How a Machine Learns to Derive the Laws of Nature ✎ express

Original: "Data-driven Progressive Discovery of Physical Laws"
· Mingkun Xia, Weiwei Zhang
arXiv:2603.13727 · 2026-03-14 · arXiv non-exclusive · independent analysis · 1 min
A new approach lets computers discover physical laws step by step, much like scientists of the past.

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When a typical computer searches for a law of nature from data, it tries to guess a complete formula in one go. It's like a cook who, without knowing the recipe, dumps all the ingredients into a pot at once and hopes for soup. Most often, the result is an inedible mess: the formula is long but meaningless, and it fails on new data.

Scientists proposed a different path: let the machine follow in the footsteps of great physicists. First, it finds a simple pattern — for example, that a planet moves faster the closer it is to the Sun. Then it adds the next link, then another. In this way, several clear pieces come together into a chain that ultimately yields an accurate law. They named this method "symbolic regression chains."

The method retraced the historical path: from Kepler's laws of planetary motion, it arrived at Newton's law of universal gravitation — exactly the step-by-step way this discovery actually happened.

Tests on three problems (turbulent boiling of a liquid, viscous flow through a pipe, and metal evaporation under a laser) showed that the new method outperforms older ones. And on data about air resistance for various aircraft, it found a pattern that had been overlooked before. This means the machine can not only rediscover known laws but also suggest new useful formulas to engineers.

This approach is like assembling a construction set: each piece is simple and understandable, and together they form a complex mechanism. And that is far more reliable than trying to guess the entire mechanism at once.

Symbolic regression is when a computer searches not just for a number, but for a formula that can be written on paper and understood in terms of how it works.

Scientists
Johannes KeplerDavid CharbonneauIsaac NewtonWilliam BoruckiGalileo GalileiPaul Dirac
Concepts
symbolic regression linear regression computational method coarse graining neural network scientific discovery cosmological simulation Dollo's law correlation coefficient pattern recognition Dynamical Systems drug discovery power law survey tensor clustering physics informed neural network drug design first principles calculations one dimensional chain lagrangian