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Data-driven method to learn the most probable transition pathway and stochastic differential equations

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arXiv 2021年

作者： Chen, Xiaoli Duan, Jinqiao Hu, Jianyu Li, Dongfang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mathematics National University of Singapore 119077 Singapore Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States

Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. We introduce the Onsager-Machlup theory and the Freidlin-Wentzell theory to quantify rare events in stochastic differential equations. By the variational principle, the most probable transition pathway is the minimizer of the action functional, which is governed by the Euler-Lagrange equation. In this paper, the physics-informed neural networks (PINNs) are presented to compute the most probable transition pathway through computing the Euler-Lagrange equation. The convergence result for the empirical loss is obtained for the forward problem. Then we investigate the inverse problem to extract the stochastic differential equation from the most probable transition pathway data. Finally, several numerical experiments are presented to verify the effectiveness of our methods. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

Stochastic Optimisation Framework using the Core Imaging Library and Synergistic Image Reconstruction Framework for PET Reconstruction

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arXiv 2024年

作者： Papoutsellis, Evangelos da Costa-Luis, Casper Deidda, Daniel Delplancke, Claire Duff, Margaret Fardell, Gemma Gillman, Ashley Jorgensen, Jakob S. Kereta, Zeljko Ovtchinnikov, Evgueni Pasca, Edoardo Schramm, Georg Thielemans, Kris Finden Ltd Rutherford Appleton Laboratory Harwell Campus United Kingdom Scientific Computing Department Science & Technology Facilities Council Harwell Campus United Kingdom National Physical Laboratory Electricité de France Research and Development France Australian e-Health Res. Ctr. CSIRO BrisbaneQLD Australia Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Department of Computer Science University College London United Kingdom Department of Imaging and Pathology Division of Nuclear Medicine KU Leuven Leuven Belgium Institute of Nuclear Medicine University College London United Kingdom

We introduce a stochastic framework into the open- source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic Average Gradient (-Amélioré), (Loopless) Stochastic Variance Reduced Gradient. We showcase the functionality of the framework with a comparative study against a deterministic algorithm on a simulated 2D PET dataset, with the use of the open-source Synergistic Image Reconstruction Framework. We observe that stochastic optimisation methods can converge in fewer passes of the data than a standard deterministic algorithm1. © 2024, CC BY.

关键词： Positron emission tomography

Hardware-Assisted Parameterized Circuit Execution

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arXiv 2024年

作者： Rajagopala, Abhi D. Hashim, Akel Fruitwala, Neelay Huang, Gang Xu, Yilun Hines, Jordan Siddiqi, Irfan Klymko, Katherine Nowrouzi, Kasra Applied Math and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Accelerator Technology and Applied Physics Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Physics University of California at Berkeley BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States National Energy Research Scientific Computing Center Lawrence Berkeley National Lab BerkeleyCA94720 United States

Standard compilers for quantum circuits decompose arbitrary single-qubit gates into a sequence of physical Xπ/2 pulses and virtual-Z phase gates. Consequently, many circuit classes implement different logic operations but have an equivalent structure of physical pulses that only differ by changes in virtual phases. When many structurally-equivalent circuits need to be measured, generating sequences for each circuit is unnecessary and cumbersome, since compiling and loading sequences onto classical control hardware is a primary bottleneck in quantum circuit execution. In this work, we develop a hardware-assisted protocol for executing parameterized circuits on our FPGA-based control hardware, QubiC. This protocol relies on a hardware-software co-design technique in which software identifies structural equivalency in circuits and "peels" off the relevant parameterized angles to reduce the overall waveform compilation time. The hardware architecture then performs real-time "stitching" of the parameters in the circuit to measure circuits that implement a different overall logical operation. This work demonstrates significant speed ups in the total execution time for several different classes of quantum circuits. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum computers

Salvinia-like slippery surface with stable and mobile water/air contact line

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National Science Review 2021年第5期8卷 119-129页

作者： Xiaomei Li Jinlong Yang Kaixuan Lv Periklis Papadopoulos Jing Sun Dehui Wang Yanhua Zhao Longquan Chen Dapeng Wang Zuankai Wang Xu Deng Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of China State Key Laboratory of Polymer Physics and Chemistry Institute of Applied ChemistryChinese Academy of Sciences Physics Department University of Ioannina University Research Center of Ioannina (URCI) Institute of Materials Science and Computing Department of Mechanical Engineering City University of Hong Kong School of Physics University of Electronic Science and Technology of China

Superhydrophobic surfaces are widely used in many industrial settings, and mainly consist of rough solid protrusions that entrap air to minimize the liquid/solid area. The stability of the superhydrophobic state favors relatively small spacing between protrusions. However, this in turn increases the lateral adhesion force that retards the mobility of drops. Here we propose a novel approach that optimizes both properties simultaneously. Inspired by the hydrophobic leaves of Salvinia molesta and the slippery Nepenthes pitcher plants, we designed a Salvinia-like slippery surface(SSS) consisting of protrusions with slippery heads. We demonstrate that compared to a control surface, the SSS exhibits increased stability against pressure and impact, and enhanced lateral mobility of water drops as well as reduced hydrodynamic drag. We also systematically investigate the wetting dynamics on the SSS. With its easy fabrication and enhanced performance, we envision that SSS will be useful in a variety of fields in industry.

关键词： slippery Cassie state Salvinia molesta stability low adhesion drag reduction

ADER Methods for Hyperbolic Equations with a Time-Reconstruction Solver for the Generalized Riemann Problem: the Scalar Case

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Communications on applied Mathematics and Computation 2020年第3期2卷 369-402页

作者： R.Demattè V.A.Titarev G.I.Montecinos E.F.Toro Department of Aerospace Science and Technology Politecnico di MilanoMilanItaly Dorodnicyn Computing Center Federal Research Center Computer Science and ControlRussianAcademy of SciencesMoscowRussia Departamento de Ciencias Naturales y Tecnología Universidad de AysénCoyhaiqueChile Laboratory of Applied Mathematics DICAMUniversity of TrentoTrentoItaly

The ADER approach to solve hyperbolic equations to very high order of accuracy has seen explosive developments in the last few years,including both methodological aspects as well as very ambitious *** spite of methodological progress,the issues of efficiency and ease of implementation of the solution of the associated generalized Riemann problem(GRP)remain the centre of attention in the ADER *** the original formulation of ADER schemes,the proposed solution procedure for the GRP was based on(i)Taylor series expansion of the solution in time right at the element interface,(ii)subsequent application of the Cauchy-Kowalewskaya procedure to convert time derivatives to functionals of space derivatives,and(iii)solution of classical Riemann problems for high-order spatial derivatives to complete the Taylor series *** realistic problems the Cauchy-Kowalewskaya procedure requires the use of symbolic manipulators and being rather cumbersome its replacement or simplification is highly *** this paper we propose a new class of solvers for the GRP that avoid the Cauchy-Kowalewskaya procedure and result in simpler ADER *** is achieved by exploiting the history of the numerical solution that makes it possible to devise a time-reconstruction procedure at the element *** relying on a time Taylor series expansion of the solution at the interface,the time derivatives are then easily calculated from the time-reconstruction *** resulting schemes are called ADER-TR.A thorough study of the linear stability properties of the linear version of the schemes is carried out using the von Neumann method,thus deducing linear stability ***,via careful numerical experiments,we deduce stability regions for the corresponding non-linear *** examples using the present simplified schemes of fifth and seventh order of accuracy in space and time show that these compare favourably with conventional ADER ***

关键词： Hyperbolic equations Finite volume ADER methods Generalized Riemann problem(GRP) Time-reconstruction(TR)

FUSDREAMER: Label-efficient Remote Sensing World Model for Multimodal Data Classification

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arXiv 2025年

作者： Wang, Jinping Song, Weiwei Chen, Hao Ren, Jinchang Zhao, Huimin School of Computer Sciences Guangdong Polytechnic Normal University Guangzhou510665 China Guangdong Provincial Key Laboratory of Intellectual Property and Big Data Guangdong Polytechnic Normal University Guangzhou510665 China Peng Cheng Laboratory Shenzhen518000 China Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom School of Computer Sciences Guangdong Polytechnic Normal University Guangzhou510640 China National Subsea Centre School of Computing Engineering and Technology Robert Gordon University AberdeenAB10 7AQ United Kingdom

World models significantly enhance hierarchical understanding, improving data integration and learning efficiency. To explore the potential of the world model in the remote sensing (RS) field, this paper proposes a label-efficient remote sensing world model for multimodal data fusion (FusDreamer). The FusDreamer uses the world model as a unified representation container to abstract common and high-level knowledge, promoting interactions across different types of data, i.e., hyperspectral (HSI), light detection and ranging (LiDAR), and text data. Initially, a new latent diffusion fusion and multimodal generation paradigm (LaMG) is utilized for its exceptional information integration and detail retention capabilities. Subsequently, an open-world knowledge-guided consistency projection (OK-CP) module incorporates prompt representations for visually described objects and aligns language-visual features through contrastive learning. In this way, the domain gap can be bridged by fine-tuning the pre-trained world models with limited samples. Finally, an end-to-end multitask combinatorial optimization (MuCO) strategy can capture slight feature bias and constrain the diffusion process in a collaboratively learnable direction. Experiments conducted on four typical datasets indicate the effectiveness and advantages of the proposed FusDreamer. The corresponding code will be released at https://***/ Cimy-wang/FusDreamer. © 2025, CC BY.

关键词： Contrastive Learning

A Modified PRP-HS Hybrid Conjugate Gradient Algorithm for Solving Unconstrained Optimization Problems

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应用数学 2025年第2期38卷 553-564页

作者： LI Xiangli WANG Zhiling LI Binglan School of Mathematics and Computing Science Guilin University of Electronic TechnologyGuilin 541004China Guangxi Colleges and University Key Laboratory of Data Analysis Guilin 541004China Center for Applied Mathmatics of Guangxi Guilin 541004China

In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient *** the condition of standard Wolfe line search,the proposed search direction is the descent *** general nonlinear functions,the method is globally ***,numerical results show that the proposed method is efficient.

关键词： Conjugate gradient method Unconstrained optimization Sufficient descent condition Global convergence

A scalable superconducting quantum simulator with long-range connectivity based on a photonic-bandgap metamaterial

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arXiv 2022年

作者： Zhang, Xueyue Kim, Eunjong Mark, Daniel K. Choi, Soonwon Painter, Oskar Thomas J. Watson Sr. Laboratory of Applied Physics Kavli Nanoscience Institute California Institute of Technology PasadenaCA91125 United States Institute for Quantum Information and Matter California Institute of Technology PasadenaCA91125 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States Aws Center for Quantum Computing PasadenaCA91125 United States

Synthesis of many-body quantum systems in the laboratory can help provide further insight into the emergent behavior of quantum materials [1-3], whose properties may provide improved methods for energy conversion, signal transport, or information processing [4]. While the majority of engineerable many-body systems, or quantum simulators, consist of particles on a lattice with local interactions, quantum systems featuring long-range interactions [5-7] are particularly challenging to model and interesting to study due to the rapid spatio-temporal growth of quantum entanglement and correlations [8, 9]. Here, we present a scalable quantum simulator architecture based on a linear array of superconducting qubits locally connected to an extensible photonic-bandgap metamaterial. The metamaterial acts both as a quantum bus mediating qubit-qubit interactions [10], and as a readout channel for multiplexed qubit-state measurement. As an initial demonstration, we realize a 10-qubit simulator of the one-dimensional Bose-Hubbard model with in situ tunability of both the hopping range and the on-site interaction. We characterize the Hamiltonian of the system using a measurement-efficient protocol based on quantum many-body chaos [11]. Further, we study the many-body quench dynamics of the system, revealing through global bit-string statistics [12] the predicted crossover from integrability to ergodicity as the hopping range increases. The metamaterial quantum bus architecture presented here can be extended to two-dimensional lattice systems [13] and used to generate a wide range of qubit interactions [10, 14], expanding the accessible Hamiltonians for analog quantum simulation and increasing the flexibility in implementing quantum circuits for gate-based computations [15-18]. Copyright © 2022, The Authors. All rights reserved.

关键词： Energy gap

Automating gamification personalization: To the user and beyond

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arXiv 2021年

作者： Rodrigues, Luiz Toda, Armando M. Oliveira, Wilk Palomino, Paula T. Vassileva, Julita Isotani, Seiji Laboratory of Applied Computing to Education and Advanced Social Technology Institute of Mathematics and Computer Science University of São Paulo São Carlos Brazil Lab Department of Computer Science University of Saskatchewan Saskatoon Canada

Personalized gamification explores knowledge about the users to tailor gamification designs to improve one-size-fits-all gamification. The tailoring process should simultaneously consider user and contextual characteristics (e.g., activity to be done and geographic location), which leads to several occasions to tailor. Consequently, tools for automating gamification personalization are needed. The problems that emerge are that which of those characteristics are relevant and how to do such tailoring are open questions, and that the required automating tools are lacking. We tackled these problems in two steps. First, we conducted an exploratory study, collecting participants’ opinions on the game elements they consider the most useful for different learning activity types (LAT) via survey. Then, we modeled opinions through conditional decision trees to address the aforementioned tailoring process. Second, as a product from the first step, we implemented a recommender system that suggests personalized gamification designs (which game elements to use), addressing the problem of automating gamification personalization. Our findings i) present empirical evidence that LAT, geographic locations, and other user characteristics affect users’ preferences, ii) enable defining gamification designs tailored to user and contextual features simultaneously, and iii) provide technological aid for those interested in designing personalized gamification. The main implications are that demographics, game-related characteristics, geographic location, and LAT to be done, as well as the interaction between different kinds of information (user and contextual characteristics), should be considered in defining gamification designs and that personalizing gamification designs can be improved with aid from our recommender system. © 2021, CC BY.

关键词： Recommender systems