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Differentiable Simulator For Dynamic & Stochastic Optimal Gas & Power Flows 63

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Differentiable Simulator For Dynamic & Stochastic Optimal Ga...

63rd IEEE Conference on Decision and Control, CDC 2024

作者： Hyett, Criston Pagnier, Laurent Alisse, Jean Goldshtein, Igal Saban, Lilah Ferrando, Robert Chertkov, Michael University of Arizona Program in Applied Mathematics & Department of Mathematics TucsonAZ United States Noga the Israel Independent System Operator Haifa Israel

ISBN: (纸本)9798350316339

In many power systems, particularly those isolated from larger intercontinental grids, reliance on natural gas is crucial. This dependence becomes particularly critical during periods of volatility or scarcity in renewable energy sources, further complicated by unpredictable consumption trends. To ensure the uninterrupted operation of these isolated gas-grid systems, innovative and efficient management strategies are essential. This paper investigates the complexities of achieving synchronized, dynamic, and stochastic optimization for autonomous transmission-level gas-grid infrastructures. We introduce a novel methodology grounded in differentiable programming, which synergizes symbolic programming, a conservative numerical method for solving gas-flow partial differential equations, and automated sensitivity analysis powered by SciML/Julia. Our methodology refines the co-optimization landscape for gas-grid systems by grounding gas dynamics in physics-adherent simulation. We demonstrate efficiency and precision of the methodology by solving a stochastic optimal gas flow problem, phrased on an open source model of Israel's gas grid model. © 2024 IEEE.

关键词： Sensitivity analysis

Preface to the special issue dedicated to Saber Elaydi on the occasion of his 80th birthday

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Journal of Difference Equations and Applications 2024年第10期30卷 1397-1404页

作者： Cushing, Jim Michael Sasu, Adina Luminiţa Department of Mathematics Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States Department of Mathematics West University of Timişoara Timişoara Romania Academy of Romanian Scientists Bucharest Romania

System-Wide Emergency Policy for Transitioning from Main to Secondary Fuel 63

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System-Wide Emergency Policy for Transitioning from Main to ...

63rd IEEE Conference on Decision and Control, CDC 2024

作者： Pagnier, Laurent Hyett, Criston Ferrando, Robert Goldshtein, Igal Alisse, Jean Saban, Lilah Chertkov, Michael University of Arizona Graduate Interdisciplinary Program in Applied Mathematics and Department of Mathematics TucsonAZ85721 United States Noga the Israel Independent System Operator Haifa Israel

ISBN: (纸本)9798350316339

Faced with the complexities of managing natural gas-dependent power system amid the surge of renewable integration and load unpredictability, this study explores strategies for navigating emergency transitions to costlier secondary fuels. Our aim is to develop decision-support tools for operators during such exigencies. We approach the problem through a Markov Decision Process (MDP) framework, accounting for multiple uncertainties. These include the potential for dual-fuel generator failures and operator response during high-pressure situations. Additionally, we consider the finite reserves of primary fuel, governed by gas-flow partial differential equations (PDEs) and constrained by nodal pressure. Other factors include the variability in power forecasts due to renewable generation and the economic impact of compulsory load shedding. For tractability, we address the MDP in a simplified context, replacing it by Markov Processes evaluated against a selection of policies and scenarios for comparison. Our study considers two models for the natural gas system: an oversimplified model tracking linepack and a more nuanced model that accounts for gas flow network heterogeneity. The efficacy of our methods is demonstrated using a realistic model replicating Israel's power-gas infrastructure. © 2024 IEEE.

关键词： Markov processes

Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence

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arXiv 2024年

作者： Chertkov, Michael Program in Applied Mathematics University of Arizona Tucson United States

The paper reflects on the future role of AI in scientific research, with a special focus on turbulence studies, and examines the evolution of AI, particularly through Diffusion Models rooted in non-equilibrium statistical mechanics. It underscores the significant impact of AI on advancing reduced, Lagrangian models of turbulence through innovative use of Deep Neural Networks. Additionally, the paper reviews various other AI applications in turbulence research and outlines potential challenges and opportunities in the concurrent advancement of AI and statistical hydrodynamics. This discussion sets the stage for a future where AI and turbulence research are intricately intertwined, leading to more profound insights and advancements in both fields. Copyright © 2024, The Authors. All rights reserved.

关键词： Deep neural networks

Detection of latent brain states from spontaneous neural activity in the amygdala

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PLoS Computational Biology 2025年第2期21卷 e1012247页

作者： Aucoin, Alexa Lin, Kevin K. Gothard, Katalin M. Program in Applied Mathematics University of Arizona TucsonAZ United States Department of Mathematics University of Arizona TucsonAZ United States Department of Physiology University of Arizona TucsonAZ United States

The amygdala responds to a large variety of socially and emotionally salient environmental and interoceptive stimuli. The context in which these stimuli occur determines their social and emotional significance. In canonical neurophysiological studies, the fast-paced succession of stimuli and events induce phasic changes in neural activity. During inter-trial intervals neural activity is expected to return to a stable and featureless level of spontaneous activity, often called baseline. In previous studies we found that context, such as the presence of a social partner, induces brain states that can transcend the fast-paced succession of stimuli and can be recovered from the spontaneous, inter-trial firing rate of neurons. Indeed, the spontaneous firing rates of neurons in the amygdala are different during blocks of gentle grooming touches delivered by a trusted social partner, and during blocks of non-social airflow stimuli delivered by a computer-controlled air valve. Here, we examine local field potentials (LFPs) recorded during periods of spontaneous activity to determine whether information about context can be extracted from these signals. We found that information about social vs. non-social context is present in the local field potential during periods of spontaneous activity between the application of grooming and airflow stimuli, as machine learning techniques can reliably decode context from spectrograms of spontaneous LFPs. No significant differences were detected between the nuclei of the amygdala that receive direct or indirect inputs from areas of the prefrontal cortex known to coordinate flexible, context-dependent behaviors. The lack of nuclear specificity suggests that context-related synaptic inputs arise from a shared source, possibly interoceptive inputs, that signal the physiological state of the body during social and non-social blocks of tactile stimulation. © 2025 Aucoin et al. This is an open access article distributed under the terms of the

关键词： Neurons

Harmonic Path Integral Diffusion

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arXiv 2024年

作者： Behjoo, Hamidreza Chertkov, Michael Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States

Harmonic Path Integral Diffusion (H-PID) introduces a novel approach to sampling from complex, continuous probability distributions by creating a time-dependent "bridge" from an initial point to the target distribution. Formulated as a Stochastic Optimal Control problem, H-PID balances control effort and accuracy through a unique three-level integrable structure: Top Level: Potential, force, and gauge terms combine to form a linearly solvable Path Integral Control system based on Green functions. Mid Level: With quadratic potentials and affine force/gauge terms, the Green functions reduce to Gaussian forms, mirroring quantum harmonic oscillators in imaginary time. Bottom Level: For a uniform quadratic case, the optimal drift/control reduces to a convolution of the target distribution with a Gaussian kernel, enabling efficient sampling. Implementation-wise the low-level H-PID operates without neural networks, allowing it to run efficiently on standard CPUs while achieving high precision. Validated on Gaussian mixtures and CIFAR-10 images, H-PID reveals a "weighted state" parameter as an order parameter in a dynamic phase transition, signaling early completion of the sampling process. This feature positions H-PID as a strong alternative to traditional methods sampling, such as simulated annealing, particularly for applications that demand analytical control, computational efficiency, and scalability. In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space at t = 0, optimally transforming it into the target distribution at t = 1. We formulate this as a Stochastic Optimal Control problem of the Path Integral Control type, with a cost function comprising (in its basic form) a quadratic control term

关键词： Cost functions

Space-Time Diffusion Bridge

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arXiv 2024年

作者： Behjoo, Hamidreza Chertkov, Michael Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground Truth (GT) samples. Central to our method is the integration of space-time mixing strategies that extend across temporal and spatial dimensions. Our methodology is underpinned by three interrelated stochastic processes designed to enable optimal transport from an easily tractable initial probability distribution to the target distribution represented by the GT samples: (a) linear processes incorporating space-time mixing that yield Gaussian conditional probability densities, (b) their diffusion bridge analogs that are conditioned to the initial and final state vectors, and (c) nonlinear stochastic processes refined through score-matching techniques. The crux of our training regime involves fine-tuning the nonlinear model, and potentially the linear models – to align closely with the GT data. We validate the efficacy of our space-time diffusion approach with numerical experiments, laying the groundwork for more extensive future theory and experiments to fully authenticate the method, particularly providing a more efficient (possibly simulation-free) inference. © 2024, CC BY.

关键词： Stochastic systems

Asymptotic Quantum State Discrimination for Mixtures of Unitarily Related States.

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arXiv 2024年

作者： Acevedo, Alberto Wehr, Janek Program in Applied Mathematics The University of Arizona Tucson85721 United States Department of Mathematics The University of Arizona Tucson85721 United States

Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements of a one-parameter unitary group, and the corresponding quantum state discrimination (QSD) problems. We will be particularly interested in QSD as time goes to infinity. We first present an approach to QSD in the case of countable mixtures and address the respective asymptotic QSD optimization problems, proving necessary and sufficient conditions for minimal error to be obtained in the asymptotic regime (we say that in such a case QSD is fully solvable). We then outline an analogous approach to uncountable mixtures, presenting some conjectures that mirror the results presented for the cases of countable mixtures. As a technical tool, we prove and use an infinite dimensional version of the well-known Barnum-Knill bound [8]. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum communication

PHEONA: An Evaluation Framework for Large Language Model-based Approaches to Computational Phenotyping

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arXiv 2025年

作者： Pungitore, Sarah A. Yadav, Shashank Subbian, Vignesh Program in Applied Mathematics The University of Arizona TucsonAZ United States College of Engineering The University of Arizona TucsonAZ United States

Computational phenotyping is essential for biomedical research but often requires significant time and resources, especially since traditional methods typically involve extensive manual data review. While machine learning and natural language processing advancements have helped, further improvements are needed. Few studies have explored using Large Language Models (LLMs) for these tasks despite known advantages of LLMs for text-based tasks. To facilitate further research in this area, we developed an evaluation framework, Evaluation of PHEnotyping for Observational Health Data (PHEONA), that outlines context-specific considerations. We applied and demonstrated PHEONA on concept classification, a specific task within a broader phenotyping process for Acute Respiratory Failure (ARF) respiratory support therapies. From the sample concepts tested, we achieved high classification accuracy, suggesting the potential for LLM-based methods to improve computational phenotyping processes. © 2025, CC BY.

关键词： Electronic health record