The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a deep learning framework for learning Koopman operators of nonlinear dynamical systems. We show that this novel method automatically selects efficient deep dictionaries, outperforming stateof-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict quantitatively 100 steps into the future, using only a single timepoint, and qualitative oscillatory behavior 400 steps into the future. arXiv:1708.06850v2 [cs.LG] 17 Nov 2017 In 1931, B. O. Koopman published a paper showing that the evolution of any set of observables on a dynamical system can be expressed through the action of an infinite dimensional linear operator, the Koopman operator [1]. Because the Koopman operator is a canonical representation of any autonomous dynamical system, in principle, its use can bring to bear linear analysis methods on nonlinear systems. The Koopman operator is especially powerful for inferring properties of dynamical systems that are either partially or completely unknown or that are too complex to express using standard methods in analysis. Examples of such systems include biological networks, extremely large physical systems (which are intractable to analyze as white-box models), social networks, cyber-physical communication networks, and distributed computing systems that are subject to varying degrees of uncertainty. For this reason, the Koopman operator has gained attention as an effective tool for data-driven model discovery. The Koopman operator provides a data-driven model for comparing the asymptotic behavior of dynamical systems [3], specifically as a function of its spectra [3, 4]. Various algorithms have extended these methods using dynamic and extended dynamic mode decomposition, both for autonomous and controlled systems [5, 6, 7].The prevailing method for learning the Koopman operator from data is dynamic mode decomposition [4]. Dynamic mode decomposition is the process of identifying a linear operator from temporally or spatially-linked data, ultimately with the objective of characterizing the spectrum of the operator.There are many variants of dynamic mode decomposition, but the most recent advances in Koopman operator learning have emerged from extended dynamic mode decomposition [5].In extended dynamic mode decomposition, the idea is to lift the set of system observables from its native vector space into a higher di...

The last decade has seen an extraordinary rise in the performance of perovskite solar cells (PSCs). State‐of‐the‐art devices now have efficiencies of over 25%, putting them on par with the best silicon solar cells. Yet despite their impressive performance, their longevity lags behind that of conventional silicon technology. Environmental factors like moisture, heat, and light can all adversely affect PSC performance and limit device lifetime. Systematically elucidating and eliminating PSC degradation pathways will be critical to the success of this technology. In situ techniques provide powerful tools to this end, as they allow structural, compositional, morphological, and optoelectronic changes to be tracked in real‐time. Because they follow a single film or device over the course of the degradation process, they can help eliminate the statistical variation that negatively affects many studies. Here we provide an overview of perovskite degradation processes, with an emphasis on in situ studies.image

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We explore methods to use thermostatically controlled loads (TCLs), such as water heaters and air conditioners, to provide ancillary services by assisting in balancing generation and load. We show that by adding simple imbedded instructions and a small amount of memory to temperature controllers of TCLs, it is possible to design open-loop control algorithms capable of creating short-term pulses of demand response without unwanted power oscillations associated with temporary synchronization of the TCL dynamics. By moving a small amount of intelligence to each of the end point TCL devices, we are able to leverage our knowledge of the time dynamics of TCLs to shape the demand response pulses for different power * Corresponding author