# An algorithm for discovering Lagrangians automatically from data

@article{Hills2015AnAF, title={An algorithm for discovering Lagrangians automatically from data}, author={Daniel J. A. Hills and Adrian M. Gr{\"u}tter and Jonathan J. Hudson}, journal={PeerJ Comput. Sci.}, year={2015}, volume={1}, pages={e31} }

An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that automates the model building process in a scientifically principled way. The algorithm can take observed trajectories from a wide variety of mechanical systems and, without any other prior knowledge or tuning of parameters, predict the future evolution of the system…

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## References

SHOWING 1-10 OF 45 REFERENCES

### Distilling Free-Form Natural Laws from Experimental Data

- PhysicsScience
- 2009

This work proposes a principle for the identification of nontriviality, and demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula, and discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation.

### Comment on the article "Distilling free-form natural laws from experimental data"

- Physics
- 2012

This work demystifies how they are able to find Hamiltonians and special classes of Lagrangians from data, and implicitly incorporates Hamilton's equations of motions and Newton's second law.

### Rediscovering Physics with BACON.3

- PhysicsIJCAI
- 1979

BACON.3 has shown its generality by rediscovering versions of the Ideal gas law, Kepler's third law, Coulomb's law, Ohm'slaw, and Galileo's laws for the pendulum and constant acceleration.

### Nonlinear black-box modeling in system identification: a unified overview

- Computer ScienceAutom.
- 1995

### The use of a genetic algorithm to optimize the functional form of a multi-dimensional polynomial fit to experimental data

- Computer Science2005 IEEE Congress on Evolutionary Computation
- 2005

The genetic algorithm method is compared with a particular genetic programming approach and it is shown that equally good results can be achieved using this simpler technique.

### Genetic Programming Theory and Practice V (Genetic and Evolutionary Computation)

- Computer Science
- 2007

The text explores the synergy between theory and practice, producing a comprehensive view of the state of the art in GP application.

### Evolutionary Computation

- Computer ScienceEncyclopedia of Machine Learning
- 2010

This chapter addresses the integration of knowledge discovery in databases (KDD) and evolutionary algorithms (EAs) and suggests that this principle should be followed in other EA applications.