170 research outputs found
Manifold learning for emulations of computer models
Computer simulations are widely used in scientific research and engineering areas. Thought they could provide accurate result, the computational expense is normally high and thus hinder their applications to problems, where repeated evaluations are required, e.g, design optimization and uncertainty quantification. For partial differential equation (PDE) models the outputs of interest are often spatial fields, leading to high-dimensional output spaces. Although emulators can be used to find faithful and computationally inexpensive approximations of computer models, there are few methods for handling high-dimensional output spaces. For Gaussian process (GP) emulation, approximations of the correlation structure and/or dimensionality reduction are necessary. Linear dimensionality reduction will fail when the output space is not well approximated by a linear subspace of the ambient space in which it lies. Manifold learning can overcome the limitations of linear methods if an accurate inverse map is available. In this thesis, manifold learning is applied to construct GP emulators for very high-dimensional output spaces arising from parameterised PDE model simulations. Artificial neural network (ANN) support vector machine (SVM) emulators using manifold learning are also studied. A general framework for the inverse map approximation and a new efficient method for diffusion maps were developed. The manifold learning based emulators are then to extend reduced order models (ROMs) based on proper orthogonal decomposition to dynamic, parameterized PDEs. A similar approach is used to extend the discrete empirical interpolation method (DEIM) to ROMs for nonlinear, parameterized dynamic PDEs
Fast emulation of anisotropies induced in the cosmic microwave background by cosmic strings
Cosmic strings are linear topological defects that may have been produced
during symmetry-breaking phase transitions in the very early Universe. In an
expanding Universe the existence of causally separate regions prevents such
symmetries from being broken uniformly, with a network of cosmic string
inevitably forming as a result. To faithfully generate observables of such
processes requires computationally expensive numerical simulations, which
prohibits many types of analyses. We propose a technique to instead rapidly
emulate observables, thus circumventing simulation. Emulation is a form of
generative modelling, often built upon a machine learning backbone. End-to-end
emulation often fails due to high dimensionality and insufficient training
data. Consequently, it is common to instead emulate a latent representation
from which observables may readily be synthesised. Wavelet phase harmonics are
an excellent latent representations for cosmological fields, both as a summary
statistic and for emulation, since they do not require training and are highly
sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a
latent representation, we develop techniques to emulate string induced CMB
anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in
under a minute on a single GPU. Beyond generating high fidelity emulations, we
provide a technique to ensure these observables are distributed correctly,
providing a more representative ensemble of samples. The statistics of our
emulations are commensurate with those calculated on comprehensive Nambu-Goto
simulations. Our findings indicate these fast emulation approaches may be
suitable for wide use in, e.g., simulation based inference pipelines. We make
our code available to the community so that researchers may rapidly emulate
cosmic string induced CMB anisotropies for their own analysis
Emulating dynamic non-linear simulators using Gaussian processes
The dynamic emulation of non-linear deterministic computer codes where the
output is a time series, possibly multivariate, is examined. Such computer
models simulate the evolution of some real-world phenomenon over time, for
example models of the climate or the functioning of the human brain. The models
we are interested in are highly non-linear and exhibit tipping points,
bifurcations and chaotic behaviour. However, each simulation run could be too
time-consuming to perform analyses that require many runs, including
quantifying the variation in model output with respect to changes in the
inputs. Therefore, Gaussian process emulators are used to approximate the
output of the code. To do this, the flow map of the system under study is
emulated over a short time period. Then, it is used in an iterative way to
predict the whole time series. A number of ways are proposed to take into
account the uncertainty of inputs to the emulators, after fixed initial
conditions, and the correlation between them through the time series. The
methodology is illustrated with two examples: the highly non-linear dynamical
systems described by the Lorenz and Van der Pol equations. In both cases, the
predictive performance is relatively high and the measure of uncertainty
provided by the method reflects the extent of predictability in each system
Compensating Inhomogeneities of Neuromorphic VLSI Devices Via Short-Term Synaptic Plasticity
Recent developments in neuromorphic hardware engineering make mixed-signal VLSI neural network models promising candidates for neuroscientific research tools and massively parallel computing devices, especially for tasks which exhaust the computing power of software simulations. Still, like all analog hardware systems, neuromorphic models suffer from a constricted configurability and production-related fluctuations of device characteristics. Since also future systems, involving ever-smaller structures, will inevitably exhibit such inhomogeneities on the unit level, self-regulation properties become a crucial requirement for their successful operation. By applying a cortically inspired self-adjusting network architecture, we show that the activity of generic spiking neural networks emulated on a neuromorphic hardware system can be kept within a biologically realistic firing regime and gain a remarkable robustness against transistor-level variations. As a first approach of this kind in engineering practice, the short-term synaptic depression and facilitation mechanisms implemented within an analog VLSI model of I&F neurons are functionally utilized for the purpose of network level stabilization. We present experimental data acquired both from the hardware model and from comparative software simulations which prove the applicability of the employed paradigm to neuromorphic VLSI devices
Manifold learning for the emulation of spatial fields from computational models
Repeated evaluations of expensive computer models in applications such as design optimization and uncertainty quantification can be computationally infeasible. For partial differential equation (PDE) models, the outputs of interest are often spatial fields leading to high-dimensional output spaces. Although emulators can be used to find faithful and computationally inexpensive approximations of computer models, there are few methods for handling high-dimensional output spaces. For Gaussian process (GP) emulation, approximations of the correlation structure and/or dimensionality reduction are necessary. Linear dimensionality reduction will fail when the output space is not well approximated by a linear subspace of the ambient space in which it lies. Manifold learning can overcome the limitations of linear methods if an accurate inverse map is available. In this paper, we use kernel PCA and diffusion maps to construct GP emulators for very high-dimensional output spaces arising from PDE model simulations. For diffusion maps we develop a new inverse map approximation. Several examples are presented to demonstrate the accuracy of our approach
Enabling real-time multi-messenger astrophysics discoveries with deep learning
Multi-messenger astrophysics is a fast-growing, interdisciplinary field that combines data, which vary in volume and speed of data processing, from many different instruments that probe the Universe using different cosmic messengers: electromagnetic waves, cosmic rays, gravitational waves and neutrinos. In this Expert Recommendation, we review the key challenges of real-time observations of gravitational wave sources and their electromagnetic and astroparticle counterparts, and make a number of recommendations to maximize their potential for scientific discovery. These recommendations refer to the design of scalable and computationally efficient machine learning algorithms; the cyber-infrastructure to numerically simulate astrophysical sources, and to process and interpret multi-messenger astrophysics data; the management of gravitational wave detections to trigger real-time alerts for electromagnetic and astroparticle follow-ups; a vision to harness future developments of machine learning and cyber-infrastructure resources to cope with the big-data requirements; and the need to build a community of experts to realize the goals of multi-messenger astrophysics
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Statistical mechanics in climate emulation: Challenges and perspectives
Climate emulators are a powerful instrument for climate modeling, especially in terms of reducing the computational load for simulating spatiotemporal processes associated with climate systems. The most important type of emulators are statistical emulators trained on the output of an ensemble of simulations from various climate models. However, such emulators oftentimes fail to capture the “physics” of a system that can be detrimental for unveiling critical processes that lead to climate tipping points. Historically, statistical mechanics emerged as a tool to resolve the constraints on physics using statistics. We discuss how climate emulators rooted in statistical mechanics and machine learning can give rise to new climate models that are more reliable and require less observational and computational resources. Our goal is to stimulate discussion on how statistical climate emulators can further be improved with the help of statistical mechanics which, in turn, may reignite the interest of statistical community in statistical mechanics of complex systems
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