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Shen, Xinyang; Chen, Hong; Dai, J. G.; Dai, Wanyang

doi:10.1023/a:1019942711261

Cited by 29 publications

(4 citation statements)

References 25 publications

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“…Here, comparison against estimates from solving the SDE for the same number of sampled points is straight forward and one observes excellent agreement between both methods. To obtain an easy benchmark case for integral and entropy estimation, we choose k = 0 and T i = T such that the steady state is Gaussian, see equation (12). We choose the integration volumes to be hyperspheres of radius r centered at the origin allowing for analytical evaluation of the Gaussian integral.…”

Section: Application 2: Diffusion In Classical Phase Spacementioning

confidence: 99%

“…The description of nearly all processes in nature is formalized and modelled by means of differential equations, which dictate the evolution of a system given its initial state. Examples include the Navier-Stokes equation in fluid mechanics [1][2][3][4], the Schrödinger equation in quantum mechanics [5][6][7], and the Fokker-Planck equation governing diffusive processes [8][9][10][11][12][13][14][15]. Analytical solutions of these equations are only available in special cases and, generally, one is forced to resort to numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variational Monte Carlo approach to partial differential equations with neural networks

Reh¹,

Gärttner²

2022

Mach. Learn.: Sci. Technol.

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The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here, we develop a variational approach for solving partial differential equations governing the evolution of high dimensional probability distributions. Our approach naturally works on the unbounded continuous domain and encodes the full probability density function through its variational parameters, which are adapted dynamically during the evolution to optimally reflect the dynamics of the density. In contrast to previous works, this dynamical adaptation of the parameters is carried out using an explicit prescription avoiding iterative gradient descent. For the considered benchmark cases we observe excellent agreement with numerical solutions as well as analytical solutions for tasks that are challenging for traditional computational approaches.

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Section: Application 2: Diffusion In Classical Phase Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variational Monte Carlo approach to partial differential equations with neural networks

Reh¹,

Gärttner²

2022

Mach. Learn.: Sci. Technol.

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show abstract

“…In practical scenario each server has a buffer queue that was indicated as M/M/1/k but this paper assumed it as M/M/1 model for our convenience. This approximation is highly reliable to the real-time environment with large finite buffers, such as datacenter, where the buffer loss probability is negligible [26,27] It considers that the request arrival rate and service rate follow a Poisson distribution with where λ arrival rate and µ service time. Where S is represents as total number of running servers and we assumed the queuing-based loss probability is zero.…”

Section: Figure 1 Web Application Hosting Architecture Of Amazon Webmentioning

confidence: 99%

Analytical Evaluation of Resource Estimation in Web Application Services

Bulla¹,

Chirra²,

Padmavathi³

et al. 2020

ISI

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Cloud computing for web application is ubiquitous in the global market and represents a generic pattern because rapid elasticity and infrastructure scaling naturally lends itself to the needs of a virtual data center. Server requirement analysis depending on the workload play a very important role in web app development and it leads to availability of service to customer at any cost and cost analysis to the application provider. To achieve proper infrastructure scaling the minimal number of servers are have to satisfy and determine SLO. Thus this paper evaluates an analytical model to formulate prediction or estimation of required servers has to satisfy the QoS performance metrics such as throughput, utilization of cloud datacenter, request loss and required number of servers. The experimental model is used to validate correctness of the analytical model that was hosted on AWS cloud platform. Finally results have presented and conclusions are drawn.

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“…The description of nearly all processes in nature is formalized and modelled by means of differential equations, which dictate the evolution of a system given its initial state. Examples include the Navier-Stokes equation in fluid mechanics [1-4], the Schrödinger equation in quantum mechanics [5][6][7], and the Fokker-Planck equation governing diffusive processes [8][9][10][11][12][13][14][15]. Analytical solutions of these equations are only available in special cases and, generally, one is forced to resort to numerical techniques.…”

mentioning

confidence: 99%