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Optimization via simulation has been well established to find optimal solutions and designs in complex systems. However, it still faces modeling and computational challenges when extended to the multi-stage setting. This survey reviews the…

Optimization and Control · Mathematics 2023-12-08 Zhuo Zhang , Dan Wang , Haoxiang Yang , Shubin Si

Processes in ocean physics, air-sea interaction and ocean biogeochemistry span enormous ranges in spatial and temporal scales, that is, from molecular to planetary and from seconds to millennia. Identifying and implementing sustainable…

Methodology · Statistics 2013-12-23 Christopher K. Wikle , Ralph F. Milliff , Radu Herbei , William B. Leeds

Software development processes are subject to variations in time and space, variations that can originate from learning effects, differences in application domains, or a number of other causes. Identifying and analyzing such differences is…

Software Engineering · Computer Science 2014-01-21 Martín Soto , Jürgen Münch

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

Optimization and Control · Mathematics 2021-05-25 George I. Boutselis , Ethan N. Evans , Marcus A. Pereira , Evangelos A. Theodorou

Molecular Dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively…

Biomolecules · Quantitative Biology 2023-07-20 Diego E. Kleiman , Hassan Nadeem , Diwakar Shukla

Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…

We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…

Numerical Analysis · Mathematics 2021-11-18 Luca Heltai , Alfonso Caiazzo

Nowadays, the amount of heterogeneous biomedical data is increasing more and more thanks to novel sensing techniques and high-throughput technologies. In reference to biomedical image analysis, the advances in image acquisition modalities…

Image and Video Processing · Electrical Eng. & Systems 2021-06-09 Leonardo Rundo

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Methodology · Statistics 2019-08-13 Itai Dattner , Shota Gugushvili , Harold Ship , Eberhard O. Voit

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…

Dynamical Systems · Mathematics 2008-11-25 Jinqiao Duan

The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in modern scientific problems from, for instance, weather and climate prediction, neurology, epidemiology, and turbulence. Multi-scale data is…

Dynamical Systems · Mathematics 2026-05-27 Karl Lapo , Sara M. Ichinaga , Nathan Kutz

Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale…

Quantitative Methods · Quantitative Biology 2015-08-27 Ulrike E. Schlägel , Mark A. Lewis

One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks - and how can…

Computational Engineering, Finance, and Science · Computer Science 2015-10-20 Dagmar Iber , Zahra Karimaddini , Erkan Ünal

We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…

Computational Engineering, Finance, and Science · Computer Science 2008-09-23 Armen Bagdasaryan

Computational models provide crucial insights into complex biological processes such as cancer evolution, but their mechanistic nature often makes them nonlinear and parameter-rich, complicating calibration. We systematically evaluate…

Analysis of PDEs · Mathematics 2025-09-24 Christina Schenk , Jacobo Ayensa Jiménez , Ignacio Romero

Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…

Biomolecules · Quantitative Biology 2026-01-13 Shreyas Arvindekar , Kartik Majila , Shruthi Viswanath

With recent advances in structural biology, including experimental techniques and deep learning-enabled high-precision structure predictions, molecular dynamics methods that scale up to large biomolecular systems are required. Current…

Biological Physics · Physics 2022-06-24 Tim Hempel , Simon Olsson , Frank Noé

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

Machine Learning · Computer Science 2023-09-20 Elizabeth J Cross , Timothy J Rogers , Daniel J Pitchforth , Samuel J Gibson , Matthew R Jones

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…

Quantitative Methods · Quantitative Biology 2025-08-01 Jun Won Park , Kangyu Zhao , Sanket Rane

Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing…

Methodology · Statistics 2021-05-27 Carles Bretó , Edward L. Ionides , Aaron A. King