976 research outputs found
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
Accelerating inference in cosmology and seismology with generative models
Statistical analyses in many physical sciences require running simulations of the system that is being examined. Such simulations provide complementary information to the theoretical analytic models, and represent an invaluable tool to investigate the dynamics of complex systems. However, running simulations is often computationally expensive, and the high number of required mocks to obtain sufficient statistical precision often makes the problem intractable. In recent years, machine learning has emerged as a possible solution to speed up the generation of scientific simulations. Machine learning generative models usually rely on iteratively feeding some true simulations to the algorithm, until it learns the important common features and is capable of producing accurate simulations in a fraction of the time. In this thesis, advanced machine learning algorithms are explored and applied to the challenge of accelerating physical simulations. Various techniques are applied to problems in cosmology and seismology, showing benefits and limitations of such an approach through a critical analysis. The algorithms are applied to compelling problems in the fields, including surrogate models for the seismic wave equation, the emulation of cosmological summary statistics, and the fast generation of large simulations of the Universe. These problems are formulated within a relevant statistical framework, and tied to real data analysis pipelines. In the conclusions, a critical overview of the results is provided, together with an outlook over possible future expansions of the work presented in the thesis
Neuromorphic, Digital and Quantum Computation with Memory Circuit Elements
Memory effects are ubiquitous in nature and the class of memory circuit
elements - which includes memristors, memcapacitors and meminductors - shows
great potential to understand and simulate the associated fundamental physical
processes. Here, we show that such elements can also be used in electronic
schemes mimicking biologically-inspired computer architectures, performing
digital logic and arithmetic operations, and can expand the capabilities of
certain quantum computation schemes. In particular, we will discuss few
examples where the concept of memory elements is relevant to the realization of
associative memory in neuronal circuits, spike-timing-dependent plasticity of
synapses, digital and field-programmable quantum computing
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