3,054 research outputs found
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
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Interpretable Machine Learning Architectures for Efficient Signal Detection with Applications to Gravitational Wave Astronomy
Deep learning has seen rapid evolution in the past decade, accomplishing tasks that were previously unimaginable. At the same time, researchers strive to better understand and interpret the underlying mechanisms of the deep models, which are often justifiably regarded as "black boxes". Overcoming this deficiency will not only serve to suggest better learning architectures and training methods, but also extend deep learning to scenarios where interpretability is key to the application. One such scenario is signal detection and estimation, with gravitational wave detection as a specific example, where classic methods are often preferred for their interpretability. Nonetheless, while classic statistical detection methods such as matched filtering excel in their simplicity and intuitiveness, they can be suboptimal in terms of both accuracy and computational efficiency. Therefore, it is appealing to have methods that achieve ``the best of both worlds'', namely enjoying simultaneously excellent performance and interpretability.
In this thesis, we aim to bridge this gap between modern deep learning and classic statistical detection, by revisiting the signal detection problem from a new perspective. First, to address the perceived distinction in interpretability between classic matched filtering and deep learning, we state the intrinsic connections between the two families of methods, and identify how trainable networks can address the structural limitations of matched filtering. Based on these ideas, we propose two trainable architectures that are constructed based on matched filtering, but with learnable templates and adaptivity to unknown noise distributions, and therefore higher detection accuracy. We next turn our attention toward improving the computational efficiency of detection, where we aim to design architectures that leverage structures within the problem for efficiency gains. By leveraging the statistical structure of class imbalance, we integrate hierarchical detection into trainable networks, and use a novel loss function which explicitly encodes both detection accuracy and efficiency. Furthermore, by leveraging the geometric structure of the signal set, we consider using signal space optimization as an alternative computational primitive for detection, which is intuitively more efficient than covering with a template bank. We theoretical prove the efficiency gain by analyzing Riemannian gradient descent on the signal manifold, which reveals an exponential improvement in efficiency over matched filtering. We also propose a practical trainable architecture for template optimization, which makes use of signal embedding and kernel interpolation.
We demonstrate the performance of all proposed architectures on the task of gravitational wave detection in astrophysics, where matched filtering is the current method of choice. The architectures are also widely applicable to general signal or pattern detection tasks, which we exemplify with the handwritten digit recognition task using the template optimization architecture. Together, we hope the this work useful to scientists and engineers seeking machine learning architectures with high performance and interpretability, and contribute to our understanding of deep learning as a whole
Resource-aware scheduling for 2D/3D multi-/many-core processor-memory systems
This dissertation addresses the complexities of 2D/3D multi-/many-core processor-memory systems, focusing on two key areas: enhancing timing predictability in real-time multi-core processors and optimizing performance within thermal constraints. The integration of an increasing number of transistors into compact chip designs, while boosting computational capacity, presents challenges in resource contention and thermal management. The first part of the thesis improves timing predictability. We enhance shared cache interference analysis for set-associative caches, advancing the calculation of Worst-Case Execution Time (WCET). This development enables accurate assessment of cache interference and the effectiveness of partitioned schedulers in real-world scenarios. We introduce TCPS, a novel task and cache-aware partitioned scheduler that optimizes cache partitioning based on task-specific WCET sensitivity, leading to improved schedulability and predictability. Our research explores various cache and scheduling configurations, providing insights into their performance trade-offs. The second part focuses on thermal management in 2D/3D many-core systems. Recognizing the limitations of Dynamic Voltage and Frequency Scaling (DVFS) in S-NUCA many-core processors, we propose synchronous thread migrations as a thermal management strategy. This approach culminates in the HotPotato scheduler, which balances performance and thermal safety. We also introduce 3D-TTP, a transient temperature-aware power budgeting strategy for 3D-stacked systems, reducing the need for Dynamic Thermal Management (DTM) activation. Finally, we present 3QUTM, a novel method for 3D-stacked systems that combines core DVFS and memory bank Low Power Modes with a learning algorithm, optimizing response times within thermal limits. This research contributes significantly to enhancing performance and thermal management in advanced processor-memory systems
Contactless excitation for electric machines: high temperature superconducting flux pumps
With the intensification of global warming and climate change, the pace of transformation to a neutral-emission society is accelerating. In various sectors, electrification has become the absolute tendency to promote such a movement, where electric machines play an important role in the current power generation system. It is widely convinced that electric machines with very high power density are essential for future applications, which, however, can be hardly achieved by conventional technologies. Owing to the maturation of the second generation (2G) high temperature superconducting (HTS) technologies, it has been recognized that superconducting machine could be a competitive candidate to realize the vision.
One significant obstacle that hinders the implementation of superconducting machines is how to provide the required magnetic fields, or in other words, how to energise them appropriately. Conventional direct injection is not suitable for HTS machines, because the current leads would bridge ambident temperature to the cryogenic environment, which can impose considerable heat load on the system and increase the operational cost. Thus, an efficient energisation method is demanded by HTS machines. As an emerging technology that can accumulate substantial flux in a closed loop without any physical contact, HTS flux pumps have been proposed as a promising solution.
Among the existing developed HTS flux pumps, rotary HTS flux pumps, or so-called HTS dynamo, can output non-zero time-averaged DC voltage and charge the rest of the circuit if a closed loop has been formed. This type of flux pump is often employed together with HTS coils, where the HTS coils can potentially work in the persistent current mode, and act like electromagnets with a considerable magnetic field, having a wide range of applications in industry. The output characteristics of rotary HTS flux pumps have been extensively explored through experiments and finite element method (FEM) simulations, yet the work on constructing statistical models as an alternative approach to capture key characteristics has not been studied. In this thesis, a 2D FEM program has been developed to model the operation of rotary HTS flux pumps and evaluate the effects of different factors on the output voltage through parameter sweeping and analysis of variance. Typical design considerations,
including the operating frequency, air gap, HTS tape width, and remanent flux density have been investigated, in particular, the bilateral effect of HTS tape width has been discovered and explained by looking at the averaged integration of the electric field over the HTS tape. Based on the data obtained from various simulations, regression analysis has been conducted through a collection of machine learning methods. It has been demonstrated that the output voltage of a rotary HTS flux pump can be obtained promptly with satisfactory accuracy via Gaussian process regression, aiming to provide a novel approach for future research and a powerful design tool for industrial applications using rotary HTS flux pumps.
To enhance the applicability of the proposed statistical models, an updated FEM program has been built to take more parameters into account. The newly added parameters, namely the rotor radius and the width of permanent magnet, together with formerly included ones, should have covered all the key design parameters for a rotary HTS flux pump. Based on data collected from the FEM model, a well-trained semi-deep neural network (DNN) model with a back-propagation algorithm has been put forward and validated. The proposed DNN model is capable of quantifying the output voltage of a rotary HTS flux pump instantly with an overall accuracy of 98% with respect to the simulated values with all design parameters explicitly specified. The model possesses a powerful ability to characterize the output behaviour of rotary HTS flux pumps by integrating all design parameters, and the output characteristics of rotary HTS flux pumps have been successfully demonstrated and visualized using this model. Compared to conventional time-consuming FEM-based numerical models, the proposed DNN model has the advantages of fast learning, accurate computation, as well as strong programmability. Therefore, the DNN model can greatly facilitate the design and optimization process for rotary HTS flux pumps. An executable application has been developed accordingly based on the DNN model, which is believed to provide a useful tool for learners and designers of rotary HTS flux pumps.
A new variant inspired by the working principles of rotary HTS flux pumps has been proposed and termed as stationary wave HTS flux pumps. The superiority of this type is that it has a simple structure without any moving components, and it utilises a controllable current-driven electromagnet to provide the required magnetic field. It has been demonstrated that the origin of the output voltage is determined by the asymmetric distribution of the dynamic resistance in the HTS tape, for which the electromagnet must be placed at such a position that its central line is not aligned with that of the HTS tape. A numerical model has
been built to simulate the operation of a stationary wave HTS flux pump, based on which the output characteristics and dynamic resistance against various parameters have been investigated. Besides, accurate and reliable statistical models have been proposed to predict the open circuit voltage and effective dynamic resistance by adapting the previously developed machine learning techniques.
The work presented in this PhD thesis can bring more insight into HTS flux pumps as an emerging promising contactless energisation technology, and the proposed statistical models can be particularly useful for the design and optimization of such devices
Unveiling the frontiers of deep learning: innovations shaping diverse domains
Deep learning (DL) enables the development of computer models that are
capable of learning, visualizing, optimizing, refining, and predicting data. In
recent years, DL has been applied in a range of fields, including audio-visual
data processing, agriculture, transportation prediction, natural language,
biomedicine, disaster management, bioinformatics, drug design, genomics, face
recognition, and ecology. To explore the current state of deep learning, it is
necessary to investigate the latest developments and applications of deep
learning in these disciplines. However, the literature is lacking in exploring
the applications of deep learning in all potential sectors. This paper thus
extensively investigates the potential applications of deep learning across all
major fields of study as well as the associated benefits and challenges. As
evidenced in the literature, DL exhibits accuracy in prediction and analysis,
makes it a powerful computational tool, and has the ability to articulate
itself and optimize, making it effective in processing data with no prior
training. Given its independence from training data, deep learning necessitates
massive amounts of data for effective analysis and processing, much like data
volume. To handle the challenge of compiling huge amounts of medical,
scientific, healthcare, and environmental data for use in deep learning, gated
architectures like LSTMs and GRUs can be utilized. For multimodal learning,
shared neurons in the neural network for all activities and specialized neurons
for particular tasks are necessary.Comment: 64 pages, 3 figures, 3 table
Low-Thrust Optimal Escape Trajectories from Lagrangian Points and Quasi-Periodic Orbits in a High-Fidelity Model
L'abstract è presente nell'allegato / the abstract is in the attachmen
Numerical simulation of surfactant flooding with relative permeability estimation using inversion method
Surfactant flooding attracts significant interest in the hydrocarbon industry, with a definite
promise to improve oil recovery from depleting oil reserves. In this thesis, surfactant flooding
is the primary area of focus as it has significant potential for integration with other chemical
enhanced oil recovery techniques, including polymer, nanofluid, alkali, and foam. This
combined approach has the potential to reduce interfacial tension to ultralow levels, decrease
adsorption, and offer other benefits. However, due to the various mechanism, surfactant
flooding poses a more complex model for simulators by encountering numerical issues (e.g.,
the appearance of spurious oscillations, erratic pulses, and numerical instabilities), rendering
the methods ineffective. To address these challenges, the analytical modelling technique of
surfactant flooding was studied, leading to the development of a novel inversion method in the
MATLAB programming environment.
Numerical accuracy issues were discovered in 1D models that used typical cell sizes found in
well-scale models, leading to pulses in the oil bank and a dip in water saturation, particularly
for low levels of adsorption, highlighting the need for more refined models. Based on these
findings, we examined the surfactant flooding technique in 2D models to recover viscous oil
in short reservoir aspect ratios. Instabilities such as viscous fingering and gravity tongue were
observed on the flood fronts, and the magnitude of the viscous fingers was influenced by
vertical dispersion, resulting in errors in computed mobility values at the fronts. Interestingly,
introducing heterogeneity only minimally affected the spreading of the front and did not
significantly impact viscous fingering or numerical artifacts. To optimize the nonlinearity of
flow behaviour and degree of mobility control at the fronts, a homogenous model was
considered to develop the inversion method.
In summary, the developed inversion method accurately estimated the two-phase relative
permeability curves, which were validated using fractional flow theory. The precision of the
inverted curves was further improved using the optimization algorithm, demonstrating the
method's ability to predict outcomes closer to the observed values for 2D models with
instabilities. The obtained results are of significant value for core flood analysis, interpretation,
matching, and upscaling, providing insights into the potential of surfactant flooding for
enhanced oil recovery. Additionally, the use of the developed MATLAB Scripts promotes open
innovation and reproducibility, contributing to the benchmarking, analytical, and numerical
method development exercises for tutorials aimed at improving the overall understanding of
surfactant flooding
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Analog Photonics Computing for Information Processing, Inference and Optimisation
This review presents an overview of the current state-of-the-art in photonics
computing, which leverages photons, photons coupled with matter, and
optics-related technologies for effective and efficient computational purposes.
It covers the history and development of photonics computing and modern
analogue computing platforms and architectures, focusing on optimization tasks
and neural network implementations. The authors examine special-purpose
optimizers, mathematical descriptions of photonics optimizers, and their
various interconnections. Disparate applications are discussed, including
direct encoding, logistics, finance, phase retrieval, machine learning, neural
networks, probabilistic graphical models, and image processing, among many
others. The main directions of technological advancement and associated
challenges in photonics computing are explored, along with an assessment of its
efficiency. Finally, the paper discusses prospects and the field of optical
quantum computing, providing insights into the potential applications of this
technology.Comment: Invited submission by Journal of Advanced Quantum Technologies;
accepted version 5/06/202
Constrained Monotonic Neural Networks
Wider adoption of neural networks in many critical domains such as finance
and healthcare is being hindered by the need to explain their predictions and
to impose additional constraints on them. Monotonicity constraint is one of the
most requested properties in real-world scenarios and is the focus of this
paper. One of the oldest ways to construct a monotonic fully connected neural
network is to constrain signs on its weights. Unfortunately, this construction
does not work with popular non-saturated activation functions as it can only
approximate convex functions. We show this shortcoming can be fixed by
constructing two additional activation functions from a typical unsaturated
monotonic activation function and employing each of them on the part of
neurons. Our experiments show this approach of building monotonic neural
networks has better accuracy when compared to other state-of-the-art methods,
while being the simplest one in the sense of having the least number of
parameters, and not requiring any modifications to the learning procedure or
post-learning steps. Finally, we prove it can approximate any continuous
monotone function on a compact subset of
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