Physics-Informed Echo State Networks for Chaotic Systems Forecasting

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapunov times as compared to conventional ESNs. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.Comment: 7 pages, 3 figure

Physics-Informed Echo State Networks for Chaotic Systems Forecasting

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapunov times as compared to conventional ESNs. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems

Magnetic field sensitivity of variable thickness microbridges in tbcco, bscco and ybco.

We describe results of a study comparing the magnetic field sensitivities of variable thickness bridge (VTB) arrays fabricated in TBCCO, BSCCO, and YBCO thin films. Identical structures were patterned in a variety of films, and the bridges were thinned by four different methods. Analysis of the data yields experimental evidence as to the suitability of these types of films for devices such as the superconducting flux flow transistor (SFFT) which is based on this geometry. The volt-ampere characteristics of the arrays were measured in low uniform magnetic fields (⩽130 G) and in nonuniform fields (⩽5 G) produced by a nearby control line. For these films in this geometry, no measurable effect of the control line magnetic field was observed. Large values of transresistance and current gain could only be attained through a thermal mechanism when the control line was driven normal. Upper bounds for (magnetically generated) transresistance (⩽5 mΩ) and current gains (⩽0.005) have been inferred from the uniform field data assuming a standard best-case device geometry. All volt-ampere curves followed closely a power law relationship (V~I n), with exponent n ~1.2-10. We suggest materials considerations that may yield improved device performancePeer Reviewe

Optimal neural network feature selection for spatial-temporal forecasting

In this paper, we show empirical evidence on how to construct the optimal feature selection or input representation used by the input layer of a feedforward neural network for the propose of forecasting spatial-temporal signals. The approach is based on results from dynamical systems theory, namely the non-linear embedding theorems. We demonstrate it for a variety of spatial-temporal signals, with one spatial and one temporal dimensions, and show that the optimal input layer representation consists of a grid, with spatial/temporal lags determined by the minimum of the mutual information of the spatial/temporal signals and the number of points taken in space/time decided by the embedding dimension of the signal. We present evidence of this proposal by running a Monte Carlo simulation of several combinations of input layer feature designs and show that the one predicted by the non-linear embedding theorems seems to be optimal or close of optimal. In total we show evidence in four unrelated systems: a series of coupled Henon maps; a series of couple Ordinary Differential Equations (Lorenz-96) phenomenologically modelling atmospheric dynamics; the Kuramoto-Sivashinsky equation, a partial differential equation used in studies of instabilities in laminar flame fronts and finally real physical data from sunspot areas in the Sun (in latitude and time) from 1874 to 2015.Comment: 11 page

Towards a hybrid computational strategy based on Deep Learning for incompressible flows

The Poisson equation is present in very different domains of physics and engineering. In most cases, this equation can not be solved directly and iterative solvers are used. For many solvers, this step is computationally intensive. In this study, an alternative resolution method based on neural networks is evaluated for incompressible flows. A fluid solver coupled with a Convolutional Neural Network is developed and trained on random cases with constant density to predict the pressure field. Its performance is tested in a plume configuration, with different buoyancy forces, parametrized by the Richardson number. The neural network is compared to a traditional Jacobi solver. The performance improvement is considerable, although the accuracy of the network is found to depend on the flow operating point: low errors are obtained at low Richardson numbers, whereas the fluid solver becomes unstable with large errors for large Richardson number. Finally, a hybrid strategy is proposed in order to benefit from the calculation acceleration while ensuring a user-defined accuracy level. In particular, this hybrid CFD-NN strategy, by maintaining the desired accuracy whatever the flow condition, makes the code stable and reliable even at large Richardson numbers for which the network was not trained for. This study demonstrates the capability of the hybrid approach to tackle new flow physics, unseen during the network training

A novel physics informed deep learning method for simulation-based modelling

In this paper, we present a brief review of the state of the art physics informed deep learning methodology and examine its applicability, limits, advantages, and disadvantages via several applications. The main advantage of this method is that it can predict the solution of the partial differential equations by using only boundary and initial conditions without the need for any training data or pre-process phase. Using physics informed neural network algorithms, it is possible to solve partial differential equations in many different problems encountered in engineering studies with a low cost and time instead of traditional numerical methodologies. A direct comparison between the initial results of the current model, analytical solutions, and computational fluid dynamics methods shows very good agreement. The proposed methodology provides a crucial basis for solution of more advance partial differential equation systems and offers a new analysis and mathematical modelling tool for aerospace application

Neutrinos below 100 TeV from the southern sky employing refined veto techniques to IceCube data

Many Galactic sources of gamma rays, such as supernova remnants, are expected to produce neutrinos with a typical energy cutoff well below 100 TeV. For the IceCube Neutrino Observatory located at the South Pole, the southern sky, containing the inner part of the Galactic plane and the Galactic Center, is a particularly challenging region at these energies, because of the large background of atmospheric muons. In this paper, we present recent advancements in data selection strategies for track-like muon neutrino events with energies below 100 TeV from the southern sky. The strategies utilize the outer detector regions as veto and features of the signal pattern to reduce the background of atmospheric muons to a level which, for the first time, allows IceCube searching for point-like sources of neutrinos in the southern sky at energies between 100 GeV and several TeV in the muon neutrino charged current channel. No significant clustering of neutrinos above background expectation was observed in four years of data recorded with the completed IceCube detector. Upper limits on the neutrino flux for a number of spectral hypotheses are reported for a list of astrophysical objects in the southern hemisphere.Comment: 19 pages, 17 figures, 2 table

Search for transient optical counterparts to high-energy IceCube neutrinos with Pan-STARRS1

In order to identify the sources of the observed diffuse high-energy neutrino flux, it is crucial to discover their electromagnetic counterparts. IceCube began releasing alerts for single high-energy ($E > 60$ TeV) neutrino detections with sky localisation regions of order 1 deg radius in 2016. We used Pan-STARRS1 to follow-up five of these alerts during 2016-2017 to search for any optical transients that may be related to the neutrinos. Typically 10-20 faint ($m < 22.5$ mag) extragalactic transients are found within the Pan-STARRS1 footprints and are generally consistent with being unrelated field supernovae (SNe) and AGN. We looked for unusual properties of the detected transients, such as temporal coincidence of explosion epoch with the IceCube timestamp. We found only one transient that had properties worthy of a specific follow-up. In the Pan-STARRS1 imaging for IceCube-160427A (probability to be of astrophysical origin of $\sim$50 %), we found a SN PS16cgx, located at 10.0' from the nominal IceCube direction. Spectroscopic observations of PS16cgx showed that it was an H-poor SN at z = 0.2895. The spectra and light curve resemble some high-energy Type Ic SNe, raising the possibility of a jet driven SN with an explosion epoch temporally coincident with the neutrino detection. However, distinguishing Type Ia and Type Ic SNe at this redshift is notoriously difficult. Based on all available data we conclude that the transient is more likely to be a Type Ia with relatively weak SiII absorption and a fairly normal rest-frame r-band light curve. If, as predicted, there is no high-energy neutrino emission from Type Ia SNe, then PS16cgx must be a random coincidence, and unrelated to the IceCube-160427A. We find no other plausible optical transient for any of the five IceCube events observed down to a 5$\sigma$ limiting magnitude of $m \sim 22$ mag, between 1 day and 25 days after detection.Comment: 20 pages, 6 figures, accepted to A&

Results from the translation and adaptation of the Iranian Short-Form McGill Pain Questionnaire (I-SF-MPQ): preliminary evidence of its reliability, construct validity and sensitivity in an Iranian pain population

<p>Abstract</p> <p>Background</p> <p>The Short Form McGill Pain Questionnaire (SF-MPQ) is one of the most widely used instruments to assess pain. The aim of this study was to translate and culturally adapt the questionnaire for Farsi (the official language of Iran) speakers in order to test its reliability and sensitivity.</p> <p>Methods</p> <p>We followed Guillemin's guidelines for cross-cultural adaption of health-related measures, which include forward-backward translations, expert committee meetings, and face validity testing in a pilot group. Subsequently, the questionnaire was administered to a sample of 100 diverse chronic pain patients attending a tertiary pain and rehabilitation clinic. In order to evaluate test-retest reliability, patients completed the questionnaire in the morning and early evening of their first visit. Finally, patients were asked to complete the questionnaire for the third time after completing a standardized treatment protocol three weeks later. Intraclass correlation coefficient (ICC) was used to evaluate reliability. We used principle component analysis to assess construct validity.</p> <p>Results</p> <p>Ninety-two subjects completed the questionnaire both in the morning and in the evening of the first visit (test-retest reliability), and after three weeks (sensitivity to change). Eight patients who did not finish treatment protocol were excluded from the study. Internal consistency was found by Cronbach's alpha to be 0.951, 0.832 and 0.840 for sensory, affective and total scores respectively. ICC resulted in 0.906 for sensory, 0.712 for affective and 0.912 for total pain score. Item to subscale score correlations supported the convergent validity of each item to its hypothesized subscale. Correlations were observed to range from r²= 0.202 to r²= 0.739. Sensitivity or responsiveness was evaluated by pair t-test, which exhibited a significant difference between pre- and post-treatment scores (p < 0.001).</p> <p>Conclusion</p> <p>The results of this study indicate that the Iranian version of the SF-MPQ is a reliable questionnaire and responsive to changes in the subscale and total pain scores in Persian chronic pain patients over time.</p