of machine learning with PDE solvers through PINNs, operator learning, and neural FEM frameworks
Practical applications in fluid mechanics, heat transfer, electromagnetics, and quantum systems
Who This Book Is Students and researchers in computational science, applied mathematics, and engineering
Developers and scientists working on AI-driven simulation and numerical modeling
Anyone aiming to understand how deep learning extends the numerical solution of PDEs
With a balance of mathematical rigor and computational implementation, Computational Partial Differential From Finite Elements to Deep Learning serves as both a reference and a practical guide to modern scientific computation from classical discretization schemes to neural operators that learn the laws of physics themselves.
This book offers a rigorous yet modern treatment of computational partial differential equations (PDEs), connecting classical numerical formulations with cutting-edge deep learning architectures for scientific computation.
Bridging the gap between finite element theory, numerical discretization, and data-driven solvers, this text provides a complete computational perspective — from variational formulations to physics-informed neural networks (PINNs).
Key Topics Mathematical foundations of elliptic, parabolic, and hyperbolic PDEs
Detailed derivations of finite difference, finite volume, and finite element methods
Implementation of solvers using Python, C++, and modern numerical libraries
Analysis of stability, convergence, and error propagation
Integration of machine learning with PDE solvers through PINNs, operator learning, and neural FEM frameworks
Practical applications in fluid mechanics, heat transfer, electromagnetics, and quantum systems
Who This Book Is Students and researchers in computational science, applied mathematics, and engineering
Developers and scientists working on AI-driven simulation and numerical modeling
Anyone aiming to understand how deep learning extends the numerical solution of PDEs
With a balance of mathematical rigor and computational implementation, Computational Partial Differential From Finite Elements to Deep Learning serves as both a reference and a practical guide to modern scientific computation from classical discretization schemes to neural operators that learn the laws of physics themselves.
96 pages, Kindle Edition
Published November 2, 2025
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