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Paper · 2006.00702 · 2020

Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation

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dimitra-maoutsa/odes_for_sdes pwc_unofficial 11 of 13
FunctionStatusWhere it lives
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code served (permissive licence) · get_code("fd775635d6cd6f7a")
color_dict Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/experiments/colors2.py
code served (permissive licence) · get_code("e87f6299b349de4e")
f Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/models/FHN_neuron.py
code served (permissive licence) · get_code("ee4a6b293a38def0")
f Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/models/two_dim_multiwell.py
code served (permissive licence) · get_code("5dc93676e0febd49")
hex_to_RGB Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/experiments/colors2.py
code served (permissive licence) · get_code("4c4733cf626a00f0")
low_rank_approx Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/experiments/2D_OU/score_function_sparse.py
code served (permissive licence) · get_code("6963771d5cd0a059")
my_cdist Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/score_estimators/score_function_estimators.py
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score_function Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/experiments/2D_OU/score_fucntion2.py
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score_function_multid_seperate Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/score_estimators/score_function_estimators.py
code served (permissive licence) · get_code("62e82dd6dedd6b5b")
score_function_multid_seperate Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/experiments/2D_OU/score_function_multid_seperate.py
code served (permissive licence) · get_code("9f6e122852349c77")
score_function_multid_seperate_all_dims Ran dimitra-maoutsa/odes_for_sdes/odes_for_sdes/score_estimators/score_function_estimators.py
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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 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.

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