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In the present work, we use symbolic regression for automated modeling of dynamical systems. Symbolic regression is a powerful and general method suitable for data-driven identification of mathematical expressions. In particular, the structure and parameters of those expressions are identified simultaneously.
We consider two main variants of symbolic regression: sparse regression-based and genetic programming-based symbolic regression. Both are applied to identification, prediction and control of dynamical systems.
We introduce a new methodology for the data-driven identification of nonlinear dynamics for systems undergoing abrupt changes. Building on a sparse regression algorithm derived earlier, the model after the change is defined as a minimum update with respect to a reference model of the system identified prior to the change. The technique is successfully exemplified on the chaotic Lorenz system and the van der Pol oscillator. Issues such as computational complexity, robustness against noise and requirements with respect to data volume are investigated.
We show how symbolic regression can be used for time series prediction. Again, issues such as robustness against noise and convergence rate are investigated us- ing the harmonic oscillator as a toy problem. In combination with embedding, we demonstrate the prediction of a propagating front in coupled FitzHugh-Nagumo oscillators. Additionally, we show how we can enhance numerical weather predictions to commercially forecast power production of green energy power plants.
We employ symbolic regression for synchronization control in coupled van der Pol oscillators. Different coupling topologies are investigated. We address issues such as plausibility and stability of the control laws found. The toolkit has been made open source and is used in turbulence control applications.
Genetic programming based symbolic regression is very versatile and can be adapted to many optimization problems. The heuristic-based algorithm allows for cost efficient optimization of complex tasks.
We emphasize the ability of symbolic regression to yield white-box models. In contrast to black-box models, such models are accessible and interpretable which allows the usage of established tool chains.
Background:
Endomyocardial biopsy is considered as the gold standard in patients with suspected myocarditis. We aimed to evaluate the impact of bioptic findings on prediction of successful return to work.
Methods:
In 1153 patients (48.9 ± 12.4 years, 66.2% male), who were hospitalized due to symptoms of left heart failure between 2005 and 2012, an endomyocardial biopsy was performed. Routine clinical and laboratory data, sociodemographic parameters, and noninvasive and invasive cardiac variables including endomyocardial biopsy were registered. Data were linked with return to work data from the German statutory pension insurance program and analyzed by Cox regression.
Results:
A total of 220 patients had a complete data set of hospital and insurance information. Three quarters of patients were virus-positive (54.2% parvovirus B19, other or mixed infection 16.7%). Mean invasive left ventricular ejection fraction was 47.1% ± 18.6% (left ventricular ejection fraction <45% in 46.3%). Return to work was achieved after a mean interval of 168.8 ± 347.7 days in 220 patients (after 6, 12, and 24 months in 61.3%, 72.2%, and 76.4%). In multivariate regression analysis, only age (per 10 years, hazard ratio, 1.27; 95% confidence interval, 1.10–1.46; p = 0.001) and left ventricular ejection fraction (per 5% increase, hazard ratio, 1.07; 95% confidence interval, 1.03–1.12; p = 0.002) were associated with increased, elevated work intensity (heavy vs light, congestive heart failure, 0.58; 95% confidence interval, 0.34–0.99; p < 0.049) with decreased probability of return to work. None of the endomyocardial biopsy–derived parameters was significantly associated with return to work in the total group as well as in the subgroup of patients with biopsy-proven myocarditis.
Conclusion:
Added to established predictors, bioptic data demonstrated no additional impact for return to work probability. Thus, socio-medical evaluation of patients with suspected myocarditis furthermore remains an individually oriented process based primarily on clinical and functional parameters.
Genetic and environmental factors both contribute to cognitive test performance. A substantial increase in average intelligence test results in the second half of the previous century within one generation is unlikely to be explained by genetic changes. One possible explanation for the strong malleability of cognitive performance measure is that environmental factors modify gene expression via epigenetic mechanisms. Epigenetic factors may help to understand the recent observations of an association between dopamine-dependent encoding of reward prediction errors and cognitive capacity, which was modulated by adverse life events. The possible manifestation of malleable biomarkers contributing to variance in cognitive test performance, and thus possibly contributing to the "missing heritability" between estimates from twin studies and variance explained by genetic markers, is still unclear. Here we show in 1475 healthy adolescents from the IMaging and GENetics (IMAGEN) sample that general IQ (gIQ) is associated with (1) polygenic scores for intelligence, (2) epigenetic modification of DRD2 gene, (3) gray matter density in striatum, and (4) functional striatal activation elicited by temporarily surprising reward-predicting cues. Comparing the relative importance for the prediction of gIQ in an overlapping subsample, our results demonstrate neurobiological correlates of the malleability of gIQ and point to equal importance of genetic variance, epigenetic modification of DRD2 receptor gene, as well as functional striatal activation, known to influence dopamine neurotransmission. Peripheral epigenetic markers are in need of confirmation in the central nervous system and should be tested in longitudinal settings specifically assessing individual and environmental factors that modify epigenetic structure.