Learning Paths

Resources from beginner to industrial deployment

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Adaptive Physics-informed Neural Networks: A Survey

Survey / Reading Material
A focused survey of PINN improvements via transfer learning and meta-learning, addressing PINN's notorious convergence difficulty and the need to re-optimize on every PDE parameter change - the engineering reference for productionizing PINNs.
arXiv preprint (copyright held by authors) PINNTransfer LearningMeta Learning

Embedding Physics Priors in Robot Learning: A Survey

Multibody
A survey on embedding physics priors in robot learning, covering how physical constraints like contact mechanics, rigid-flexible coupling, and multibody dynamics improve sample efficiency and reliability of learned policies.
See LICENSE file robot learningphysics priorsmultibody dynamics

Machine Learning with Physics Knowledge for Prediction: A Survey

Survey / Reading Material
A systematic survey of physics-knowledge + ML methods for PDE prediction, splitting the field into architectural-level (loss, structured prediction, augmentation) and data-level (multi-task, meta, contextual) approaches, with industrial perspective and open-source ecosystem review.
arXiv preprint (copyright held by authors) Physics-informed MLPDEMulti-task Learning

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

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

DeepONet Getting Started

Neural Operator / Beginner Tutorial
Systematic DeepONet theory and DeepXDE implementation - for PINN developers handling multiphysics-parameter scenarios.
MIT DeepONetNeural OperatorDeepXDE

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

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.
MIT PINNTutorialBeginner