609 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Learning and Control of Dynamical Systems
Despite the remarkable success of machine learning in various domains in recent years, our understanding of its fundamental limitations remains incomplete. This knowledge gap poses a grand challenge when deploying machine learning methods in critical decision-making tasks, where incorrect decisions can have catastrophic consequences. To effectively utilize these learning-based methods in such contexts, it is crucial to explicitly characterize their performance. Over the years, significant research efforts have been dedicated to learning and control of dynamical systems where the underlying dynamics are unknown or only partially known a priori, and must be inferred from collected data. However, much of these classical results have focused on asymptotic guarantees, providing limited insights into the amount of data required to achieve desired control performance while satisfying operational constraints such as safety and stability, especially in the presence of statistical noise.
In this thesis, we study the statistical complexity of learning and control of unknown dynamical systems. By utilizing recent advances in statistical learning theory, high-dimensional statistics, and control theoretic tools, we aim to establish a fundamental understanding of the number of samples required to achieve desired (i) accuracy in learning the unknown dynamics, (ii) performance in the control of the underlying system, and (iii) satisfaction of the operational constraints such as safety and stability. We provide finite-sample guarantees for these objectives and propose efficient learning and control algorithms that achieve the desired performance at these statistical limits in various dynamical systems. Our investigation covers a broad range of dynamical systems, starting from fully observable linear dynamical systems to partially observable linear dynamical systems, and ultimately, nonlinear systems.
We deploy our learning and control algorithms in various adaptive control tasks in real-world control systems and demonstrate their strong empirical performance along with their learning, robustness, and stability guarantees. In particular, we implement one of our proposed methods, Fourier Adaptive Learning and Control (FALCON), on an experimental aerodynamic testbed under extreme turbulent flow dynamics in a wind tunnel. The results show that FALCON achieves state-of-the-art stabilization performance and consistently outperforms conventional and other learning-based methods by at least 37%, despite using 8 times less data. The superior performance of FALCON arises from its physically and theoretically accurate modeling of the underlying nonlinear turbulent dynamics, which yields rigorous finite-sample learning and performance guarantees. These findings underscore the importance of characterizing the statistical complexity of learning and control of unknown dynamical systems.</p
Causal Sampling, Compressing, and Channel Coding of Streaming Data
With the emergence of the Internet of Things, communication systems, such as those employed in distributed control and tracking scenarios, are becoming increasingly dynamic, interactive, and delay-sensitive. The data in such real-time systems arrive at the encoder progressively in a streaming fashion. An intriguing question is: what codes can transmit streaming data with both high reliability and low latency? Classical non-causal (block) encoding schemes can transmit data reliably but under the assumption that the encoder knows the entire data block before the transmission. While this is a realistic assumption in delay-tolerant systems, it is ill-suited to real-time systems due to the delay introduced by collecting data into a block. This thesis studies causal encoding: the encoder transmits information based on the causally received data while the data is still streaming in and immediately incorporates the newly received data into a continuing transmission on the fly.
This thesis investigates causal encoding of streaming data in three scenarios: causal sampling, causal lossy compressing, and causal joint source-channel coding (JSCC). In the causal sampling scenario, a sampler observes a continuous-time source process and causally decides when to transmit real-valued samples of it under a constraint on the average number of samples per second; an estimator uses the causally received samples to approximate the source process in real time. We propose a causal sampling policy that achieves the best tradeoff between the sampling frequency and the end-to-end real-time estimation distortion for a class of continuous Markov processes. In the causal lossy compressing scenario, the sampling frequency constraint in the causal sampling scenario is replaced by a rate constraint on the average number of bits per second. We propose a causal code that achieves the best causal distortion-rate tradeoff for the same class of processes. In the causal JSCC scenario, the noiseless channel and the continuous-time process in the previous scenarios are replaced by a discrete memoryless channel with feedback and a sequence of streaming symbols, respectively. We propose a causal joint sourcechannel code that achieves the maximum exponentially decaying rate of the error probability compatible with a given rate. Remarkably, the fundamental limits in the causal lossy compressing and the causal JSCC scenarios achieved by our causal codes are no worse than those achieved by the best non-causal codes. In addition to deriving the fundamental limits and presenting the causal codes that achieve the limits, we also show that our codes apply to control systems, are resilient to system deficiencies such as channel delay and noise, and have low complexities.</p
APPLICATION OF HIERARCHICAL SPECIES DISTRIBUTION MODELS TO AVIAN SPECIES OF SOUTH DAKOTA AND THE UPPER MISSOURI RIVER BASIN
Recognizing the distributional patterns of species can inform management actions and increase scientific knowledge about species. Habitat Suitability Models (HSMs) are valuable tools in modeling species’ niches and effects of climate change and anthropogenic and natural disturbances on species’ distributions and abundances. In this dissertation, I expanded the application of hierarchical HSMs for a rare bird (Virginia’s warbler) and an economically valuable bird (ring-necked pheasant) in South Dakota. Also, we developed multiscale HSMs for grassland birds in the Upper Missouri River Basin (UMRB) to quantify current habitat associations and predict the influences of climate and landcover change associated with the implementation of bioenergy with carbon capture and storage (BECCS) and other carbon mitigation scenarios. We found that applying an Ensemble of Small Models (ESMs) approach within a hierarchical framework can lead to detailed information about niches of rare species, limiting factors at each habitat selection order, and potential distribution, which could help inform multiscale management. At the broadest habitat selection order, Virginia’s warbler had a narrow climatic niche. The importance of environmental variables changed across finer orders, such that at broader orders many covariates were important whereas at finer orders certain covariates became more important than others. For the model of pheasant abundance, my results showed that our hierarchical Bayesian approach allows for simultaneous selection of variables and scales of effect. I found that pheasant abundance was positively affected by intermediate levels of grassland cover. Scales of effect and spatiotemporal variation influenced predictor variable impacts on pheasant abundance. For the modeling of grassland birds across the UMRB, my results showed that the influence of climate change on abundance, distribution and species richness of grassland species is more pronounced than the influence of landcover changes due to implementing BECCS scenarios. This finding implies that regardless of landcover and land-use changes, climate change may limit or expand abundance and distribution of grassland bird species in the UMRB. Further, we found that grassland birds will be more affected by regional increases in temperature than decreases in precipitation
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Brain Computations and Connectivity [2nd edition]
This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations.
Brain Computations and Connectivity is about how the brain works. In order to understand this, it is essential to know what is computed by different brain systems; and how the computations are performed.
The aim of this book is to elucidate what is computed in different brain systems; and to describe current biologically plausible computational approaches and models of how each of these brain systems computes.
Understanding the brain in this way has enormous potential for understanding ourselves better in health and in disease. Potential applications of this understanding are to the treatment of the brain in disease; and to artificial intelligence which will benefit from knowledge of how the brain performs many of its extraordinarily impressive functions.
This book is pioneering in taking this approach to brain function: to consider what is computed by many of our brain systems; and how it is computed, and updates by much new evidence including the connectivity of the human brain the earlier book: Rolls (2021) Brain Computations: What and How, Oxford University Press.
Brain Computations and Connectivity will be of interest to all scientists interested in brain function and how the brain works, whether they are from neuroscience, or from medical sciences including neurology and psychiatry, or from the area of computational science including machine learning and artificial intelligence, or from areas such as theoretical physics
Inferring the equation of state with multi-messenger signals from binary neutron star mergers
The joint detection of the GW170817 and its electromagnetic counterparts was a milestone in multi-messenger astronomy. We investigate the observational constraints on the neutron star equation of state provided by multi-messenger data of binary neutron star mergers, analyzing the gravitational-wave transient GW170817 and its kilonova counterpart AT2017gfo and exploring new scenarios with next-generation gravitational-wave detectors. The LIGO-Virgo data of GW170817 are analyzed using different template models focusing on the implications for neutron star matter properties. We study the systematic tidal errors between current gravitational-wave models finding that waveform systematics dominate over statistical errors at signal-to-noise ratio ≳ 100. We study AT2017gfo using semi-analytical model showing that observational data favor multi-component anisotropic geometries to spherically symmetric profiles. By joining GW170817 and AT2017gfo information with the NICER measurements, we infer the neutron star equation of state constraining the radius of a 1.4M☉ neutron star to 12.39+0.70-0.65 km and the maximum mass MTOV to 2.08+0.16-0.09 M☉ (90% credible level). Finally, we explore future constraints on extreme-matter delivered by postmerger gravitational-waves from binary neutron star merger remnants. These transients can be detected with matched-filtering techniques and numerical-relativity-informed models for signal-to-noise ratios ≳ 7. Postmerger remnants can probe the high-density regimes of the nuclear equation of state, allowing the inference of the maximum neutron star mass MTOV with an accuracy of 12% (90% max credible level). Moreover, postmerger transients can be used to infer the presence of non-nucleonic matter phases through the inference of softening of the equation of state. For particular binary configurations, softening effects of the equation of state can lead to breaking of quasiuniversal properties and earlier collapse into black hole
Operational Research: methods and applications
This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
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