arXiv - STAT - Machine Learning最新文献_第9页

Modelling Global Trade with Optimal Transport 以最佳运输方式模拟全球贸易

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06554

Thomas Gaskin, Marie-Therese Wolfram, Andrew Duncan, Guven Demirel

引用次数: 0

Quasi-potential and drift decomposition in stochastic systems by sparse identification 通过稀疏识别进行随机系统中的准势垒和漂移分解

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06886

Leonardo Grigorio, Mnerh Alqahtani

{"title":"Quasi-potential and drift decomposition in stochastic systems by sparse identification","authors":"Leonardo Grigorio, Mnerh Alqahtani","doi":"arxiv-2409.06886","DOIUrl":"https://doi.org/arxiv-2409.06886","url":null,"abstract":"The quasi-potential is a key concept in stochastic systems as it accounts for\u0000the long-term behavior of the dynamics of such systems. It also allows us to\u0000estimate mean exit times from the attractors of the system, and transition\u0000rates between states. This is of significance in many applications across\u0000various areas such as physics, biology, ecology, and economy. Computation of\u0000the quasi-potential is often obtained via a functional minimization problem\u0000that can be challenging. This paper combines a sparse learning technique with\u0000action minimization methods in order to: (i) Identify the orthogonal\u0000decomposition of the deterministic vector field (drift) driving the stochastic\u0000dynamics; (ii) Determine the quasi-potential from this decomposition. This\u0000decomposition of the drift vector field into its gradient and orthogonal parts\u0000is accomplished with the help of a machine learning-based sparse identification\u0000technique. Specifically, the so-called sparse identification of non-linear\u0000dynamics (SINDy) [1] is applied to the most likely trajectory in a stochastic\u0000system (instanton) to learn the orthogonal decomposition of the drift.\u0000Consequently, the quasi-potential can be evaluated even at points outside the\u0000instanton path, allowing our method to provide the complete quasi-potential\u0000landscape from this single trajectory. Additionally, the orthogonal drift\u0000component obtained within our framework is important as a correction to the\u0000exponential decay of transition rates and exit times. We implemented the\u0000proposed approach in 2- and 3-D systems, covering various types of potential\u0000landscapes and attractors.","PeriodicalId":501340,"journal":{"name":"arXiv - STAT - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uncertainty Quantification in Seismic Inversion Through Integrated Importance Sampling and Ensemble Methods 通过综合重要度采样和集合方法量化地震反演中的不确定性

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06840

Luping Qu, Mauricio Araya-Polo, Laurent Demanet

{"title":"Uncertainty Quantification in Seismic Inversion Through Integrated Importance Sampling and Ensemble Methods","authors":"Luping Qu, Mauricio Araya-Polo, Laurent Demanet","doi":"arxiv-2409.06840","DOIUrl":"https://doi.org/arxiv-2409.06840","url":null,"abstract":"Seismic inversion is essential for geophysical exploration and geological\u0000assessment, but it is inherently subject to significant uncertainty. This\u0000uncertainty stems primarily from the limited information provided by observed\u0000seismic data, which is largely a result of constraints in data collection\u0000geometry. As a result, multiple plausible velocity models can often explain the\u0000same set of seismic observations. In deep learning-based seismic inversion,\u0000uncertainty arises from various sources, including data noise, neural network\u0000design and training, and inherent data limitations. This study introduces a\u0000novel approach to uncertainty quantification in seismic inversion by\u0000integrating ensemble methods with importance sampling. By leveraging ensemble\u0000approach in combination with importance sampling, we enhance the accuracy of\u0000uncertainty analysis while maintaining computational efficiency. The method\u0000involves initializing each model in the ensemble with different weights,\u0000introducing diversity in predictions and thereby improving the robustness and\u0000reliability of the inversion outcomes. Additionally, the use of importance\u0000sampling weights the contribution of each ensemble sample, allowing us to use a\u0000limited number of ensemble samples to obtain more accurate estimates of the\u0000posterior distribution. Our approach enables more precise quantification of\u0000uncertainty in velocity models derived from seismic data. By utilizing a\u0000limited number of ensemble samples, this method achieves an accurate and\u0000reliable assessment of uncertainty, ultimately providing greater confidence in\u0000seismic inversion results.","PeriodicalId":501340,"journal":{"name":"arXiv - STAT - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Applications of machine learning to predict seasonal precipitation for East Africa 应用机器学习预测东非季节性降水量

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06238

Michael Scheuerer, Claudio Heinrich-Mertsching, Titike K. Bahaga, Masilin Gudoshava, Thordis L. Thorarinsdottir

{"title":"Applications of machine learning to predict seasonal precipitation for East Africa","authors":"Michael Scheuerer, Claudio Heinrich-Mertsching, Titike K. Bahaga, Masilin Gudoshava, Thordis L. Thorarinsdottir","doi":"arxiv-2409.06238","DOIUrl":"https://doi.org/arxiv-2409.06238","url":null,"abstract":"Seasonal climate forecasts are commonly based on model runs from fully\u0000coupled forecasting systems that use Earth system models to represent\u0000interactions between the atmosphere, ocean, land and other Earth-system\u0000components. Recently, machine learning (ML) methods are increasingly being\u0000investigated for this task where large-scale climate variability is linked to\u0000local or regional temperature or precipitation in a linear or non-linear\u0000fashion. This paper investigates the use of interpretable ML methods to predict\u0000seasonal precipitation for East Africa in an operational setting. Dimension\u0000reduction is performed by decomposing the precipitation fields via empirical\u0000orthogonal functions (EOFs), such that only the respective factor loadings need\u0000to the predicted. Indices of large-scale climate variability--including the\u0000rate of change in individual indices as well as interactions between different\u0000indices--are then used as potential features to obtain tercile forecasts from\u0000an interpretable ML algorithm. Several research questions regarding the use of\u0000data and the effect of model complexity are studied. The results are compared\u0000against the ECMWF seasonal forecasting system (SEAS5) for three seasons--MAM,\u0000JJAS and OND--over the period 1993-2020. Compared to climatology for the same\u0000period, the ECMWF forecasts have negative skill in MAM and JJAS and significant\u0000positive skill in OND. The ML approach is on par with climatology in MAM and\u0000JJAS and a significantly positive skill in OND, if not quite at the level of\u0000the OND ECMWF forecast.","PeriodicalId":501340,"journal":{"name":"arXiv - STAT - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extending Explainable Ensemble Trees (E2Tree) to regression contexts 将可解释集合树（E2Tree）扩展到回归情境中

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06439

Massimo Aria, Agostino Gnasso, Carmela Iorio, Marjolein Fokkema

引用次数: 0

The Weak Form Is Stronger Than You Think 弱者比你想象的更强大

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06751

Daniel A. Messenger, April Tran, Vanja Dukic, David M. Bortz

引用次数: 0

Variational Search Distributions 变量搜索分布

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06142

Daniel M. Steinberg, Rafael Oliveira, Cheng Soon Ong, Edwin V. Bonilla

引用次数: 0

Joint trajectory and network inference via reference fitting 通过参考拟合进行联合轨迹和网络推理

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06879

Stephen Y Zhang

引用次数: 0

A Primer on Variational Inference for Physics-Informed Deep Generative Modelling 物理信息深度生成模型的变量推理入门指南

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06560

Alex Glyn-Davies, Arnaud Vadeboncoeur, O. Deniz Akyildiz, Ieva Kazlauskaite, Mark Girolami

{"title":"A Primer on Variational Inference for Physics-Informed Deep Generative Modelling","authors":"Alex Glyn-Davies, Arnaud Vadeboncoeur, O. Deniz Akyildiz, Ieva Kazlauskaite, Mark Girolami","doi":"arxiv-2409.06560","DOIUrl":"https://doi.org/arxiv-2409.06560","url":null,"abstract":"Variational inference (VI) is a computationally efficient and scalable\u0000methodology for approximate Bayesian inference. It strikes a balance between\u0000accuracy of uncertainty quantification and practical tractability. It excels at\u0000generative modelling and inversion tasks due to its built-in Bayesian\u0000regularisation and flexibility, essential qualities for physics related\u0000problems. Deriving the central learning objective for VI must often be tailored\u0000to new learning tasks where the nature of the problems dictates the conditional\u0000dependence between variables of interest, such as arising in physics problems.\u0000In this paper, we provide an accessible and thorough technical introduction to\u0000VI for forward and inverse problems, guiding the reader through standard\u0000derivations of the VI framework and how it can best be realized through deep\u0000learning. We then review and unify recent literature exemplifying the creative\u0000flexibility allowed by VI. This paper is designed for a general scientific\u0000audience looking to solve physics-based problems with an emphasis on\u0000uncertainty quantification.","PeriodicalId":501340,"journal":{"name":"arXiv - STAT - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Deep Neural Networks: Multi-Classification and Universal Approximation 深度神经网络：多分类和通用逼近

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI: arxiv-2409.06555

Martín Hernández, Enrique Zuazua

引用次数: 0