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Explore MSNM finite element books and the Machine & Deep Learning teaching-module series—from first-principles mathematics to practical MATLAB, Python and PyTorch implementations.
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Search all 11 resources below by title, topic, DOI, year or ISBN, including FEM, NDM, NLFEM, RPIM, EFG, MATLAB, PINN, author names, publication year and ISBN numbers.
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Finite element methods, from structures to coupled physical problems.
The two volumes develop finite-element formulations through mathematical principles and computational implementation. The linked MSNM GitHub repository provides the available teachers’ copies.
Finite Element Formulations for Statics and Dynamics of Plane Structures (with Matlab)
One-dimensional structural elements, statics, structural dynamics, eigenvalue problems and MATLAB-based finite-element formulation.
Open book on GitHub ↗All FEM books ↗
2D Finite Element Formulations for Heat, Solids and Fluids (with Matlab)
Two-dimensional FEM in heat transfer, solid mechanics and fluid-flow applications, linking governing equations with MATLAB programming.
Open book on GitHub ↗All FEM books ↗Modules for Machine and Deep Learning.
A connected teaching sequence combining derivations, coding and engineering applications. These module descriptions are drawn from the original PDF materials supplied by the authors.
Fundamentals and Single-hidden Layer Network
Introduction to neural-network mathematics, single hidden layer training and implementation in MATLAB.
MATLAB · neural networks · forward pass · backpropagation
Visit AI modules repository ↗
Multi-Layer Neural Network
Extends the introductory network to multilayer architectures, data preprocessing and training in PyTorch.
PyTorch · normalization · datasets · Google Colab
Visit AI modules repository ↗
Convolutional Neural Network and an FEM Surrogate Model
Builds convolution, pooling and feature extraction toward a neural-network surrogate of a hypothetical FEM matrix system.
CNN · FEM · convolution · PyTorch
Visit AI modules repository ↗
Recurrent Neural Network and Flood-Routing Surrogate
Explains recurrent states and backpropagation through time, followed by a reservoir flood-routing surrogate.
RNN · flood routing · time series · PyTorch
Visit AI modules repository ↗
Physics-Informed Neural Network from Scratch — Part A
A first-principles unscaled single-hidden-layer PINN for the 1D wave equation, with manual derivatives and Python implementation.
PINN · 1D wave equation · Python · physics loss
Visit AI modules repository ↗Journal articles and research contributions.
A curated selection of numerical-methods papers associated with MSNM’s research community. These are publications by the listed researchers, not a claim that MSNM is the journal publisher. Links lead to original journal or document sources; access conditions depend on the publisher.
NURBS-Divergence-Meshless (NDM) method
Computers & Mathematics with Applications · Vol. 196 · pp. 151–171
Introduces a divergence-theorem meshless discretisation in NURBS parameter space, with line integration and MLS/RBF field approximation.
DOI: 10.1016/j.camwa.2025.07.011
View article at source ↗Coupling of NURBS and Meshfree RPIM for plane stress of web with openings
Engineering Analysis with Boundary Elements · Vol. 138 · pp. 266–279
Combines exact NURBS geometry with meshfree radial point interpolation for plane-stress analysis of cellular beam webs.
DOI: 10.1016/j.enganabound.2022.02.018
View article at source ↗NLFEM with Higher Order Interpolation Function for Efficient Analysis of Irregular Domain
Malaysian Journal of Civil Engineering · Vol. 34(3) · pp. 17–24
Develops a NURBS–Lagrange FEM coupling with higher-order interpolation and demonstrates it using curved-boundary heat transfer.
View article at source ↗Element Free Galerkin (EFG) Formulation in Solving Kinematic Wave Equation for Hydrological Modelling
Journal of Advanced Research in Applied Sciences and Engineering Technology · Vol. 37(2) · pp. 1–13
Applies Element Free Galerkin approximation to kinematic-wave modelling and compares numerical results against established methods and observations.
View article at source ↗Browse the official repositories.
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