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Discovering Equations from Data: A Practical Guide to Symbolic Regression and Model Discovery
A hands-on guide to recovering governing equations from data with symbolic regression, SINDy, and PDE discovery. Every method is built from scratch in Python, with the discipline to tell a genuine law from a plausible fit.
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About the Book
A predictor tells you what happens next. An equation tells you why.
Most books about learning from data teach prediction. This one teaches something older and deeper: how to discover the governing equation behind your data. That equation is a compact, interpretable law that a scientist can reason with, build on, teach, and trust.
Discovering Equations from Data is a hands-on guide to symbolic regression and model discovery. Every method is built from first principles in plain Python, so nothing stays a black box. You hand-code genetic programming and sparse regression before you touch any library, then move on to PySR, SINDy, and PDE-FIND. Each chapter ends with a case study whose answer can be checked.
What you will learn
- Why discover equations: prediction vs understanding, from Kepler to Eureqa to SINDy
- The landscape: search-based symbolic regression vs selection-based sparse regression, and when each one wins
- Honest setup: the data you need, the derivative problem, and train/validate/extrapolate splits
- Feature libraries and why “more terms” is a trap
- Symbolic regression from scratch: genetic programming, then PySR
- SINDy: discovering dynamics by sparse regression
- Taming noise: smoothing, numerical derivatives, and the weak formulation
- Discovering PDEs from spatiotemporal data
- Putting physics in: constraints, units, dimensional analysis, and conservation laws
- Model selection: sparsity, the Pareto front, and choosing the right model
- Validation and verification: how to trust a discovered equation
- Case studies and deployment: from discovery to a reusable model
Who this book is for
Researchers, engineers, and graduate students who write intermediate Python and remember some calculus and linear algebra, but have never built a discovery pipeline. No background in these specific methods is assumed.
This is the third book in a trilogy with Physics-Informed Machine Learning: A Practical Guide and AI Agents for Scientists and Engineers: A Practical Guide. Each stands alone. Together they cover three ways of uniting data and physics: embedding what is known, orchestrating what is available, and discovering what is unknown.
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About the Author
Kompri Kompri
Kompri is an academic, author, investor, and educator based in Jambi, Indonesia. He holds a doctorate in Education Management and a bachelor’s degree in Physics, and has written and published dozens of books along with numerous other scholarly works. An avid reader, he is one of today’s most productive researchers. Alongside his academic career, he publishes both theoretical and practical books for readers around the world. His work rests on one conviction: knowledge is most valuable when it is clear, usable, and shared, so that anyone, in any country, can put it to work.
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