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Scalable Solvers of Random Quadratic Equations via Stochastic Truncated Amplitude Flow

Gang Wang, Georgios B. Giannakis, Jie Chen
2017 IEEE Transactions on Signal Processing  

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2016 pre-print arXiv:1610.09540v1 fatcat:72yi4g3ctvem5ogyiuayfeawcq
A novel approach termed stochastic truncated amplitude flow (STAF) is developed to reconstruct an unknown n-dimensional real-/complex-valued signal x from m 'phaseless' quadratic equations of the form  ...  ; and, s2) A series of iterative refinements of the initialization using stochastic truncated gradient iterations.  ...  Truncated Amplitude Flow In this section, the two stages of TAF are outlined [17] .  ... 
doi:10.1109/tsp.2017.2652392 fatcat:ndb3pnyr2fcq7ban4jaisfeixu
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Gang Wang, Georgios B. Giannakis, Jie Chen. "Scalable Solvers of Random Quadratic Equations via Stochastic Truncated Amplitude Flow." IEEE Transactions on Signal Processing 65.8 (2017) 1961-1974

Solving Large-Scale Systems Of Random Quadratic Equations Via Stochastic Truncated Amplitude Flow

Jie Chen, Georgios B. Giannakis, Gang Wang
2018 Zenodo  

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Publication in the conference proceedings of EUSIPCO, Kos island, Greece, 2017  ...  STOCHASTIC TRUNCATED AMPLITUDE FLOW To begin, relevant concepts are introduced. If x ∈ R n solves (1), so does −x.  ...  Truncated amplitude flow In this section, the two stages of TAF are first reviewed [8] .  ... 
doi:10.5281/zenodo.1159277 fatcat:omxho2grarblvfk2kqpldphihq
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Jie Chen, Georgios B. Giannakis, Gang Wang. "Solving Large-Scale Systems Of Random Quadratic Equations Via Stochastic Truncated Amplitude Flow." Zenodo (2018)

Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow [article]

Gang Wang and Georgios B. Giannakis and Yonina C. Eldar
2017 arXiv   pre-print

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2016 pre-print
arXiv:1605.08285v1 fatcat:srhy2gdte5b3bjpo2uat7zy4sm
2016 pre-print
arXiv:1605.08285v3 fatcat:acxfdu2aj5dtjjqlajkaft6dhi
2016 pre-print
arXiv:1605.08285v2 fatcat:yo4txmqwmjaedibb4bzn334ske
2016 pre-print
arXiv:1605.08285v4 fatcat:3yl4tao22zdfxoh3x7vi2f4qsi
This paper presents a new algorithm, termed truncated amplitude flow (TAF), to recover an unknown vector x from a system of quadratic equations of the form y_i=|〈a_i,x〉|^2, where a_i's are given random  ...  Stage two refines the initial estimate by successive updates of scalable truncated generalized gradient iterations, which are able to handle the rather challenging nonconvex and nonsmooth amplitude-based  ...  John Duchi for pointing out an error in an initial draft of this paper. We also thank Mahdi Soltanolkotabi, Yuxin Chen, Kejun Huang, and Ju Sun for helpful discussions.  ... 
arXiv:1605.08285v5 fatcat:lisjm5cj55a2zlesjiirua3bxy
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Gang Wang and Georgios B. Giannakis and Yonina C. Eldar. "Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow." arXiv (2017)

Solving Almost all Systems of Random Quadratic Equations [article]

Gang Wang and Georgios B. Giannakis and Yousef Saad and Jie Chen
2017 arXiv   pre-print

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This paper deals with finding an n-dimensional solution x to a system of quadratic equations of the form y_i=|〈a_i,x〉|^2 for 1< i < m, which is also known as phase retrieval and is NP-hard in general.  ...  equations, namely, m=2n-1 in the real-valued Gaussian case; and, ii) (nearly) optimal statistical accuracy in the presence of additive noise of bounded support.  ...  CONCLUSIONS This paper put forth a linear-time algorithm termed reweighted amplitude flow (RAF) for solving systems of random quadratic equations.  ... 
arXiv:1705.10407v1 fatcat:khpmh6kwfrezlmv7itz2m5mye4
Citation

Gang Wang and Georgios B. Giannakis and Yousef Saad and Jie Chen. "Solving Almost all Systems of Random Quadratic Equations." arXiv (2017)

Sparse Phase Retrieval via Truncated Amplitude Flow [article]

Gang Wang and Liang Zhang and Georgios B. Giannakis and Mehmet Akcakaya and Jie Chen
2017 arXiv   pre-print

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2016 pre-print
arXiv:1611.07641v1 fatcat:minneggkivefxgzmdmpy4nldxq
This paper develops a novel algorithm, termed SPARse Truncated Amplitude flow (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements.  ...  SPARTA is a simple yet effective, scalable, and fast sparse PR solver.  ...  Xiaodong Li for sharing the codes of the thresholded Wirtinger flow algorithm.  ... 
arXiv:1611.07641v2 fatcat:wyrx4rugtzh6nkjk2zu5oivwdu
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Gang Wang and Liang Zhang and Georgios B. Giannakis and Mehmet Akcakaya and Jie Chen. "Sparse Phase Retrieval via Truncated Amplitude Flow." arXiv (2017)

Scalable Methods for Computing Sharp Extreme Event Probabilities in Infinite-Dimensional Stochastic Systems [article]

Timo Schorlepp, Shanyin Tong, Tobias Grafke, Georg Stadler
2023 arXiv   pre-print

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2023 pre-print arXiv:2303.11919v1 fatcat:cvcsir7f2rbt7hnndw5eghyre4

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2023 accepted
doi:10.1007/s11222-023-10307-2 arXiv:2303.11919v3 fatcat:gv3tabe3efhzlfb2p57i6unjpq
To study the performance of the methods, we consider examples of stochastic differential and stochastic partial differential equations, including the randomly forced incompressible three-dimensional Navier-Stokes  ...  The method estimates the limiting exponential scaling using a single realization of the random variable, the large deviation minimizer.  ...  T.S. acknowledges the support received from the Ruhr University Research School, funded by Germany's Excellence Initiative [DFG GSC 98/3], that enabled a research visit at the Courant Institute of Mathematical  ... 
arXiv:2303.11919v2 fatcat:ix5i7daitradfd6tg5ib6sftym
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Timo Schorlepp, Shanyin Tong, Tobias Grafke, Georg Stadler. "Scalable Methods for Computing Sharp Extreme Event Probabilities in Infinite-Dimensional Stochastic Systems." arXiv (2023)

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

Paris Perdikaris, George Em Karniadakis
2016 Journal of the Royal Society Interface  

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The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one-and three-dimensional models, whereas the  ...  We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian  ...  In the first two cases, consider the important aspect of calibrating outflow boundary conditions of blood flow simulations in truncated arterial domains.  ... 
doi:10.1098/rsif.2015.1107 pmid:27194481 pmcid:PMC4892258 fatcat:az5ko72p3vendl2rw45kky2h2e
Citation

Paris Perdikaris, George Em Karniadakis. "Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond." Journal of the Royal Society Interface 13.118 (2016) 20151107

2018 Index IEEE Transactions on Automatic Control Vol. 63

2018 IEEE Transactions on Automatic Control  

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., +, TAC Jan. 2018 262-268 A Numerically Stable Solver for Positive Semidefinite Quadratic Programs Based on Nonnegative Least Squares.  ...  ., +, TAC March 2018 672-681 Structure Preserving Truncation of Nonlinear Port Hamiltonian Systems.  ... 
doi:10.1109/tac.2019.2896796 fatcat:bwmqasulnzbwhin5hv4547ypfe
Citation

"2018 Index IEEE Transactions on Automatic Control Vol. 63." IEEE Transactions on Automatic Control 63.12 (2018) 4453-4509

On closures for reduced order models - A spectrum of first-principle to machine-learned avenues [article]

Shady E. Ahmed, Suraj Pawar, Omer San, Adil Rasheed, Traian Iliescu, Bernd R. Noack
2021 arXiv   pre-print

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2021 pre-print
arXiv:2106.14954v1 fatcat:ubqh4ghflraqrekkrmbidfpcbm
Early examples include Galerkin models inspired by the Orr-Sommerfeld stability equation and numerous vortex models, of which the von K\'arm\'an vortex street is one of the most prominent.  ...  Finally, we outline our vision on how state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.  ...  In other words, the projection of the flow field onto the truncated space is treated as a realization or sample of the stochastic component of the flow and is modeled using Brownian motion.  ... 
arXiv:2106.14954v2 fatcat:q6jzbxfjabc3vg3nsn24z4lbyy
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Shady E. Ahmed, Suraj Pawar, Omer San, Adil Rasheed, Traian Iliescu, Bernd R. Noack. "On closures for reduced order models - A spectrum of first-principle to machine-learned avenues." arXiv (2021)

On Aronsson Equation and Deterministic Optimal Control

Pierpaolo Soravia
2008 Applied Mathematics and Optimization  

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We prove the existence of a solution to a free boundary problem modeling blood flow in viscoelastic arteries.  ...  The second equation describes the rate of change of the manufacturer's inventory. The last equation describes a retailer's inventory. Problems of profit maximization are stated and solved.  ...  MS18 Scalable Nonlinear Multigrid Solvers for Inverse Reaction-Diffusion Problems In this talk we present multigrid smoothers for saddle-point Euler Lagrange equations related to inverse problems for systems  ... 
doi:10.1007/s00245-008-9048-7 fatcat:kihxqtczfzdn5pbmvsd42axbk4
Citation

Pierpaolo Soravia. "On Aronsson Equation and Deterministic Optimal Control." Applied Mathematics and Optimization 59.2 (2008) 175-201

A Survey of Quantum Computing for Finance [article]

Dylan Herman, Cody Googin, Xiaoyuan Liu, Alexey Galda, Ilya Safro, Yue Sun, Marco Pistoia, Yuri Alexeev
2022 arXiv   pre-print

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2022 pre-print
arXiv:2201.02773v1 fatcat:mg337iaiz5ebronqmxtsiu6n4e
2022 pre-print
arXiv:2201.02773v2 fatcat:um2gpdwpcnbndiyullazt2ygx4
2022 pre-print
arXiv:2201.02773v3 fatcat:aqcl6blbyvbljg627ot6zxtaj4
This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning  ...  We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance.  ...  The evolution of such stochastic processes is governed by stochastic differential equations (SDEs), and stochastic modeling aims to solve the SDEs for the expectation value of a certain random variable  ... 
arXiv:2201.02773v4 fatcat:e5hon5dy4bgmbgrizs6isx7y5u
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Dylan Herman, Cody Googin, Xiaoyuan Liu, Alexey Galda, Ilya Safro, Yue Sun, Marco Pistoia, Yuri Alexeev. "A Survey of Quantum Computing for Finance." arXiv (2022)

7 Data-driven methods for reduced-order modeling [chapter]

2020 Snapshot-Based Methods and Algorithms  

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The selection of observables (features) for the DMD/Koopman architecture can yield accurate low-dimensional embeddings for nonlinear partial differential equations (PDEs) while limiting computational costs  ...  activity, (ii) embed the dynamics in the subspace in an equation-free manner (i. e., the governing equations are unknown), unlike Galerkin projection onto proper orthogonal decomposition modes, and (iii  ...  However, for very large data sets, DMD can leverage randomized methods [55, 85, 48] to produce a scalable randomized DMD [49, 18] .  ... 
doi:10.1515/9783110671490-007 fatcat:wc6wctzwnfcnznb4scr6s5lyou
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"7 Data-driven methods for reduced-order modeling." Snapshot-Based Methods and Algorithms (2020) 307-344

Koopman von Neumann mechanics and the Koopman representation: A perspective on solving nonlinear dynamical systems with quantum computers [article]

Yen Ting Lin, Robert B. Lowrie, Denis Aslangil, Yiğit Subaşı, Andrew T. Sornborger
2022 arXiv   pre-print

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2022 pre-print
arXiv:2202.02188v1 fatcat:26l2ut653zehbj7cnd3lfkfxz4
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function  ...  We also aim to show that, despite the fact that quantum simulation of nonlinear classical systems may be possible with such linear representations, a necessary projection into a feasible finite-dimensional  ...  Security Administration of the U.S.  ... 
arXiv:2202.02188v2 fatcat:4fm7bp6hfbe5lkxeumqa42wipu
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Yen Ting Lin, Robert B. Lowrie, Denis Aslangil, Yiğit Subaşı, Andrew T. Sornborger. "Koopman von Neumann mechanics and the Koopman representation: A perspective on solving nonlinear dynamical systems with quantum computers." arXiv (2022)

Measurement Based Feedback Quantum Control With Deep Reinforcement Learning for Double-well Non-linear Potential [article]

Sangkha Borah, Bijita Sarma, Michael Kewming, Gerard J. Milburn, Jason Twamley
2021 arXiv   pre-print

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2021 pre-print
arXiv:2104.11856v1 fatcat:ltij7c2ccngqzdwh7bymbk2cm4
In the case when the quantum Hamiltonian is quadratic in x and p, there are known optimal control techniques to drive the dynamics towards particular states e.g. the ground state.  ...  Closed loop quantum control uses measurement to control the dynamics of a quantum system to achieve either a desired target state or target dynamics.  ...  GJM and MK acknowledge the support of the Australian Research Council Centre of Excellence for Engineered Quantum Systems CE170100009.  ... 
arXiv:2104.11856v2 fatcat:6dcsmoe7qvbvze2txlvsuacf44
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Sangkha Borah, Bijita Sarma, Michael Kewming, Gerard J. Milburn, Jason Twamley. "Measurement Based Feedback Quantum Control With Deep Reinforcement Learning for Double-well Non-linear Potential." arXiv (2021)

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  

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The model is based on Navier-Stokes equations for viscous incompressible flow and convection-diffusion equation describing pollution transport.  ...  We develop a mathematical model of air flow and pollution transport in 2D street canyon.  ...  , is discretised via stochastic Galerkin and stochastic collocation techniques.  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e
Citation

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz. "Numerical Stabilization of the Melt Front for Laser Beam Cutting." Numerical Mathematics and Advanced Applications 2009 (2010) 69-76

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