Building General Langevin Models from Discrete Datasets

Ferretti, Federica; Chardès, Victor; Mora, Thierry; Walczak, Aleksandra M.; Giardina, Irene

doi:10.1103/physrevx.10.031018

Cited by 36 publications

(42 citation statements)

References 45 publications

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“…The entropy rate changes dramatically as missing (and predictive) velocity information is incorporated into the state ( K > 2 frames). Notably, the reconstructed state is not fully Markovian at K = 2 frames, a memory effect induced by the Euler-scheme used for simulation [57, 59, 60]. As expected for this continuous stochastic process h ( K, N ) → ∞ with increasing N , except when finite size effects result in the underestimation of the entropy rate.…”

Section: Resultsmentioning

confidence: 98%

“…S5(A), indicative of the finite memory sitting in the measurement time series from the missing degree of freedom. Notably, the dynamics is not fully memoryless with K = 2 delays, as one would naively expect, a result due to the Euler-scheme update which induces memory effects on the infinitesimal propagator P (x k+1 |x k , x k−1 ) [61][62][63][64]. We choose K * = 7 frames = 0.35 s for subsequent analysis, which recovers the equipartition theorem, showing that momentum information is accurately captured by the reconstructed state, Fig.…”

Section: Brownian Particle In a Double Well Potentialmentioning

confidence: 95%

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Maximally predictive ensemble dynamics from data

Costa

Ahamed

Jordan³

et al. 2021

Preprint

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We leverage the interplay between microscopic variability and macroscopic order to connect physical descriptions across scales directly from data, without underlying equations. We reconstruct a state space by concatenating measurements in time, building a maximum entropy partition of the resulting sequences, and choosing the sequence length to maximize predictive information. Trading non-linear trajectories for linear, ensemble evolution, we analyze reconstructed dynamics through transfer operators. The evolution is parameterized by a transition time τ: capturing the source entropy rate at small τ and revealing timescale separation with collective, coherent states through the operator spectrum at larger τ. Applicable to both deterministic and stochastic systems, we illustrate our approach through the Langevin dynamics of a particle in a double-well potential and the Lorenz system. Applied to the behavior of the nematode worm C. elegans, we derive a "run-and-pirouette" navigation strategy directly from posture dynamics. We demonstrate how sequences simulated from the ensemble evolution recover effective diffusion in the worm's centroid trajectories and introduce a top-down, operator-based clustering which reveals subtle subdivisions of the "run" behavior.

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Section: Resultsmentioning

confidence: 98%

Section: Brownian Particle In a Double Well Potentialmentioning

confidence: 95%

Maximally predictive ensemble dynamics from data

Costa

Ahamed

Jordan³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…From the short-timescale dynamics of the measured cell trajectories

, we infer the second-order stochastic differential equation that governs the motion ( 26 , 27 , 44 , 60 ). Specifically, to infer the terms of our model ( Eq.…”

Section: Methodsmentioning

confidence: 99%

Learning the dynamics of cell–cell interactions in confined cell migration

Brückner

Arlt

Fink

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell–cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive. Here, we monitor stochastic cell trajectories in a minimal experimental cell collider: a dumbbell-shaped micropattern on which pairs of cells perform repeated cellular collisions. We observe different characteristic behaviors, including cells reversing, following, and sliding past each other upon collision. Capitalizing on this large experimental dataset of coupled cell trajectories, we infer an interacting stochastic equation of motion that accurately predicts the observed interaction behaviors. Our approach reveals that interacting noncancerous MCF10A cells can be described by repulsion and friction interactions. In contrast, cancerous MDA-MB-231 cells exhibit attraction and antifriction interactions, promoting the predominant relative sliding behavior observed for these cells. Based on these experimentally inferred interactions, we show how this framework may generalize to provide a unifying theoretical description of the diverse cellular interaction behaviors of distinct cell types.

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“…Many approaches have been developed to face this kind of problem, most of which are based on the assumption that a relatively simple stochastic differential equation properly describes the dynamics. The coefficients can be found by mean of a careful analysis of conditioned moments 17,18 , even in the case of memory kernels 19 , or via a Bayesian approach 20 . This kind of strategy has been successfully em-ployed in many fields of physics, including turbulence, soft matter and biophysics 18,[21][22][23] .…”

Section: Introductionmentioning

confidence: 99%

Using machine-learning modeling to understand macroscopic dynamics in a system of coupled maps

Borra

Baldovin

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Machine-learning techniques not only offer efficient tools for modeling dynamical systems from data but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original dynamics, which would otherwise require sophisticated ad hoc techniques, can be obtained by a careful usage of such methods. To illustrate this point, we consider as a case study the macroscopic motion emerging from a system of globally coupled maps. We build a coarse-grained Markov process for the macroscopic dynamics both with a machine-learning approach and with a direct numerical computation of the transition probability of the coarse-grained process, and we compare the outcomes of the two analyses. Our purpose is twofold: on the one hand, we want to test the ability of the stochastic machine-learning approach to describe nontrivial evolution laws as the one considered in our study. On the other hand, we aim to gain some insight into the physics of the macroscopic dynamics. By modulating the information available to the network, we are able to infer important information about the effective dimension of the attractor, the persistence of memory effects, and the multiscale structure of the dynamics.

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Building General Langevin Models from Discrete Datasets

Cited by 36 publications

References 45 publications

Maximally predictive ensemble dynamics from data

Maximally predictive ensemble dynamics from data

Learning the dynamics of cell–cell interactions in confined cell migration

Using machine-learning modeling to understand macroscopic dynamics in a system of coupled maps

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