A four-stage learning path from numerical foundations to neural operators — 15 tutorials and surveys sequenced for a smooth ride from zero background to industrial practice.
Updated Oct 12, 2026 15 resources
Introduction
Why this collection
Physics AI resources are scattered across papers, course notes and GitHub repos, and newcomers rarely know where to start. This collection arranges 15 curated resources into four stages, so you always know what to read next.
Stage 1 · Foundations — build intuition for numerical simulation before touching neural networks.
Stage 2 · Core methods — get hands-on with PINNs and understand why they converge (or don't).
Stage 3 · Neural operators — move from solving one PDE to learning a family of solution operators.
Stage 4 · Domain deep-dives — see how physics priors land in power systems, robotics and continuous-time models.
Each item carries an editorial note explaining *why* it sits at that position and *what to focus on*.
A free online textbook from TU Munich covering physics + deep learning: differentiable physics, PINNs, neural operators and turbulence modeling, with runnable code.
A classic Chinese structured tutorial implementing PINN from minimal dependencies, paired with Raissi's original repo - the best start for Chinese-speaking learners.
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
💬Editor note: 跑通代码后回来补理论：把物理知识注入 ML 的方法按架构层与数据层系统分类，并提供工业落地视角与开源生态清单
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
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
A practical focused review of neural operators covering DeepONet, FNO and PCANet with hands-on training strategies; benchmarked on Poisson and linear elasticity, and demonstrated as surrogates for Bayesian inversion - an engineering-ready primer.
arXiv preprint (copyright held by authors)Neural OperatorDeepONetFNO
A survey of data-driven and physics-informed neural operators, organizing the architecture landscape (DeepONet / FNO / GNO / PINO / Transformer-based / diffusion) along three axes: scalability, generalizability, and data sensitivity.
arXiv preprint (copyright held by authors)Neural OperatorScientific MLDeepONet
A systematic review of physics-informed machine learning applications in electricity system design, monitoring, and control, focusing on hybrid architectures and physics constraint embedding methods.
See LICENSE filePhysics-Informed LearningElectricity SystemsElectromagnetic Simulation
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 filerobot learningphysics priorsmultibody dynamics
A survey developing a unified, concept-driven view of major continuous-time machine learning branches, characterizing their mathematical relationships and design trade-offs.
See LICENSE filecontinuous-time modelsneural ODEstime series
PhD course lecture notes from University of Bozen/Bolzano covering Physics Informed Neural Networks and Neural Operators with PyTorch implementation tutorials.
