Vizuara Books
Scientific Machine Learning (SciML)
Physics-informed neural networks, Neural ODEs, and UDEs in Julia.
Learn Scientific Machine Learning from the math up: the three pillars — PINNs, Neural ODEs, and Universal Differential Equations — built by hand in Julia. Then take a real project all the way to a publishable first-author research paper.
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00Foundations of Scientific ML5 capsules
Foundations of Scientific ML — 5 chapters.
01Why Scientific Machine Learning?intuitionfree14 min02Transitioning into ML from a Science Backgroundconcept🔒12 min03The SciML Landscape: A Technical Overviewconcept🔒14 min04ODEs and PDEs in One Pagemath🔒14 min05The Problems SciML Can Solveintuition🔒16 min01The Julia Language for SciML4 capsules
The Julia Language for SciML — 4 chapters.
06Why Julia for Scientific MLconcept🔒13 min07Installing Julia and Meeting the REPLcode🔒13 min08Project Environments and the Package Managercode🔒12 min09Julia Fundamentals for Numericscode🔒15 min02Differential Equations in Julia6 capsules
Differential Equations in Julia — 6 chapters.
10Solving Your First ODE in Juliacode🔒15 min11Systems of ODEs and Choosing a Solvercode🔒13 min12PDE Mathematics and Boundary Conditionsmath🔒15 min13The Method of Linesmath🔒15 min14Solving the Heat and Brusselator PDEscode🔒15 min15Project: Solving the Schrodinger Equationproject🔒15 min03Neural Network Foundations4 capsules
Neural Network Foundations — 4 chapters.
16Feedforward Neural Networksconcept🔒13 min17Gradient Descent: A Mountain Perspectiveintuition🔒15 min18Backpropagation from Scratchmath🔒13 min19Automatic Differentiation: The Engine of SciMLdeep-dive🔒15 min04Pillar 1 — Physics-Informed Neural Networks4 capsules
Pillar 1 — Physics-Informed Neural Networks — 4 chapters.
20PINNs: Encoding Physics in the Lossconcept🔒12 min21The Math of the PINN Residualmath🔒15 min22Building Your First PINN in Juliacode🔒15 min23Project: The 1D Wave Equation with a PINNproject🔒16 min05Pillar 2 — Neural ODEs4 capsules
Pillar 2 — Neural ODEs — 4 chapters.
24Neural ODEs: Networks as Continuous Dynamicsconcept🔒14 min25Training Neural ODEs: The Adjoint Methodmath🔒13 min26Building Your First Neural ODE in Juliacode🔒15 min27Project: Neural ODEs and Their Applicationsproject🔒13 min06Pillar 3 — Universal Differential Equations4 capsules
Pillar 3 — Universal Differential Equations — 4 chapters.
28UDEs: Known Physics Plus a Learned Termconcept🔒12 min29From Learned Term to Discovered Equationdeep-dive🔒12 min30Building Your First UDE in Juliacode🔒15 min31Project: Recovering Predator-Prey Dynamicsproject🔒14 min07Hands-On Research Projects4 capsules
Hands-On Research Projects — 4 chapters.
32Framing a Scientific Problem as a SciML Problemintuition🔒14 min33Research Project: Covid-19 Prediction with a Quarantine-SIR UDEproject🔒12 min34Research Project: Black Hole Dynamics with SciMLproject🔒14 min35Reading and Reusing the Project Codecode🔒13 min08From Results to Published Research4 capsules
From Results to Published Research — 4 chapters.
36From a Project to a Research Paperconcept🔒13 min37Crafting Figures and the Scientific Narrativeintuition🔒13 min38Choosing a SciML Research Topicconcept🔒13 min39The SciML Capstone: Putting It All Togetherproject🔒14 minRatings & reviews
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