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Multilevel Particle Filters for Partially Observed McKean-Vlasov Stochastic Differential Equations

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arXiv 2024年

作者： Awadelkarim, Elsiddig Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

NOMAD: Nonlinear Manifold Decoders for Operator Learning

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arXiv 2022年

作者： Seidman, Jacob H. Kissas, Georgios Perdikaris, Paris Pappas, George J. Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost. © 2022, CC BY-NC-SA.

关键词： Benchmarking

Ranking docked models of protein-protein complexes using predicted partner-specific protein-protein interfaces: A preliminary study 11

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Ranking docked models of protein-protein complexes using pre...

2011 ACM Conference on Bioinformatics, computational Biology and Biomedicine, ACM-BCB 2011

作者： Xue, Li C. Jordan, Rafael A. El-Manzalawy, Yasser Dobbs, Drena Honavar, Vasant Bioinformatics and Computational Biology Program Iowa State University Ames IA 50011 United States Department of Genetics Development and Cell Biology Iowa State University Ames 50011 United States Department of Computer Science Iowa State University Ames IA 50011 United States Department of Computer Science Pontificia Universidad Javeriana Cali Colombia Department of Systems and Computer Engineering AI-Azhar University Cairo Egypt

ISBN: (纸本)9781450307963

computational protein-protein docking is a valuable tool for determining the conformation of complexes formed by interacting proteins. Selecting near-native conformations from the large number of possible models generated by docking software presents a significant challenge in practice. We introduce a novel method for ranking docked conformations based on the degree of overlap between the interface residues of a docked conformation formed by a pair of proteins with the set of predicted interface residues between them. Our approach relies on a method, called PS-HomPPI, for reliably predicting proteinprotein interface residues by taking into account information derived from both interacting proteins. PS-HomPPI infers the residues of a query protein that are likely to interact with a partner protein based on known interface residues of the homo-interologs of the query-partner protein pair, i.e., pairs of interacting proteins that are homologous to the query protein and partner protein. Our results on Docking Benchmark 3.0 show that the quality of the ranking of docked conformations using our method is consistently superior to that produced using ClusPro cluster-size-based and energy-based criteria for 61 out of the 64 docking complexes for which PS-HomPPI produces interface predictions. An implementation of our method for ranking docked models is freely available at: http://***/DockRank/. Copyright © 2011 ACM.

关键词： Proteins

A layered scripting language technique for avatar behavior representation and control

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A layered scripting language technique for avatar behavior r...

13th International Conference on AIS 2004

作者： Kim, Jae-Kyung Sohn, Won-Sung Cho, Beom-Joon Lim, Soon-Bum Choy, Yoon-Chul Dept. of Computer Science Yonsei University Shinchon-dong Seodaemun-gu 120-749 Seoul Korea Republic of Computational Design Program School of Architecture Carnegie Mellon University Pittsburgh PA 15213 United States Department of Computer Engineering Chosun University Kwangju Korea Republic of Department of Multimedia Science Sookmyung Women's University Chungpa-dong Yongsan-gu 140-742 Seoul Korea Republic of

The paper proposes a layered scripting language technique for representation and control of avatar behavior for simpler avatar control in various domain environments. We suggest three layered architecture which is consisted of task-level behavior, high-level motion, and primitive motion script language. These layers brides gap between application domain and implementation environments, so that end user can control the avatar through easy and simple task-level scripting language without concerning low-level animation and the script can be applied various implementations regardless of application domain types. Our goal is to support flexible and extensible representation and control of avatar behavior by layered approach separating application domains and implementation tools. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Computer programming languages

Stochastic Dynamics and Probability Analysis for a Generalized Epidemic Model with Environmental Noise

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arXiv 2024年

作者： Boukanjime, Brahim Maama, Mohamed Laboratory of Mathematical Modeling and Economic Calculations Hassan First University of Settat Morocco Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia

In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global positive solution to the model, ensuring that it remains well-defined over time. Through the application of Young’s inequality and Chebyshev’s inequality, we demonstrate the concepts of stochastic ultimate boundedness and stochastic permanence, providing insights into the long-term behavior of the epidemic dynamics under random perturbations. Furthermore, we derive conditions for stochastic extinction, which describes scenarios where the epidemic may eventually die out, and V-geometric ergodicity, which indicates the rate at which the system’s state converges to its equilibrium. Finally, we perform numerical simulations to verify our theoretical results and assess the model’s behavior under different parameters. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic models

Opportunities and Challenges from Using Animal Videos in Reinforcement Learning for Navigation

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IFAC-PapersOnLine 2023年第2期56卷 9056-9061页

作者： Vittorio Giammarino James Queeney Lucas C. Carstensen Michael E. Hasselmo Ioannis Ch Paschalidis Division of Systems Engineering Boston University Boston MA 02215 USA Center for Systems Neuroscience Department of Psychological and Brain Sciences and Graduate Program for Neuroscience Boston University Boston MA 02215 USA College of Engineering and Hariri Institute for Computing & Computational Science & Engineering Boston University Boston MA 02215 USA

We investigate the use of animal videos (observations) to improve Reinforcement Learning (RL) efficiency and performance in navigation tasks with sparse rewards. Motivated by theoretical considerations, we make use of weighted policy optimization for off-policy RL and describe the main challenges when learning from animal videos. We propose solutions and test our ideas on a 2D navigation task. We show how the use of animal videos improves performance over RL algorithms that do not leverage such observations.

关键词： Learning for Control Reinforcement Learning Deep Learning RL with demonstrations Imitation Learning Bio-inspired Control

Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

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arXiv 2023年

作者： Jasra, Ajay Kamatani, Kengo Maama, Mohamed Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Ordinary differential equations

Multiscale modeling in rodent ventricular myocytes

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Multiscale modeling in rodent ventricular myocytes

作者： Lu, Shaoying Michailova, Anushka Saucerman, Jeffrey Cheng, Yuhui Yu, Zeyun Kaiser, Timothy Li, Wilfred Bank, Randolph Holst, Michael McCammon, J. Hayashi, Takeharu Hoshijima, Masahiko Arzberger, Peter McCulloch, Andrew Bioengineering Department University of Illinois United States Bioengineering Department UCSD United States Department of Biomedical Engineering University of Virginia United States Department of Mathematics UCSD United States UCSD United States College of Computer Science and Technology Jilin University China Department of Mathematics Center for Computational Mathematics and the Computational Science Mathematics and Engineering Doctoral Program at UCSD Department of Pharmacology UCSD United States Center for Research in Biological Systems UCSD United States Department of Bioengineering UCSD United States Department of Bioengineering PFBH 241 University of California San Diego 9500 Gilman Drive San Diego CA 92093-0412 United States

There is a growing body of experimental evidence suggesting that the Ca2+ signaling in ventricular myocytes is characterized by a high gradient near the cell membrane and a more uniform Ca2+ distribution in the cell interior [1]--[7]. An important reason for this phenomenon might be that in these cells the t-tubular system forms a network of extracellular space, extending deep into the cell interior. This allows the electrical signal, that propagates rapidly along the cell membrane, to reach the vicinity of the sarcoplasmic reticulum (SR), where intracellular Ca2+ required for myofilament activation is stored [1], [8]--[11]. Early studies of cardiac muscle showed that the t-tubules are found at intervals of about 2 lm along the longitudinal cell axis in close proximity to the Z-disks of the sarcomeres [12]. Subsequent studies have demonstrated that the t-tubular system has also longitudinal extensions [9]--[11], [13].

关键词： Cells

An analysis of reconstruction noise from undersampled 4D flow MRI

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arXiv 2022年

作者： Partin, Lauren Schiavazzi, Daniele E. Long, Carlos A. Sing Department Of Applied And Computational Mathematics And Statistics University Of Notre Dame Notre DameIN United States Institute For Mathematical And Computational Engineering Institute For Biological And Medical Engineering Pontificia Universidad Católica De Chile Santiago Chile ANID - Millennium Science Initiative Program Millennium Nucleus Center For The Discovery Of Structures In Complex Data Chile ANID - Millennium Science Initiative Program Millennium Nucleus Center For Cardiovascular Magnetic Resonance Chile

Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction methods from undersampled measurements are routinely used, that leverage representations designed to increase image compressibility. Reconstructed anatomical and hemodynamic images may present visual artifacts. Although some of these artifact are essentially reconstruction errors, and thus a consequence of undersampling, others may be due to measurement noise or the random choice of the sampled frequencies. Said otherwise, a reconstructed image becomes a random variable, and both its bias and its covariance can lead to visual artifacts;the latter leads to spatial correlations that may be misconstrued for visual information. Although the nature of the former has been studied in the literature, the latter has not received as much attention. In this study, we investigate the theoretical properties of the random perturbations arising from the reconstruction process, and perform a number of numerical experiments on simulated and MR aortic flow. Our results show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with recovery algorithms based on 1-norm minimization. However, the correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., 8× or 16× compression), and different reconstruction methods. © 2022, CC BY-NC-ND.

关键词： Magnetic resonance