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Spectral Galerkin method for solving elastic wave scattering problems with multiple open arcs

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arXiv 2022年

作者： Jerez-Hanckes, Carlos Pinto, José Yin, Tao Facultad de Ingeniería y Ciencias Universidad Adolfo Ibáñez Santiago Chile LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin method for solving the associated weakly- and hyper-singular boundary integral equations (BIEs) arising from Dirichlet and Neumann boundary conditions, respectively. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions' edge behavior. We show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arcs geometries. Numerical examples demonstrate the accuracy and robustness of the proposed method with respect to number of arcs and wavenumber. © 2022, CC BY-NC-SA.

关键词： Elastic waves

Spectral Galerkin Method for Solving Elastic Wave Scattering Problems with Multiple Open Arcs

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SSRN

SSRN 2022年

作者： Jerez-Hanckes, Carlos Pinto, José Yin, Tao Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Diagonal Las Torres 2700 Peñalolén Santiago Chile Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin method for solving the associated weakly- and hyper-singular boundary integral equations (BIEs) arising from Dirichlet and Neumann boundary conditions, respectively. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions’ edge behavior. We show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arcs geometries. Numerical examples demonstrate the accuracy and robustness of the proposed method with respect to number of arcs and wavenumber. © 2022, The Authors. All rights reserved.

关键词： Boundary integral equations

PRefLexOR: preference-based recursive language modeling for exploratory optimization of reasoning and agentic thinking

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npj Artificial Intelligence

npj Artificial Intelligence 2025年第1期1卷 1-38页

作者： Markus J. Buehler Center for Computational Science and Engineering Schmarzman College of Computing Laboratory for Atomistic and Molecular Mechanics (LAMM) Massachusetts Institute of Technology Cambridge MA USA

We introduce PRefLexOR (Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that integrates preference optimization with reinforcement learning (RL) concepts for self-improving scientific reasoning. PRefLexOR employs a recursive approach, refining intermediate steps before producing final outputs in training and inference. It optimizes log odds between preferred and non-preferred responses using an in-situ dataset generation algorithm. A dynamic knowledge graph contextualizes reasoning with retrieval-augmented data. Preference optimization enhances performance via rejection sampling, masking reasoning steps to focus on discovery. Recursive optimization, guided by feedback loops, refines reasoning. This process mirrors biological adaptation, enabling real-time learning. We find that even small models (3B parameters) self-teach deeper reasoning, solving open-domain problems effectively. Our method integrates into existing LLMs and demonstrates success in biological materials science, leveraging multi-agent self-improvement for enhanced reasoning depth and cross-domain adaptability, offering flexibility and integration into larger agentic systems.

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Generative modeling, design and analysis of spider silk protein sequences for enhanced mechanical properties

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arXiv 2023年

作者： Lu, Wei Kaplan, David L. Buehler, Markus J. Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States Department of Civil and Environmental Engineering Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States Tufts University MedfordMA United States Center for Computational Science and Engineering Schwarzman College of Computing Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States

Spider silks are remarkable materials characterized by superb mechanical properties such as strength, extensibility and lightweightedness. Yet, to date, limited models are available to fully explore sequence-property relationships for analysis and design. Here we propose a custom generative large-language model to enable design of novel spider silk protein sequences to meet complex combinations of target mechanical properties. The model, pretrained on a large set of protein sequences, is fine-tuned on ~1,000 major ampullate spidroin (MaSp) sequences for which associated fiber-level mechanical properties exist, to yield an end-to-end forward and inverse generative strategy. Performance is assessed through: (1), a novelty analysis and protein type classification for generated spidroin sequences through BLAST searches, (2) property evaluation and comparison with similar sequences, (3) comparison of molecular structures, as well as, and (4) a detailed sequence motif analyses. We generate silk sequences with property combinations that do not exist in nature, and develop a deep understanding the mechanistic roles of sequence patterns in achieving overarching key mechanical properties (elastic modulus, strength, toughness, failure strain). The model provides an efficient approach to expand the silkome dataset, facilitating further sequence-structure analyses of silks, and establishes a foundation for synthetic silk design and optimization. © 2023, CC BY.

关键词： Proteins

Joint design of hybrid beamforming and reflection coefficients in RIS-aided mmWave MIMO systems

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arXiv 2022年

作者： Li, Renwang Guo, Bei Tao, Meixia Liu, Ya-Feng Yu, Wei Department of Electronic Engineering Shanghai Jiao Tong University Shanghai China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Electrical and Engineering University of Toronto TorontoONM5S 3G4 Canada

This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under the signalto-interference-plus-noise ratio (SINR) constraints at all users. The problem is highly challenging to solve due to the nonconvex SINR constraints as well as the unit-modulus phase shift constraints for both the RIS reflection coefficients and the analog beamformer. A two-layer penalty-based algorithm is proposed to decouple variables in SINR constraints, and manifold optimization is adopted to handle the non-convex unitmodulus *** also propose a low-complexity sequential optimization method, which optimizes the RIS reflection coefficients, the analog beamformer, and the digital beamformer sequentially without iteration. Furthermore, the relationship between the power minimization problem and the max-min fairness (MMF) problem is discussed. Simulation results show that the proposed penalty-based algorithm outperforms the stateof-the-art semidefinite relaxation (SDR)-based algorithm. Results also demonstrate that the RIS plays an important role in the power reduction. Copyright © 2022, The Authors. All rights reserved.

关键词： Millimeter waves

Minimum tracking linear response Hubbard and Hund corrected Density Functional Theory in CP2K

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arXiv 2024年

作者： Chai, Ziwei Si, Rutong Chen, Mingyang Teobaldi, Gilberto O'Regan, David D. Liu, Li-Min Beijing Computational Science Research Center Beijing100193 China School of Physics Beihang University Beijing100191 China School of Materials Science and Engineering University of Science and Technology Beijing Beijing100083 China Scientific Computing Department STFC UKRI Rutherford Appleton Laboratory Harwell Campus DidcotOX11 0QX United Kingdom School of Physics SFI AMBER Centre CRANN Institute Trinity College Dublin The University of Dublin Ireland

We present the implementation of the Hubbard (U) and Hund (J) corrected Density Functional Theory (DFT+U+J) functionality in the Quickstep program, which is part of the CP2K suite. The tensorial and Löwdin subspace representations are implemented and compared. Full analytical DFT+U+J forces are implemented and benchmarked for the tensorial and Löwdin representations. We also present the implementation of the recently proposed minimum-tracking linear-response method that enables the U and J parameters to be calculated on first principles basis without reference to the Kohn-Sham eigensystem. These implementations are benchmarked against recent results for different materials properties including DFT+U band gap opening in NiO, the relative stability of various polaron distributions in TiO2, the dependence of the calculated TiO2 band gap on +J corrections, and, finally, the role of the +U and +J corrections for the computed properties of a series of the hexahydrated transition metals. Our implementation provides results consistent with those already reported in the literature from comparable methods. We conclude the contribution with tests on the influence of the Löwdin orthonormalization on the occupancies, calculated parameters, and derived properties. © 2024, CC BY.

关键词： Titanium dioxide

Generative retrieval-augmented ontologic graph and multi-agent strategies for interpretive large language model-based materials design

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arXiv 2023年

作者： Buehler, Markus J. Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States Department of Civil and Environmental Engineering Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States Center for Computational Science and Engineering Schwarzman College of Computing Massachusetts Institute of Technology 77 Massachusetts Ave. CambridgeMA02139 United States

Transformer neural networks show promising capabilities, in particular for uses in materials analysis, design and manufacturing, including their capacity to work effectively with both human language, symbols, code, and numerical data. Here we explore the use of large language models (LLMs) as a tool that can support engineering analysis of materials, applied to retrieving key information about subject areas, developing research hypotheses, discovery of mechanistic relationships across disparate areas of knowledge, and writing and executing simulation codes for active knowledge generation based on physical ground truths. When used as sets of AI agents with specific features, capabilities, and instructions, LLMs can provide powerful problem solution strategies for applications in analysis and design problems. Our experiments focus on using a fine-tuned model, MechGPT, developed based on training data in the mechanics of materials domain. We first affirm how finetuning endows LLMs with reasonable understanding of domain knowledge. However, when queried outside the context of learned matter, LLMs can have difficulty to recall correct information. We show how this can be addressed using retrieval-augmented Ontological Knowledge Graph strategies that discern how the model understands what concepts are important and how they are related. Illustrated for a use case of relating distinct areas of knowledge – here, music and proteins – such strategies can also provide an interpretable graph structure with rich information at the node, edge and subgraph level. We discuss nonlinear sampling strategies and agent-based modeling applied to complex question answering, code generation and execution in the context of automated force field development from actively learned Density Functional Theory (DFT) modeling, and data analysis. © 2023, CC BY-NC-SA.

关键词： Modeling languages

4D-Precise: Learning-Based 3D Motion Estimation and High Temporal Resolution 4DCT Reconstruction from In-Treatment 2D t X-Ray Projections

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SSRN

SSRN 2023年

作者： Zakeri, Arezoo Hokmabadi, Alireza Nix, Michael G. Gooya, Ali Wijesinghe, Isuru Taylor, Zeike A. Centre for Computational Imaging and Simulation Technologies in Biomedicine School of Computing University of Leeds Leeds United Kingdom Department of Infection Immunity & Cardio Disease University of Sheffield Sheffield United Kingdom Leeds Cancer Centre Leeds Teaching Hospitals NHS Trust United Kingdom School of Computing Science University of Glasgow Glasgow United Kingdom Alan Turing Institute London United Kingdom Centre for Computational Imaging and Simulation Technologies in Biomedicine School of Mechanical Engineering University of Leeds Leeds United Kingdom

Background and Objective: In radiotherapy treatment planning, respiration-induced motion introduces uncertainty that, if not appropriately considered, could result in dose delivery problems. 4D cone-beam computed tomography (4D-CBCT) has been developed to provide imaging guidance by reconstructing a pseudo-motion sequence of CBCT volumes through binning projection data into breathing phases. However, it suffers from artefacts and erroneously characterizes the averaged breathing motion. Furthermore, conventional 4D-CBCT can only be generated post-hoc using the full sequence of kV projections after the treatment is complete, limiting its utility. Hence, our purpose is to develop a deep-learning motion model for estimating 3D+t CT images from kV projection series during ***: We propose an end-to-end learning-based 3D motion modelling and 4DCT reconstruction model named 4D-Precise, abbreviated from \textbf{P}robabilistic \textbf{rec}onstruction of \textbf{i}mage \textbf{se}quences from CBCT kV projections. The model estimates voxel-wise motion fields and simultaneously reconstructs a 3DCT volume at any arbitrary time point of the input projections by transforming a reference CT volume. Developing a Torch-DRR module, it enables end-to-end training by computing Digitally Reconstructed Radiographs (DRRs) in PyTorch. During training, DRRs with matching projection angles to the input kVs are automatically extracted from reconstructed volumes and their structural dissimilarity to inputs is penalised. We introduced a novel loss function to regulate spatio-temporal motion field variations across the CT scan, leveraging planning 4DCT for prior motion distribution ***: The model is trained patient-specifically using three kV scan series, each including over 1200 angular/temporal projections, and tested on three other scan series. Imaging data from five patients are analysed here. Also, the model is validated on a simulated paired 4DCT-DRR dataset and

关键词： Computerized tomography

***: A Comprehensive Genomic Visualisation Database for Malaysian Species

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***: A Comprehensive Genomic Visualisation Database for Mala...

2022 IEEE International Conference on computing, ICOCO 2022

作者： Chan, Vei Siang Mohamed, Farhan Bin Salleh, Faezah Mohd Iglesias, Andres Wagiran, Alina Binti Selamat, Ali Bin Universiti Teknologi Malaysia School of Computing Faculty of Engineering Johor Bahru Malaysia Universiti Teknologi Malaysia Media and Game Innovation Center of Excellence Johor Bahru Malaysia Universiti Teknologi Malaysia Dept. of Biosciences Faculty of Science Johor Bahru Malaysia University of Cantabria Dept. of Applied Mathematics and Computational Sciences Santander Spain University of Technology Malaysia Malaysia-Japan International Institute of Technology Kuala Lumpur Malaysia

ISBN: (纸本)9781665489966

Malaysia is one of the most megadiverse regions in the world. Therefore, it is important to record these rich biodiversity data to safeguard and improve national conservation efforts. However, the lack of nationwide genomic sequencing hampers a more sophisticated species identification, data management, and analytics activities. Thus, this project aims to design and implement ***, a comprehensive one-stop online DNA reference database with integrated DNA visualisation and digital references to allow the users to search, retrieve and analyse the collected DNA sequencing data interactively. This paper documented the system architecture and implementation methods to create ***. The results of *** can display taxonomy information of biodiversity in the web's user interfaces and visualise the complex set of DNA data to allow new insights. Lastly, the authors identified several future works to improve *** including improve user interaction, add visualisation methods to support more bioinformatics tasks, and conduct formal user evaluation. © 2022 IEEE.

关键词： Taxonomies