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Main Title: Interacting particle solutions of Fokker–Planck equations through gradient–log–density estimation
Author(s): Maoutsa, Dimitra
Reich, Sebastian
Opper, Manfred
Type: Article
Abstract: Fokker–Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker–Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker–Planck equations in low and moderate dimensions. The proposed gradient–log–density estimator is also of independent interest, for example, in the context of optimal control.
Subject(s): stochastic systems
Fokker-Planck equation
interacting particles
multiplicative noise
gradient flow
stochastic differential equations
Issue Date: 22-Jul-2020
Date Available: 11-Jan-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2020
DFG, 318763901, SFB 1294: Datenassimilation: Die nahtlose Verschmelzung von Daten und Modellen
Journal Title: Entropy
Publisher: MDPI
Volume: 22
Issue: 8
Article Number: 802
Publisher DOI: 10.3390/e22080802
EISSN: 1099-4300
TU Affiliation(s): Fak. 4 Elektrotechnik und Informatik » Inst. Softwaretechnik und Theoretische Informatik » FG Methoden der Künstlichen Intelligenz
Appears in Collections:Technische Universität Berlin » Publications

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