TY - JOUR A1 - Reich, Sebastian T1 - A dynamical systems framework for intermittent data assimilation JF - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians N2 - We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory. KW - Data assimilation KW - Ensemble Kalman filter KW - Dynamical systems KW - Nonlinear filters KW - Optimal transportation Y1 - 2011 U6 - https://doi.org/10.1007/s10543-010-0302-4 SN - 0006-3835 VL - 51 IS - 1 SP - 235 EP - 249 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Quade, Markus A1 - Isele, Thomas A1 - Abel, Markus T1 - Machine learning control BT - explainable and analyzable methods JF - Physica : D, Nonlinear phenomena N2 - Recently, the term explainable AI came into discussion as an approach to produce models from artificial intelligence which allow interpretation. For a long time, symbolic regression has been used to produce explainable and mathematically tractable models. In this contribution, we extend previous work on symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In earlier publications, network control was achieved by automated machine learning control using genetic programming. Here, we focus on the subsequent path continuation analysis of the mathematical expressions which result from the machine learning model. In particular, we use AUTO to analyze the solution properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable symbolic regression models over less accessible neural networks. In particular, the roadmap of future works may be to integrate such analyses into the optimization loop itself to filter out robust solutions by construction. KW - Explainable AI KW - Machine learning control KW - Dynamical systems KW - Synchronization control KW - Genetic programming Y1 - 2020 U6 - https://doi.org/10.1016/j.physd.2020.132582 SN - 0167-2789 SN - 1872-8022 VL - 412 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Tobin, Stephen J. A1 - Nam, Hosung A1 - Fowler, Carol A. T1 - Phonetic drift in Spanish-English bilinguals: Experiment and a self-organizing model JF - Journal of phonetics N2 - Studies of speech accommodation provide evidence for change in use of language structures beyond the critical/sensitive period. For example, Sancier and Fowler (1997) found changes in the voice-onset-times (VOTs) of both languages of a Portuguese-English bilingual as a function of her language context. Though accommodation has been studied widely within a monolingual context, it has received less attention in and between the languages of bilinguals. We tested whether these findings of phonetic accommodation, speech accommodation at the phonetic level, would generalize to a sample of Spanish-English bilinguals. We recorded participants reading Spanish and English sentences after 3–4 months in the US and after 2–4 weeks in a Spanish speaking country and measured the VOTs of their voiceless plosives. Our statistical analyses show that participants’ English VOTs drifted towards those of the ambient language, but their Spanish VOTs did not. We found considerable variation in the extent of individual participants’ drift in English. Further analysis of our results suggested that native-likeness of L2 VOTs and extent of active language use predict the extent of drift. We provide a model based on principles of self-organizing dynamical systems to account for our Spanish-English phonetic drift findings and the Portuguese-English findings. KW - Speech accommodation KW - Gestural drift KW - Phonetic drift KW - Bilingualism KW - Self-organization KW - Dynamical systems KW - Computational model Y1 - 2017 U6 - https://doi.org/10.1016/j.wocn.2017.05.006 SN - 0095-4470 VL - 65 SP - 45 EP - 59 PB - Elsevier CY - London ER - TY - JOUR A1 - Gout, Julien A1 - Quade, Markus A1 - Shafi, Kamran A1 - Niven, Robert K. A1 - Abel, Markus T1 - Synchronization control of oscillator networks using symbolic regression JF - Nonlinear Dynamics N2 - 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. KW - Dynamical systems KW - Synchronization control KW - Genetic programming Y1 - 2017 U6 - https://doi.org/10.1007/s11071-017-3925-z SN - 0924-090X SN - 1573-269X VL - 91 IS - 2 SP - 1001 EP - 1021 PB - Springer CY - Dordrecht ER -