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arXiv 2023年

作者： Hyett, Criston Pagnier, Laurent Alisse, Jean Sabban, Lilach Goldshtein, Igal Chertkov, Michael Applied Mathematics The University of Arizona United States The University of Arizona United States Paris University France The Technion Israel Institute of Technology The Graduate Interdisciplinary Program in Applied Mathematics The University of Arizona United States

We build and experiment with a realistic but reduced natural gas model of Israel. The system is unusual because (a) it is controlled from a limited number of points which are at, or close to, the gas extraction sites offshore of Israel's Mediterranean coast;(b) control specifies average flux at inlet, not pressure;(c) there are no inland compressors to regulate pressure;(d) power system is the main consumer of gas (70% of Israel's power is generated at gas-fired power plants distributed across the country). Nature of the system suggests that a special attention should be given to understanding dynamics driven by fast transients in gas consumption meeting intraday variations in the electricity demand, and accounting for increasing role of uncertain renewable generation (mainly solar). Based on all of the above we pose and resolve a sequence of dynamic and control challenges, such as: How to time ramping up- and down- injection of gas to guarantee a healthy intra-day line-pack which meets both pressure constraints and gas-extraction patterns? We report simulation results and utilize monotonicity properties of the natural gas flows which render robustness of our conclusions to the uncertainties of the edge withdrawals of gas. © 2023, CC BY-SA.

关键词： Gases

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Engaging Engineering mathematics students online: Tutoring using MS Teams

Engaging Engineering Mathematics students online: Tutoring u...

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2022 IEEE IFEES World Engineering Education Forum - Global Engineering Deans Council, WEEF-GEDC 2022

作者： Padayachee, Pragashni Campbell, Anita Fredericks, Ebrahim Academic Support Program in Engineering University of Cape Town Cape Town South Africa Centre for Research in Engineering Education University of Cape Town Cape Town South Africa Mathematics University of Cape Town Department of Mathematics and Applied Cape Town South Africa

ISBN: (纸本)9781665475280

Uncommon in the South African higher education landscape, online learning came to the fore during the global pandemic. We present an account of the use of Microsoft Teams for hybrid mathematics tutorials in a one-semester Vector Calculus course at a South African university in 2022. Interviews with the lecturer, analysed through a Community of Inquiry lens, showed the lecturer's perspective of the design and experience for tutors and students. Our aim is to improve the design of future hybrid tutorials to ensure engineering students' capacity in mathematics is well developed, their communication skills are improved, and that they experience working in a team. Future research will evaluate students' and tutors' accounts of their experiences. Our findings raise awareness of the possibilities and potential difficulties when using Microsoft Teams for communication, teaching and learning mathematics. © 2022 IEEE.

关键词： Students

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A Mathematical Framework for Learning Probability Distributions

arXiv

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arXiv 2022年

作者： Yang, Hongkang Program in Applied and Computational Mathematics Princeton University United States

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and texts. Nevertheless, a theoretical understanding of its success is still incomplete. One mystery is the paradox between memorization and generalization: In theory, the model is trained to be exactly the same as the empirical distribution of the finite samples, whereas in practice, the trained model can generate new samples or estimate the likelihood of unseen samples. Likewise, the overwhelming diversity of distribution learning models calls for a unified perspective on this subject. This paper provides a mathematical framework such that all the well-known models can be derived based on simple principles. To demonstrate its efficacy, we present a survey of our results on the approximation error, training error and generalization error of these models, which can all be established based on this framework. In particular, the aforementioned paradox is resolved by proving that these models enjoy implicit regularization during training, so that the generalization error at early-stopping avoids the curse of dimensionality. Furthermore, we provide some new results on landscape analysis and the mode collapse *** Codes 68T07, 62G05, 60-08 Copyright © 2022, The Authors. All rights reserved.

关键词： Probability distributions

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Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study

IEEE Transactions on Energy Markets, Policy and Regulation

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IEEE Transactions on Energy Markets, Policy and Regulation 2024年第1期2卷 40-51页

作者： Ferrando, Robert Pagnier, Laurent Mieth, Robert Liang, Zhirui Dvorkin, Yury Bienstock, Daniel Chertkov, Michael University of Arizona Program in Applied Mathematics and Department of Mathematics TucsonAZ85721 United States Department of Industrial and Systems Engineering at Rutgers University PiscatawayNJ08854 United States Johns Hopkins University Department of Electrical and Computer Engineering BaltimoreMD21218-2625 United States Elec. and Comp. Eng. and Ralph o'Connor Sustainable Energy Institute Department of Civil and Systems Engineering Johns Hopkins University BaltimoreMD21218-2625 United States Columbia University IEOR New YorkNY10027 United States

This article addresses the challenge of efficiently recovering exact solutions to the optimal power flow problem in real-time electricity markets. The proposed solution, named Physics-Informed Market-Aware Active Set learning OPF (PIMA-AS-OPF), leverages physical constraints and market properties to ensure physical and economic feasibility of market-clearing outcomes. Specifically, PIMA-AS-OPF employs the active set learning technique and expands its capabilities to account for curtailment in load or renewable power generation, which is a common challenge in real-world power systems. The core of PIMA-AS-OPF is a fully-connected neural network that takes the net load and the system topology as input. The outputs of this neural network include active constraints such as saturated generators and transmission lines, as well as non-zero load shedding and wind curtailments. These outputs allow for reducing the original market-clearing optimization to a system of linear equations, which can be solved efficiently and yield both the dispatch decisions and the locational marginal prices (LMPs). The dispatch decisions and LMPs are then tested for their feasibility with respect to the requirements for efficient market-clearing results. The accuracy and scalability of the proposed method is tested on a realistic 1814-bus NYISO system with current and future renewable energy penetration levels. © 2023 IEEE.

关键词： Costs

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Majorization theoretical approach to entanglement enhancement via local filtration

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Physical Review A 2024年第4期110卷 042430页

作者： Zacharie Van Herstraeten Nicolas J. Cerf Saikat Guha Christos N. Gagatsos Wyant College of Optical Sciences The Centre for Quantum Information and Communication École Polytechnique de Bruxelles CP 165 Department of Electrical and Computer Engineering Department of Electrical and Computer Engineering The Program in Applied Mathematics The

From the perspective of majorization theory, we study how to enhance the entanglement of a two-mode squeezed vacuum (TMSV) state by using local filtration operations. We present several schemes achieving entanglement enhancement with photon addition and subtraction, and then consider filtration as a general probabilistic procedure consisting in acting with local (nonunitary) operators on each mode. From this, we identify a sufficient set of two conditions for these filtration operators to successfully enhance the entanglement of a TMSV state, namely, the operators must be Fock orthogonal (i.e., preserving the orthogonality of Fock states) and Fock amplifying (i.e., giving larger amplitudes to larger Fock states). Our results notably prove that ideal photon addition, subtraction, and any concatenation thereof always enhance the entanglement of a TMSV state in the sense of majorization theory. We further investigate the case of realistic photon addition (subtraction) and are able to upper bound the distance between a realistic photon-added (-subtracted) TMSV state and a nearby state that is provably more entangled than the TMSV, thus extending entanglement enhancement to practical schemes via the use of a notion of approximate majorization. Finally, we consider the state resulting from k-photon addition (on each of the two modes) on a TMSV state. We prove analytically that the state corresponding to k=1 majorizes any state corresponding to 2≤k≤8 and we conjecture the validity of the statement for all k≥9.

关键词： Entanglement production Measures of continuous variables entanglement Quantum correlations, foundations & formalism Quantum entanglement

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Neural network representation of electronic structure from ab initio molecular dynamics

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Science Bulletin 2022年第1期67卷 29-37,M0003页

作者： Qiangqiang Gu Linfeng Zhang Ji Feng International Center for Quantum Materials School of PhysicsPeking UniversityBeijing 100871China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Collaborative Innovation Center of Quantum Matter Beijing 100871China

Despite their rich information content,electronic structure data amassed at high volumes in ab initio molecular dynamics simulations are generally *** introduce a transferable high-fidelity neural network representation of such data in the form of tight-binding Hamiltonians for crystalline *** predictive representation of ab initio electronic structure,combined with machinelearning boosted molecular dynamics,enables efficient and accurate electronic evolution and *** it is applied to a one-dimension charge-density wave material,carbyne,we are able to compute the spectral function and optical conductivity in the canonical *** spectral functions evaluated during soliton-antisoliton pair annihilation process reveal significant renormalization of low-energy edge modes due to retarded electron-lattice coupling beyond the Born-Oppenheimer *** availability of an efficient and reusable surrogate model for the electronic structure dynamical system will enable calculating many interesting physical properties,paving the way to previously inaccessible or challenging avenues in materials modeling.

关键词： Neural network Tight-binding model Electronic structure ab initio molecular dynamics

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Learning algorithms for mean field optimal control

arXiv

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arXiv 2025年

作者： Soner, H. Mete Teichmann, Josef Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Department of Mathematics ETH Zürich Switzerland Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an N-particle system and leverage the exchangeability of the particles to obtain substantial computational efficiency. In addition to several numerical examples, a convergence analysis is provided. We also developed a universal approximation theorem on Wasserstein *** Codes 35Q89, 35D40, 49L25, 60G99 © 2025, CC BY-NC-ND.

关键词： Optimal control systems

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Electrohydrodynamic flow about a colloidal particle suspended in a non-polar fluid

arXiv

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arXiv 2024年

作者： Wang, Zhanwen Miksis, Michael J. Vlahovska, Petia M. Theoretical and Applied Mechanics Program Northwestern University EvanstonIL60208 United States Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL60208 United States

Nonlinear electrokinetic phenomena, where electrically driven fluid flows depend nonlinearly on the applied voltage, are commonly encountered in aqueous suspensions of colloidal particles. A prime example is the induced-charge electro-osmosis, driven by an electric field acting on diffuse charge induced near a polarizable surface. Nonlinear electrohydrodynamic flows also occur in non-polar fluids, driven by the electric field acting on space charge induced by conductivity gradients. Here, we analyze the flows about a charge-neutral spherical solid particle in an applied uniform electric field that arise from conductivity dependence on local field intensity. The flow pattern varies with particle conductivity: while the flow about a conducting particle has a quadrupolar pattern similar to induced-charge electro-osmosis albeit with opposite direction, the flow about an insulating particle has a more complex structure. We find that this flow induces a force on a particle near an electrode that varies non-trivially with particle conductivity: while it is repulsive for perfectly insulating particle and particles more conductive than the suspending medium, there exists a range of particle conductivities where the force is attractive. The force decays as inverse square of the distance to the electrode and thus can dominate the dielectrophoretic attraction due to the image dipole, which falls off with the fourth power with the distance. This electrohydrodynamic lift opens new possibilities for colloidal manipulation and driven assembly by electric fields. © 2024, CC BY-NC-ND.

关键词： Electrohydrodynamics

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Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

引用

Physical Review B 2025年第9期111卷 094113-094113页

作者： Pinchen Xie Yixiao Chen Weinan E Roberto Car Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA AI for Science Institute Beijing China and Center for Machine Learning Research and School of Mathematical Sciences Peking University Beijing China

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

关键词： Ferroelectricity

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Low-Rank Decomposition of Plasma Kinetic Distributions in the Collisional Transition Regime

Low-Rank Decomposition of Plasma Kinetic Distributions in th...

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2022 IEEE International Conference on Plasma Science, ICOPS 2022

作者： Coughlin, J. Shumlak, U. Hu, J. University of Washington Applied Mathematics SeattleWA United States University of Washington Computational Plasma Dynamics Laboratory Aerospace and Energetics Research Program SeattleWA United States

ISBN: (纸本)9781665479257

The strength of collisional effects in a plasma can be summarized by the non-dimensional Knudsen number Kn. For very small values of Kn, plasma behavior is well-described by the 5N moment fluid model, including the Braginskii closure. When Kn is large, plasmas are best described by a fully kinetic model such as the Vlasov-Maxwell system. For intermediate values of the Knudsen number, i.e. 10-2 © 2022 IEEE.

关键词： Collisional plasmas

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