Prediction of dynamical systems by symbolic regression

Quade, Markus; Abel, Markus; Shafi, Kamran; Niven, Robert K.; Noack, Bernd R.

doi:10.1103/physreve.94.012214

Cited by 106 publications

(63 citation statements)

References 35 publications

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“…cascaded tanks, a chem- ical distillation tower, and an industrial wind turbine. GPSR has also been applied to testing the efficient market hypothesis, 52 formulating the synchronization control in oscillator networks, 43 identifying the structure of helicopter engine dynamics, 53 real-time runoff forecasting in France 54 and Singapore, 55 designing circuits, 30 predicting solar power production, 56 finding dynamical equations for metabolic networks 57 in both cases where a starting model was known and from scratch, modelling global temperature changes, 58 and synthesizing second-order coefficient insensitive digital filter structures. 59 The existing uses of GPSR within chemistry are more extensive than that for materials science.…”

Section: Applications Of Symbolic Regressionmentioning

confidence: 99%

Symbolic regression in materials science

2019

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We showcase the potential of symbolic regression as an analytic method for use in materials research. First, we briefly describe the current state-of-the-art method, genetic programming-based symbolic regression (GPSR), and recent advances in symbolic regression techniques. Next, we discuss industrial applications of symbolic regression and its potential applications in materials science. We then present two GPSR use-cases: formulating a transformation kinetics law and showing the learning scheme discovers the well-known Johnson-Mehl-Avrami-Kolmogorov (JMAK) form, and learning the Landau free energy functional form for the displacive tilt transition in perovskite LaNiO3. Finally, we propose that symbolic regression techniques should be considered by materials scientists as an alternative to other machine-learning-based regression models for learning from data.

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Section: Applications Of Symbolic Regressionmentioning

confidence: 99%

Symbolic regression in materials science

2019

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“…Under the adopted experimental conditions (pH > 10.52) the terms $ and -[ ] ] are negligible and the overall kinetic law is given in Eq. 35.…”

Section: First-order Kinetic Lawmentioning

confidence: 99%

Identifying Physico-Chemical Laws from the Robotically Collected Data

Cao¹,

Russo²,

Vassiliadis³

et al. 2019

Preprint

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A mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed to identify physical models from noisy experimental data. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the number of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was coupled with the collection of experimental data in an automated fashion, and was proven to be successful in identifying the correct physical models describing the relationship between the shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of reactions. Future work will focus on addressing the limitations of the formulation presented in this work, by extending it to be able to address larger complex physical models.

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“…One way to address this issue is to design a cost function where both the performance (e.g., controller error in our case) and length of solutions are considered explicitly in determining the quality of a solution. Such a multi-objective cost mechanism allows introducing an explicit selection pressure in the evolutionary process and preferring smaller well-performing solutions over their longer counterparts [22]. Following this line, a multi-objective cost evaluation method is adopted in our implementation of GP in this work.…”

Section: Multi-objective Cost Evaluationmentioning

confidence: 99%

“…Breeding: Mutation and crossover operations on expression trees. Source: Adapted from[22]; used with permission.…”

mentioning

confidence: 99%

Synchronization control of oscillator networks using symbolic regression

et al. 2017

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Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far-reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly effective and interpretable control functions for such systems.

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Prediction of dynamical systems by symbolic regression

Cited by 106 publications

References 35 publications

Symbolic regression in materials science

Symbolic regression in materials science

Identifying Physico-Chemical Laws from the Robotically Collected Data

Synchronization control of oscillator networks using symbolic regression

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