Physics Simulation & ML Integration Roadmap
Learning Roadmap / Systematic Overview
Systematic path from classical PDE numerics to data-driven physics AI - FEM, FVM, surrogates, PINN and their evolution.
CC BY 4.0 RoadmapPDENumerical Method
Learning Paths
Resources from beginner to industrial deployment
FNO (Fourier Neural Operator) Tutorial
Fourier Neural Operator / Beginner Tutorial
Systematic FNO from theory to code - for engineers and researchers wanting neural operators as PDE surrogates.
MIT FNONeural OperatorSurrogate
DeepONet Getting Started
Neural Operator / Beginner Tutorial
Systematic DeepONet theory and DeepXDE implementation - for PINN developers handling multiphysics-parameter scenarios.
MIT DeepONetNeural OperatorDeepXDE
Finite Element from Scratch in Python
Finite Element / From Scratch
Build a 2D linear-elastic FEM solver from NumPy/SciPy - no FEniCS/Abaqus - to deeply understand every matrix derivation and assembly step.
GPL-3.0 FEMFinite ElementPython
Operator Learning: A Survey
Survey / Reading Material
A systematic survey of operator learning covering the theory, architectures and error analysis of DeepONet, FNO and their variants - the reference entry point to learning infinite-dimensional maps.
arXiv preprint (copyright held by authors) Operator LearningSurveyDeepONet
Physics-Based Deep Learning (Online Book)
Textbook / Systematic Course
A free online textbook from TU Munich covering physics + deep learning: differentiable physics, PINNs, neural operators and turbulence modeling, with runnable code.
CC BY-NC-SA 4.0 TextbookDifferentiable PhysicsPINN
PINN from Scratch
Beginner Tutorial
A classic Chinese structured tutorial implementing PINN from minimal dependencies, paired with Raissi's original repo - the best start for Chinese-speaking learners.
Open source (see repository) PINNTutorialBeginner