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Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows [article]

Ruizhi Deng, Bo Chang, Marcus A. Brubaker, Greg Mori, Andreas Lehrmann
2021 arXiv   pre-print
In this work, we propose a novel type of normalizing flow driven by a differential deformation of the Wiener process.  ...  Furthermore, our continuous treatment provides a natural framework for irregular time series with an independent arrival process, including straightforward interpolation.  ...  base continuous Wiener process into a complex observable process using a dynamic instance of normalizing flows.  ... 
arXiv:2002.10516v4 fatcat:75xbi3uiuff35mp2tlqguriy6q

Continuous Latent Process Flows [article]

Ruizhi Deng, Marcus A. Brubaker, Greg Mori, Andreas M. Lehrmann
2021 arXiv   pre-print
We tackle these challenges with continuous latent process flows (CLPF), a principled architecture decoding continuous latent processes into continuous observable processes using a time-dependent normalizing  ...  flow driven by a stochastic differential equation.  ...  Driven by different trajectories of the latent stochastic process continuously evolving with time, the dynamic normalizing flow can map a simple base process to a diverse class of observable processes.  ... 
arXiv:2106.15580v2 fatcat:p6b5f6wghjf7laqk4sjlhzg4xy

Educational Technology in Economics Instruction

Ahmet Kara
2015 Procedia - Social and Behavioral Sciences  
In the third model, we have interrelated markets for two goods with discontinuous stochastic demand and nonlinear stochastic supply functions.  ...  Each function involves a stochastic term. In the second model, we do not have a continuous and continuously differentiable demand function but only a demand schedule.  ...  The stochastic terms are assumed to be normally distributed with zero means and unit variances.  ... 
doi:10.1016/j.sbspro.2015.01.709 fatcat:rzjo6ahhl5gajaqiiawrssiv4i

Modeling the spatial and temporal dynamics of riparian vegetation induced by river flow fluctuation

Xiaoguang You, Jingling Liu
2018 Ecology and Evolution  
These zones provide important ecosystem services, including nutrient cycling, flood attenuation, riverbank stabilization, water purification, groundwater recharge, and flow regulation (Kauffman,  ...  The mathematical forms in this model are essentially stochastic differential equations with explicit physical meaning. They are solved into stochastic process solutions.  ...  Stationarity of the stochastic river flow fluctuation is not an intrinsic requirement in the model, because the model and its results are both process-based.  ... 
doi:10.1002/ece3.3886 pmid:29686846 pmcid:PMC5901219 fatcat:4cd2kegotval3eqd4cjjhjhwlu


Serhii Yermakov, Hutsol Taras, Krzysztof Mudryk, Krzysztof Dziedzic, Liudmyla Mykhailova
2019 Environment Technology Resources Proceedings of the International Scientific and Practical Conference  
The statically stable formation and dynamic arches that prevent the uniform and continuous unloading are in evidence.  ...  It is analytically and experimentally determined that woody crops cuttings flow occurs according to dry friction laws and inverse-square law and the flow is normal in nature.  ...  Stochastic process of origin and fracture of arches is observed with any kind of discrete bulk material flow from the discharge opening of tankers. This process is both discrete and continuous.  ... 
doi:10.17770/etr2019vol3.4159 fatcat:hyrpc6jcb5fq3dosdbduel3nvy

Generative stochastic modeling of strongly nonlinear flows with non-Gaussian statistics [article]

Hassan Arbabi, Themistoklis Sapsis
2022 arXiv   pre-print
Here, we propose a data-driven framework to model stationary chaotic dynamical systems through nonlinear transformations and a set of decoupled stochastic differential equations (SDEs).  ...  These systems are difficult to model and analyze due to combination of high dimensionality and uncertainty, and there has been much interest in obtaining reduced models, in the form of stochastic closures  ...  strongly nonlinear flows [45] . 2 Stochastic generative modeling of strongly nonlinear flows Problem setup Consider a dynamical system given as ẋ = f (x), (1) y = g(x) with the state variable x in  ... 
arXiv:1908.08941v5 fatcat:z6ionhdarbdldm4qg7rbku7rnm

Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems

David P. Watling, Giulio E. Cantarella
2013 Networks and Spatial Economics  
We review and advance the state-of-the-art in the modelling of transportation systems as a stochastic process. The conceptual and theoretical basis of the approach is explained in detail.  ...  Our overall objective is to establish the applicability of this approach as a unifying framework for modelling approaches involving dynamic and stochastic elements, developing further the ideas put forward  ...  The financial assistance of Prof Terry Friesz is also gratefully acknowledged, in supporting the visit of the first-named author to deliver the keynote paper at the DTA 2012 International Symposium on Dynamic  ... 
doi:10.1007/s11067-013-9198-2 fatcat:6mq6noimtzgcbl3a5cr5ksfj6u


2014 American Journal of Applied Sciences  
melt blowing process.  ...  Abstact A probabilistic modeling approach has been proposed to correlate motion of a filament to the web structural formation in single filament melt blowing.  ...  The state space of a stochastic process can be discrete or continuous. A continuous stochastic process has a continuous (real-valued) state space, and its parameter space is also continuous.  ... 
doi:10.3844/ajassp.2014.611.622 fatcat:ur3s6u6sazarnhlj23oregmxrm


2017 Journal of Natural Sciences, Engineering and Technology  
Such events that have to flow with time or space are called dynamical systems.  ...  Most real world situations involve modelling of physical processes that evolve with time and space, especially those exhibiting high variability.  ...  The study considered dynamical system as a random process with independent increments and as a result can be modelled with Markov chains models.  ... 
doi:10.51406/jnset.v16i1.1801 fatcat:2svk4wjmw5cyxkfllh4ztkncwm

A stochastic differential equation analysis of cerebrospinal fluid dynamics

Kalyan Raman
2011 Fluids and Barriers of the CNS  
Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP.  ...  A key finding is that the probabilities display strong threshold effects with respect to noise.  ...  Marek Czosnyka, Neuroscience Group, University of Cambridge, UK, for introducing him to the key issues in CSF dynamics and hydrocephalus, for making data available from infusion studies conducted at Addenbrooke's  ... 
doi:10.1186/2045-8118-8-9 pmid:21349157 pmcid:PMC3042983 fatcat:qx3rsvhnxfc27n6oqsb2ydthki

Stochastic Hybrid Systems: Application to Communication Networks [chapter]

João P. Hespanha
2004 Lecture Notes in Computer Science  
We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains  ...  As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number  ...  Acknowledgments The author would like to thank Roger Brockett for providing a preprint of [7] ; Martin Arlitt for making available the processed data regarding the transfer-size distribution reported  ... 
doi:10.1007/978-3-540-24743-2_26 fatcat:vpppntcfxndyxgkcbxh7dnupru

Cash Flow Valuation Model in Continuous Time

2013 IOSR Journal of Mathematics  
Three equivalent forms of this value process is established with each of which has its own merits. Local dynamics of the values process is also considered.  ...  This paper present valuation models which is define as the expected discounted value of a stream of each flows at a time.  ...  Introduction The advantage of the stochastic calculus of semimartigales, especially on Ito diffusion model gives us an opportunity to consider the cash flow in continuous time.  ... 
doi:10.9790/5728-0731218 fatcat:po6lvmxfuja3znxl76lophirfi

Neural Hybrid Automata: Learning Dynamics with Multiple Modes and Stochastic Transitions [article]

Michael Poli, Stefano Massaroli, Luca Scimeca, Seong Joon Oh, Sanghyuk Chun, Atsushi Yamashita, Hajime Asama, Jinkyoo Park, Animesh Garg
2021 arXiv   pre-print
Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows  ...  Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes.  ...  Stochastic Hybrid Systems A stochastic hybrid system (SHS) [2] , [15] is a right-continuous stochastic process X t taking values in X ⊆ R nx with a latent mode process Z t conditioning the dynamics  ... 
arXiv:2106.04165v1 fatcat:mvac3aynxfdghlv7rela5ssaiu

Dynamic Reliability of Continuous Rigid-Frame Bridges under Stochastic Moving Vehicle Loads

Naiwei Lu, Kai Wang, Honghao Wang, Yang Liu, Yuan Luo, Xinhui Xiao
2020 Shock and Vibration  
The prototype bridge is a continuous rigid-frame bridge with a midspan length of 200 m and a pier height of 182 m.  ...  The site-specific traffic monitoring data of a highway in China were utilized to establish stochastic traffic models.  ...  It was concluded by many researchers that dynamic response of bridges under stochastic vehicle flow can be assumed as stationary random process [31] .  ... 
doi:10.1155/2020/8811105 doaj:fe3e8c6f998c46189b24b549ccb56f50 fatcat:dlxmxoocnbatxnmw7uih4xxinq

Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas [article]

Yubin Lu, Yang Li, Jinqiao Duan
2021 arXiv   pre-print
Specifically, we use the normalizing flows technology to estimate the transition probability density function (solution of nonlocal Fokker-Planck equation) from data, and then substitute it into the recently  ...  This approach will become an effective tool for discovering stochastic governing laws and understanding complex dynamical behaviors.  ...  Data Availability Research code is shared via ning-Laws-by-Nonlocal-Kramers-Moyal-Formulas.  ... 
arXiv:2108.12570v2 fatcat:hby5sx7sobehzcgjsyiz3ki2ja
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