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A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

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Communications on applied mathematics and Computation 2023年第1期5卷 403-427页

作者： Liang Li Jun Zhu Chi-Wang Shu Yong-Tao Zhang Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Applied and Computational Mathematics and Statistics University of Notre DameNotre DameIN 46556USA

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local ***,they are easy to be applied to a general hyperbolic *** deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the *** this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing *** experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the *** results show highorder accuracy and good performance of the ***,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state *** examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

关键词： Fixed-point fast sweeping methods Multi-resolution WENO schemes Steady state ILW procedure Convergence

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CLEARING SECTIONS OF LATTICE LIABILITY NETWORKS

arXiv

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arXiv 2025年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Riess, Hans Department of Mathematics and Electrical & Systems Engineering University of Pennsylvania Philadelphia PA Department of Mathematics University of Pennsylvania Philadelphia PA Applied Mathematics & Computational Science University of Pennsylvania Philadelphia PA School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA

Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present a mathematical framework that unifies and extends these scenarios by recasting the classical Eisenberg-Noe model of financial clearing in terms of lattice liability networks. Each node in the network carries a complete lattice of possible states, while edges encode nominal liabilities. Our framework generalizes the scalar-valued clearing vectors of the classical model to lattice-valued clearing sections, preserving the elegant fixed-point structure while dramatically expanding its descriptive power. Our main theorem establishes that such networks possess clearing sections that themselves form a complete lattice under the product order. This structure theorem enables tractable analysis of equilibria in diverse domains, including multi-currency financial systems, decentralized finance with automated market makers, supply chains with resource transformation, and permission networks with complex authorization structures. We further extend our framework to chain-complete lattices for term structure models and multivalued mappings for complex negotiation systems. Our results demonstrate how lattice theory provides a natural language for understanding complex network dynamics across multiple domains, creating a unified mathematical foundation for analyzing systemic risk, resource allocation, and network *** Codes 91G40, 06B23, 91D30, 68Q85 Copyright © 2025, The Authors. All rights reserved.

关键词： Lattice theory

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New insight into pyrrolic-N site effect towards the first NIR window absorption of pyrrolic-N-rich carbon dots

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Nano Research 2023年第4期16卷 6001-6009页

作者： Fitri Aulia Permatasari Reza Umami Citra Deliana Dewi Sundari Tirta Rona Mayangsari Atthar Luqman Ivansyah Fahdzi Muttaqien Takashi Ogi Ferry Iskandar Department of Physics Faculty Mathematics and Natural SciencesInstitut Teknologi BandungJalan Ganesha 10BandungWest Java 40132Indonesia Collaboration Research Center for Advanced Energy Materials National Research and Innovation Agency-Institut Teknologi BandungJalan Ganesha 10BandungWest Java 40132Indonesia Department of Chemistry Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJl.Ganesha 10BandungWest Java 40132Indonesia Department of Chemistry Education UIN Sunan Gunung Djati BandungJl.CimincrangBandungWest Java 40292Indonesia Department of Chemistry Universitas PertaminaJakarta 12220Indonesia Master Program in Computational Science Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJl.Ganesha 10BandungWest Java 40132Indonesia Instrumentation and Computational Physics Research Group Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJl.Ganesha 10Bandung 40132Indonesia Research Center for Nanoscience and Nanotechnology Institut Teknologi BandungJalan Ganesha 10BandungWest Java 40132Indonesia Chemical Engineering Program Department of Advanced Science and EngineeringGraduate School of Advanced Science and EngineeringHiroshima UniversityHigashi-Hiroshima 739-8527Japan

Controlled C-N configurations,i.e.,pyrrolic-N,pyridinic-N,and graphitic-N,are promising strategies to tailor the carbon dots’(CDs)optical properties into the first near infrared(NIR)window(650-900 nm),a responsive range for biomedical ***,a deep understanding of the role of the C-N configuration in the CDs’properties is still challenging and thoughtprovoking owing to their complex ***,an underlying pyrrolic-N concentration and position effect on the pyrrolic-N-rich CDs’absorption was comprehensively elucidated based on the integrated experimental and computational *** assynthesized pyrrolic-N-rich CDs exhibit a first NIR window absorption centered at 650 nm with high photothermal ***-N concentrations from 1.4%to 11.3%and positions(edge and mid-site)were systematically investigated.A mid-site pyrrolic-N was subsequently generated after the pyrrolic-N concentration more than 10%.Edge-site pyrrolic-N induces a frontier orbital hybridization,reducing bandgap energy,while mid-site pyrrolic-N plays a critical role in inducing a first NIR window absorption owing to their high charge ***,pyrrolic-N-rich CDs inherit a bowl-like topological feature,elevating the CDs’layer thickness as much as 0.71 *** study shed light on the design and optimization of pyrrolic-N on CDs for the first NIR window responsive materials in any biomedical application.

关键词： absorption carbon dots charge transfer first near infrared(NIR)window frontier orbital hybridization mid-site pyrrolic-N

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

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

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IEEE Conference on Decision and Control

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

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

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.

关键词： Renewable energy sources Uncertainty Navigation Biological system modeling Partial differential equations Power systems Fuels Surges Natural gas Load modeling

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Nonparametric estimation of non-crossing quantile regression process with deep ReQU neural networks

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 4314-4388页

作者： Guohao Shen Yuling Jiao Yuanyuan Lin Joel L. Horowitz Jian Huang Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong SAR China School of Mathematics and Statistics and Hubei Key Laboratory of Computational Science Wuhan University Wuhan China Department of Statistics The Chinese University of Hong Kong Hong Kong SAR China Department of Economics Northwestern University Evanston IL Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong SAR China

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating Cs smooth functions with s > 1 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests for nonparametric quantile regression.

关键词： approximation error quantile process deep neural networks monotonic constraints non-asymptotic error bound

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Stochastic Exploration of Real Varieties via Variety Distributions

arXiv

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arXiv 2024年

作者： Kahle, David Hauenstein, Jonathan D. Department of Statistical Science Baylor University United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States

Nonlinear systems of polynomial equations arise naturally in many applied settings, for example loglinear models on contingency tables and Gaussian graphical models. The solution sets to these systems over the reals are often positive dimensional spaces that in general may be very complicated yet have very nice local behavior almost everywhere. Standard methods in real algebraic geometry for describing positive dimensional real solution sets include cylindrical algebraic decomposition and numerical cell decomposition, both of which can be costly to compute in many practical applications. In this work we communicate recent progress towards a Monte Carlo framework for exploring such real solution sets. After describing how to construct probability distributions whose mass focuses on a variety of interest, we describe how Hamiltonian Monte Carlo methods can be used to sample points near the variety that may then be moved to the variety using endgames. We conclude by showcasing trial experiments using practical implementations of the method in the Bayesian engine Stan. Copyright © 2024, The Authors. All rights reserved.

关键词： Monte Carlo methods

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MEAN FIRST PASSAGE TIMES FOR TRANSPORT EQUATIONS

arXiv

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arXiv 2024年

作者： Hillen, Thomas D’Orsogna, Maria R. Mantooth, Jacob C. Lindsay, Alan E. Department of Mathematics University of Alberta Canada Department of Mathematics California State University at Northridge Los AngelesCA91330 United States Deptartment of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame IN46656 United States

Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that allow for various diffusive forms and geometries but where only initial and final positions are taken into account. Here, we develop a general theory for the mean first passage time (MFPT) for velocity jump processes. For random walkers, both position and velocity are tracked and the resulting Fokker-Planck equation takes the form of a kinetic transport equation. Starting from the forward and backward formulations we derive a general elliptic integro-PDE for the MFPT of a random walker starting at a given location with a given velocity. We focus on two scenarios that are relevant to biological modelling;the diffusive case and the anisotropic case. For the anisotropic case we also perform a parabolic scaling, leading to a well known anisotropic MFPT equation. To illustrate the results we consider a two-dimensional circular domain under radial symmetry, where the MFPT equations can be solved explicitly. Furthermore, we consider the MFPT of a random walker in an ecological habitat that is perturbed by linear features, such as wolf movement in a forest habitat that is crossed by seismic lines. © 2024, CC BY.

关键词： Fokker Planck equation

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Hardware Acceleration for HPS Algorithms in Two and Three Dimensions

arXiv

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arXiv 2025年

作者： Melia, Owen Fortunato, Daniel Hoskins, Jeremy Willett, Rebecca Department of Computer Science University of Chicago United States Center for Computational Mathematics Flatiron Institute United States Center for Computational Biology Flatiron Institute United States Data Science Institute University of Chicago United States Computational and Applied Mathematics Department of Statistics University of Chicago United States

We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU;in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [2019] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems. © 2025, CC BY.

关键词： Graphics processing unit

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LINFA: A PYTHON LIBRARY FOR VARIATIONAL INFERENCE WITH NORMALIZING FLOW AND ANNEALING

arXiv

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arXiv 2023年

作者： Wang, Yu Cobian, Emma R. Lee, Jubilee Liu, Fang Hauenstein, Jonathan D. Schiavazzi, Daniele E. Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States

Variational inference is an increasingly popular method in statistics and machine learning for approximating probability distributions. We developed LINFA (Library for Inference with Normalizing Flow and Annealing), a Python library for variational inference to accommodate computationally expensive models and difficult-to-sample distributions with dependent parameters. We discuss the theoretical background, capabilities, and performance of LINFA in various benchmarks. LINFA is publicly available on GitHub at https://***/desResLab/LINFA. Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

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Unraveling energy and charge transfer in type-II van der Waals heterostructures

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npj computational Materials 2021年第1期7卷 1774-1782页

作者： Junyi Liu Zi Li Xu Zhang Gang Lu Department of Physics and Astronomy California State UniversityNorthridgeCA 91330-8268USA Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088China

Recent experiments observed significant energy transfer in type-II van der Waals(vdW)heterostructures,such as WS_(2)/MoSe_(2),which is surprising due to their staggered band alignment and weak spectral *** this work,we carry out first-principles calculations to shed light on energy and charge transfer in WS_(2)/MoSe_(2) *** excitonic effect in nonadiabatic electronic dynamics,our first-principles calculations uncover a two-step process in competing energy and charge transfer,unravel their relative efficiencies and explore the means to control their *** both Dexter and Förster mechanisms can be responsible for energy transfer,they are shown to operate at different *** excitonic effect is revealed to drive ultrafast energy and charge transfer in type-II WS_(2)/MoSe_(2) *** work provides a comprehensive picture of exciton dynamics in vdW heterostructures and paves the way for rational design of novel vdW heterostructures for optoelectronic and photovoltaic applications.

关键词： transfer energy charge

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