Reading material
Books, lectures, guides and blog posts from outside the site, by the problem you have: what to read, and why.
Select a cover to see what it is and what to read in it. Research papers are on Papers.
I have a few hundred runs and need a few numbers: lift, drag, peak stress.
BookStart here
Engineering Design via Surrogate Modelling
Forrester, Sóbester and Keane (Wiley, 2008)
A book on sampling plans, kriging, validation, multi-fidelity and infill, with MATLAB code.
Our noteWritten by engineers for engineers: sampling plans, kriging, validation, multi-fidelity and infill, with MATLAB code. For a few scalar outputs from a few hundred runs, its methods are often enough. Read it before any neural network.
DocsStart here
SMT: Surrogate Modeling Toolbox
SMT developers
The documentation of a Python toolbox: kriging, multi-fidelity kriging and sampling plans, with engineering examples.
Our notePython kriging, multi-fidelity kriging and sampling plans with engineering examples. A short way from a spreadsheet of runs to a surrogate you can check.
Free book
Gaussian Processes for Machine Learning
Rasmussen and Williams (MIT Press, free PDF)
A book on Gaussian processes, free as a PDF. Chapter 2 is on regression, chapter 4 on covariance functions (the kernels) and chapter 5 on fitting the kernel’s hyperparameters; other chapters are on classification.
Our noteA standard reference for kriging as machine learning. Chapters 2 (regression), 4 (covariance functions: the kernels) and 5 (fitting the kernel’s hyperparameters) are what you need; the classification chapters can be skipped.
I need the whole field, on one grid or one mesh.
LecturesStart here
Physics Informed Machine Learning (lecture series)
Steve Brunton (YouTube)
A series of short lectures on YouTube on where machine learning meets physics: what to model, which architecture, how to put physics in.
Our noteShort, clear lectures on where machine learning meets physics: what to model, which architecture, how to put physics in. Find the series in the channel’s playlists; the first few talks give a clear overview.
Book
Data-Driven Science and Engineering (2nd ed.)
Brunton and Kutz (Cambridge, 2022)
A book with chapters on the SVD and POD and a part on reduced-order models. Lecture videos for each chapter and code downloads are on the book’s site.
Our noteThe SVD and POD chapters and the reduced-order-model part are the classical way to predict fields: compress the snapshots, predict the weights. Lecture videos for each chapter and code downloads on the book’s site.
My geometry changes from design to design, on meshes of millions of cells.
Guide
From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing
arXiv 2503.05598
An introduction to neural operators in scientific computing, with code, on arXiv.
Our noteA gentler entry into neural operators than the theory papers, with code. Read it before the FNO and GINO papers on Papers.
Paper
Learning Mesh-Based Simulation with Graph Networks (MeshGraphNets)
Pfaff et al., ICLR 2021
A paper on learning mesh-based simulation with graph networks. Its appendix lists the datasets and hyperparameters.
Our noteA widely used starting point for mesh-based structural and crash surrogates. Read the method, then the appendix: it lists the datasets and hyperparameters, which is where the practical lessons are.
DocsVendor material
DoMINO on DrivAerML (PhysicsNeMo example)
NVIDIA
NVIDIA’s documentation of an end-to-end workflow for its DoMINO model in PhysicsNeMo, from data preparation to training on a public car dataset.
Our noteAn end-to-end workflow, from data preparation to training on a public car dataset. It is NVIDIA’s own material on its own model and framework: read the recipe, not the claims.
I come from machine learning and need the simulation side.
GuideStart here
CFD Python: 12 steps to Navier–Stokes
Lorena Barba (Jupyter notebooks)
Short Jupyter notebooks that build a flow solver step by step, from finite differences on a 1D equation to the Navier–Stokes equations.
Our noteShort notebooks that build a flow solver step by step, from finite differences on a 1D equation to the Navier–Stokes equations. Writing one small solver yourself shows where the training data of a surrogate comes from, and what can go wrong in it.
Paper
Machine Learning for Fluid Mechanics
Brunton, Noack and Koumoutsakos, Annual Review of Fluid Mechanics 2020
A review written from the fluid-mechanics side: what flow data looks like, which problems the field works on, and where machine learning has been tried on them.
Our noteA review written from the fluid-mechanics side: what flow data looks like, which problems the field cares about, and where machine learning has been tried on them.
I want the theory and the wider picture.
Free book
Physics-based Deep Learning
Thuerey et al. (free online book)
A free online book on supervised surrogates, physical losses, differentiable solvers and diffusion models for physics, each with a runnable notebook.
Our noteSupervised surrogates, physical losses, differentiable solvers and diffusion models for physics, each with a runnable notebook. The supervised chapters are the ones an engineer needs first.
Paper
Neural Operator: Learning Maps Between Function Spaces
Kovachki et al., JMLR 2023
A long, mathematical paper on neural operators, with an introduction, a section on four architectures, and proofs.
Our noteA standard reference for neural operators. Long and mathematical: read the introduction and the section on the four architectures, and come back to the proofs only if you need them.
Free book
Parallel Computing and Scientific Machine Learning (SciMLBook)
Rackauckas et al., MIT 18.337
A free online book from MIT’s 18.337 on automatic differentiation, adjoints and differential equations with learned parts. In Julia.
Our noteFor engineers who want the numerical-methods side: automatic differentiation, adjoints and differential equations with learned parts. Julia rather than Python.
Free book
Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
Bronstein, Bruna, Cohen and Veličković (draft chapters online; MIT Press, announced for 2026)
A textbook, in the authors’ words “intended to help students and practitioners enter the field of geometric deep learning”. Nine draft chapters are free to read online: foundations of supervised, equivariant and geometric deep learning, then graphs, grids, group convolution on homogeneous spaces and geometric graphs.
I need to judge a paper or a vendor’s claim.
- Start hereOn this site
- Open
PaperStart here
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related PDEs
McGreivy and Hakim, Nature Machine Intelligence 2024
A paper on weak baselines and reporting biases in papers that claim to beat numerical solvers on fluid-related PDEs.
Our noteShows that many papers claiming to beat numerical solvers on fluid PDEs compared against weak baselines, and that reporting biases inflate the results. Read it before believing any “1,000× faster”, including the ones quoted on this site.
List
awesome-scientific-machine-learning
Martinuzzi et al. (GitHub)
A long list of scientific machine learning resources, on GitHub.
Our noteA long list, when you want more. No judgement in it; this shelf is the opposite.
Each entry says what it is, as its source describes it. The note, where there is one, is our own, on what to read or skip. Nothing is sponsored. Links checked 4 Nov 2026.
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