Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. The computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions

GMC Collisions As Triggers of Star Formation. IV. The Role of Ambipolar Diffusion

We investigate the role of ambipolar diffusion (AD) in collisions between magnetized giant molecular clouds (GMCs), which may be an important mechanism for triggering star cluster formation. Three dimensional simulations of GMC collisions are performed using a version of the Enzo magnetohydrodynamics code that has been extended to include AD. The resistivities are calculated using the 31-species chemical model of Wu et al. (2015). We find that in the weak-field, $10\:{\rm \mu G}$ case, AD has only a modest effect on the dynamical evolution during the collision. However, for the stronger-field, $30\:{\rm \mu G}$ case involving near-critical clouds, AD results in formation of dense cores in regions where collapse is otherwise inhibited. The overall efficiency of formation of cores with $n_{\rm H}\geq10^{6}\:{\rm cm}^{-3}$ in these simulations is increases from about 0.2% to 2% once AD is included, comparable to observed values in star-forming GMCs. The gas around these cores typically has relatively slow infall at speeds that are a modest fraction of the free-fall speed.Comment: 15 pages, 15 figures, Accepted to Ap

An average-case depth hierarchy theorem for Boolean circuits

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of $\mathsf{AND}$, $\mathsf{OR}$, and $\mathsf{NOT}$ gates. Our hierarchy theorem says that for every $d \geq 2$, there is an explicit $n$-variable Boolean function $f$, computed by a linear-size depth-$d$ formula, which is such that any depth-$(d-1)$ circuit that agrees with $f$ on $(1/2 + o_n(1))$ fraction of all inputs must have size $\exp({n^{\Omega(1/d)}}).$ This answers an open question posed by H{\aa}stad in his Ph.D. thesis. Our average-case depth hierarchy theorem implies that the polynomial hierarchy is infinite relative to a random oracle with probability 1, confirming a conjecture of H{\aa}stad, Cai, and Babai. We also use our result to show that there is no "approximate converse" to the results of Linial, Mansour, Nisan and Boppana on the total influence of small-depth circuits, thus answering a question posed by O'Donnell, Kalai, and Hatami. A key ingredient in our proof is a notion of \emph{random projections} which generalize random restrictions

Where and Who? Automatic Semantic-Aware Person Composition

Image compositing is a method used to generate realistic yet fake imagery by inserting contents from one image to another. Previous work in compositing has focused on improving appearance compatibility of a user selected foreground segment and a background image (i.e. color and illumination consistency). In this work, we instead develop a fully automated compositing model that additionally learns to select and transform compatible foreground segments from a large collection given only an input image background. To simplify the task, we restrict our problem by focusing on human instance composition, because human segments exhibit strong correlations with their background and because of the availability of large annotated data. We develop a novel branching Convolutional Neural Network (CNN) that jointly predicts candidate person locations given a background image. We then use pre-trained deep feature representations to retrieve person instances from a large segment database. Experimental results show that our model can generate composite images that look visually convincing. We also develop a user interface to demonstrate the potential application of our method.Comment: 10 pages, 9 figure

GMC Collisions As Triggers of Star Formation. IV. The Role of Ambipolar Diffusion

We investigate the role of ambipolar diffusion (AD) in collisions between magnetized giant molecular clouds (GMCs), which may be an important mechanism for triggering star cluster formation. Three dimensional simulations of GMC collisions are performed using a version of the Enzo magnetohydrodynamics code that has been extended to include AD. The resistivities are calculated using the 31-species chemical model of Wu et al. (2015). We find that in the weak-field, $10\:{\rm \mu G}$ case, AD has only a modest effect on the dynamical evolution during the collision. However, for the stronger-field, $30\:{\rm \mu G}$ case involving near-critical clouds, AD results in formation of dense cores in regions where collapse is otherwise inhibited. The overall efficiency of formation of cores with $n_{\rm H}\geq10^{6}\:{\rm cm}^{-3}$ in these simulations is increases from about 0.2% to 2% once AD is included, comparable to observed values in star-forming GMCs. The gas around these cores typically has relatively slow infall at speeds that are a modest fraction of the free-fall speed.Comment: 15 pages, 15 figures, Accepted to Ap

The Interstellar Medium and Star Formation of Galactic Disks. I. ISM and GMC properties with Diffuse FUV and Cosmic Ray Backgrounds

We present a series of adaptive mesh refinement (AMR) hydrodynamic simulations of flat rotation curve galactic gas disks with a detailed treatment of the interstellar medium (ISM) physics of the atomic to molecular phase transition under the influence of diffuse FUV radiation fields and cosmic ray backgrounds. We explore the effects of different FUV intensities, including a model with a radial gradient designed to mimic the Milky Way. The effects of cosmic rays, including radial gradients in their heating and ionization rates, are also explored. The final simulations in this series achieve $4\:$pc resolution across the $\sim20\:$kpc global disk diameter, with heating and cooling followed down to temperatures of $\sim10\:$K. The disks are evolved for $300\:$Myr, which is enough time for the ISM to achieve a quasi-statistical equilibrium. In particular, the mass fraction of molecular gas stabilizes by $\sim$200 Myr. Additional global ISM properties are analysed. Giant molecular clouds (GMCs) are also identified and the statistical properties of their populations examined. GMCs are tracked as the disks evolve. GMC collisions, which may be a means of triggering star cluster formation, are counted and the rates compared with analytic models. Relatively frequent GMC collision rates are seen in these simulations and their implications for understanding GMC properties, including the driving of internal turbulence, are discussed.Comment: Accepted by PASJ (cloud-cloud collision special issue

Computational Modelling of Wing Downwash Profile with Reynolds-Averaged and Delayed Detached-Eddy Simulations

This paper describes the computational model to predict downwash for a conventional fixed wing configuration at flight scales (ReMAC = 2.26 × 107 ). The lack of resolution in the downwash wake region resulted in an over-dissipation of the turbulent behaviour of airflow in the wing’s wake. This artificially inflates the effectiveness of the horizontal stabilizer where an over-prediction of pitch stiffness was observed. To resolve this over-dissipation, both the Reynolds-Averaged and Delayed Detached-Eddy Simulation methodology were adopted to accurately capture the downwash profile leaving the wing. Comparisons between the estimation of wall shear stresses and viscous wall unit against a ‘first-cut’ simulation are made and discussed. Fundamental features of the downwash profile including the spatial and temporal scales used for the mesh are also presented and detailed in this paper

Ensemble candidate classification for the LOTAAS pulsar survey

One of the biggest challenges arising from modern large-scale pulsar surveys is the number of candidates generated. Here, we implemented several improvements to the machine learning (ML) classifier previously used by the LOFAR Tied-Array All-Sky Survey (LOTAAS) to look for new pulsars via filtering the candidates obtained during periodicity searches. To assist the ML algorithm, we have introduced new features which capture the frequency and time evolution of the signal and improved the signal-to-noise calculation accounting for broad profiles. We enhanced the ML classifier by including a third class characterizing RFI instances, allowing candidates arising from RFI to be isolated, reducing the false positive return rate. We also introduced a new training data set used by the ML algorithm that includes a large sample of pulsars misclassified by the previous classifier. Lastly, we developed an ensemble classifier comprised of five different Decision Trees. Taken together these updates improve the pulsar recall rate by 2.5 per cent, while also improving the ability to identify pulsars with wide pulse profiles, often misclassified by the previous classifier. The new ensemble classifier is also able to reduce the percentage of false positive candidates identified from each LOTAAS pointing from 2.5 per cent (∼500 candidates) to 1.1 per cent (∼220 candidates)