Inferring Systems of Ordinary Differential Equations via Grammar-Based Immune Programming

Bernardino, Heder S.; Barbosa, Hélio J. C.

doi:10.1007/978-3-642-22371-6_19

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…To compare our proposed method against symbolic regression based on genetic algorithms, we implemented such a baseline using the following genetic algorithm to search the space of the grammar 2. A function corresponding to an admissible word within the grammar 2 is represented by a bitstring similar to (Bernardino & Barbosa, 2011). The genetic algorithm explores this space of finite-length bitstrings to find a symbolic equation of the ODE which generated the available data.…”

Section: Methodsmentioning

confidence: 99%

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Inferring the Structure of Ordinary Differential Equations

Weilbach,

Gerwinn,

Weilbach

et al. 2021

Preprint

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Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and are less amenable for further expert investigation. Alternatively, the dynamics can be analysed via symbolic regression. In this paper, we extend the approach by (Udrescu et al., 2020) called AI Feynman to the dynamic setting to perform symbolic regression on ODE systems based on observations from the resulting trajectories. We compare this extension to state-of-the-art approaches for symbolic regression empirically on several dynamical systems for which the ground truth equations of increasing complexity are available. Although the proposed approach performs best on this benchmark, we observed difficulties of all the compared symbolic regression approaches on more complex systems, such as Cart-Pole.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inferring the Structure of Ordinary Differential Equations

Weilbach,

Gerwinn,

Weilbach

et al. 2021

Preprint

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“…Iba [7] proposes an improvement over the previous approach, where coefficients are optimized through a least mean square technique, and a Runge-Kutta method of 4th order is used to build a solution. Bernardino and Barbos [8] use GrammarBased Immune Programming to tackle the problem. It is important to notice that, while quite effective, all these concepts rely upon the use of ad-hoc individual construction, and significant computational costs to first solve the candidate equations and then compare them to experimental data.…”

Section: Introductionmentioning

confidence: 99%

Learning Dynamical Systems Using Standard Symbolic Regression

Gaucel¹,

Keijzer²,

Lutton³

et al. 2014

Lecture Notes in Computer Science

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Abstract. 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.

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