Machine learning for phase behavior in active matter systems

Dulaney, Austin R.; Brady, John F.

doi:10.1039/d1sm00266j

Cited by 22 publications

(20 citation statements)

References 25 publications

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“…47 We would like to point out that the DRM is based on the combination of variational principles in physics and the deep learning method that has the capacity of mining highdimensional information from deep neural networks. In comparison to other machine learning methods proposed particularly for active matter physics, [48][49][50][51] the DRM has several advantages as follows. (1) The DRM is naturally nonlinear, naturally adaptive, and relatively insensitive to the complexity of the energy functional.…”

Section: Deep Ritz Methods (Drm): Deep Learning-based Methods Of Solv...mentioning

confidence: 99%

Variational methods and deep Ritz method for active elastic solids

Wang

Zou

et al. 2022

Soft Matter

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Section: Deep Ritz Methods (Drm): Deep Learning-based Methods Of Solv...mentioning

confidence: 99%

Variational methods and deep Ritz method for active elastic solids

Wang

Zou

et al. 2022

Soft Matter

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“…We would like to point out that the deep Ritz method is based on the combination of classical variational principles in physics and the deep learning method that has the capacity of mining high dimensional information from deep neural networks. In comparison to other machine learning methods proposed particularly for active matter physics [45][46][47][48], the deep Ritz method has several advantages as follows. It is naturally nonlinear, naturally adaptive and is relatively insensitive to the complexity of the energy functional, the dimensions of both physical space and state variables, and the order of the derivatives of state variables.…”

Section: Deep Ritz Method: Deep Learning-based Methods Of Solving Var...mentioning

confidence: 99%

“…The deep Ritz method mentioned above for the statics of active matter is developed [44] by combining Ritz's variational method of approximation [42] with deep learning methods that are based on deep neural networks and stochastic gradient descent algorithms. Similar deep learning methods can also be developed [45][46][47][70][71][72] for the dynamics of soft matter and active matter by combining the variational method of approximation based on Onsager's variational principle (OVP) [43] with deep learning methods. Furthermore, the input of the neural networks should generally include both spatial and temporal coordinates; the output can be not only displacement fields, but also other slow variables such as polarization, concentration, etc.…”

Section: Conclusion and Remarksmentioning

confidence: 99%

Variational methods and deep Ritz method for active elastic solids

Wang,

Zou,

et al. 2022

Preprint

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Variational methods have been widely used in soft matter physics for both static and dynamic problems. These methods are mostly based on two variational principles: the variational principle of minimum free energy (MFEVP) and Onsager's variational principle (OVP). Our interests lie in the applications of these variational methods to active matter physics. In our former work [Soft Matter, 2021, 17, 3634], we have explored the applications of OVP-based variational methods for the modeling of active matter dynamics. In the present work, we explore variational (or energy) methods that are based on MFEVP for static problems in active elastic solids. We show that MFEVP can be used not only to derive equilibrium equations, but also to develop approximate solution methods, such as Ritz method, for active solid statics. Moreover, the power of Ritz-type method can be further enhanced using deep learning methods if we use deep neural networks to construct the trial solutions of the variational problems. We then apply these variational methods and the deep Ritz method to study the spontaneous bending and contraction of a thin active circular plate that is induced by internal asymmetric active contraction. The circular plate is found to be bent towards its bending side. The study of such a simple toy system gives implications for understanding the morphogenesis of solid-like confluent cell monolayers. In addition, we introduce a so-called activogravity length to characterize the importance of gravitational forces relative to internal active contraction in driving the bending of the active plate. When the lateral plate dimension is larger than the activogravity length (about 100 micron), gravitational forces become important. Such gravitaxis behaviors at multicellular scales may play significant roles in the morphogenesis and in the up-down symmetry broken during tissue development.

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“…This includes a large class of non-equilibrium systems of self-driven or active particles often called active matter in the literature of statistical physics [150], [52], [151], [152], [153], [154], [129]. Understanding complex non-linear dynamics operating at different modeling scales remains challenging and currently attracts much attention, notably through data-based approaches [30], [155], [6], [3], [156].…”

Section: Knowledge-based Models For Understanding and Predictingmentioning

confidence: 99%

Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approaches

Korbmacher¹,

Tordeux²

2021

Preprint

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In crowd scenarios, predicting trajectories of pedestrians is a complex and challenging task depending on many external factors. The topology of the scene and the interactions between the pedestrians are just some of them. Due to advancements in data-science and data collection technologies deep learning methods have recently become a research hotspot in numerous domains. Therefore, it is not surprising that more and more researchers apply these methods to predict trajectories of pedestrians. This paper compares these relatively new deep learning algorithms with classical knowledge-based models that are widely used to simulate pedestrian dynamics. It provides a comprehensive literature review of both approaches, explores technical and application oriented differences, and addresses open questions as well as future development directions. Our investigations point out that the pertinence of knowledge-based models to predict local trajectories is nowadays questionable because of the high accuracy of the deep learning algorithms. Nevertheless, the ability of deep-learning algorithms for large-scale simulation and the description of collective dynamics remains to be demonstrated. Furthermore, the comparison shows that the combination of both approaches (the hybrid approach) seems to be promising to overcome disadvantages like the missing explainability of the deep learning approach.

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Machine learning for phase behavior in active matter systems

Abstract: We demonstrate that deep learning techniques can be used to predict motility-induced phase separation (MIPS) in suspensions of active Brownian particles (ABPs) by creating a notion of phase at the...

Cited by 22 publications

References 25 publications

Variational methods and deep Ritz method for active elastic solids

Variational methods and deep Ritz method for active elastic solids

Variational methods and deep Ritz method for active elastic solids

Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approaches

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