Learning Dynamical Systems Using Standard Symbolic Regression
Symbolic regression has many successful applications in learning free-form regular equations from data. Trying to apply the same approach to differential equations is the logical next step: so far, however, results have not matched the quality obtained with regular equations, mainly due to additional constraints and dependencies between variables that make the problem extremely hard to tackle. In this paper we propose a new approach to dynamic systems learning. Symbolic regression is used to obtain a set of first-order Eulerian approximations of differential equations, and mathematical properties of the approximation are then exploited to reconstruct the original differential equations. Advantages of this technique include the de-coupling of systems of differential equations, that can now be learned independently; the possibility of exploiting established techniques for standard symbolic regression, after trivial operations on the original dataset; and the substantial reduction of computational effort, when compared to existing ad-hoc solutions for the same purpose. Experimental results show the efficacy of the proposed approach on an instance of the Lotka-Volterra model.
KeywordsDifferential Equations Dynamic Systems Evolutionary Algorithms Genetic Programming Symbolic Regression
Unable to display preview. Download preview PDF.
- 2.Pickardt, C., Branke, J., Hildebrandt, T., Heger, J., Scholz-Reiter, B.: Generating dispatching rules for semiconductor manufacturing to minimize weighted tardiness. In: Proceedings of the 2010 Winter Simulation Conference (WSC), pp. 2504–2515. IEEE (2010)Google Scholar
- 3.Soule, T., Heckendorn, R.B.: A practical platform for on-line genetic programming for robotics. In: Genetic Programming Theory and Practice X, pp. 15–29. Springer (2013)Google Scholar
- 4.Koza, J.R.: Genetic Programming: On the programming of computers by means of natural selection, vol. 1. MIT Press (1992)Google Scholar
- 5.Babovic, V., Keijzer, M., Aguilera, D.R., Harrington, J.: An evolutionary approach to knowledge induction: Genetic programming in hydraulic engineering. In: Proceedings of the World Water and Environmental Resources Congress, vol. 111, p. 64 (2001)Google Scholar
- 9.Keijzer, M.: Inducing differential/flow equations. Invited talk to the GECCO Conference (July 2013)Google Scholar
- 10.Zill, D.G.: A First Course in Differential Equations: With Modeling Applications. Cengage Learning (2008)Google Scholar
- 11.Euler, L.: Institutionum calculi integralis. Imp. Acad. imp. Saènt, vol. 1 (1768)Google Scholar
- 12.Vanneschi, L., Castelli, M., Silva, S.: Measuring bloat, overfitting and functional complexity in genetic programming. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, pp. 877–884. ACM (2010)Google Scholar
- 15.Goodwin, R.M.: A growth cycle. In: Socialism, Capitalism and Economic Growth, pp. 54–58 (1967)Google Scholar