Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport

Baptista, R.; Cao, Lianghao; Chen, Joshua; Ghattas, Omar; Li, Fengyi; Marzouk, Youssef; Oden, J. Tinsley

doi:10.48550/arxiv.2206.11343

Cited by 2 publications

(3 citation statements)

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“…On the theoretical side, the microscopic construction of mobility functions was studied [100][101][102]. Further work considered Bayesian model calibration [103], the influence of correlations on polymer dynamics [104], memory effects [105,106], micelle relaxation [107], and morphological phase transitions [108]. The relation to other relaxation models was briefly discussed in [109].…”

Section: Chemistrymentioning

confidence: 99%

“…DDFT was also used to test a new Brownian dynamics simulation method [201]. A particularly rapidly growing subfield is the application of machine learning, which can be used to learn static free energy functionals [103,[202][203][204][205] that can be used also in DDFT to overcome limitation 3 (inaccurate free energy functionals) from the list in section 2.2. However, machine learning is also used in the dynamical case [206][207][208][209][210][211].…”

Section: Mathematics and Softwarementioning

confidence: 99%

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Perspective: New directions in dynamical density functional theory

Vrugt

Wittkowski

2022

J. Phys.: Condens. Matter

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Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

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Section: Chemistrymentioning

confidence: 99%

Section: Mathematics and Softwarementioning

confidence: 99%

Perspective: New directions in dynamical density functional theory

Vrugt

Wittkowski

2022

J. Phys.: Condens. Matter

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“…Moreover, they inherit sparsity from the conditional independence structure of P 0 and η, and thus have important connections to probabilistic graphical models; see [45] for a full discussion. Other applications of triangular maps include simulation-based inference [3] and nonlinear filtering [44]. Both the evaluation of Jacobian determinants and numerical inversion are convenient for triangular maps, making them an appealing choice from a computational perspective.…”

mentioning

confidence: 99%

On minimax density estimation via measure transport

Wang¹,

Marzouk²

2022

Preprint

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We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference distribution under a transport map, where the map is chosen via a maximum likelihood objective (equivalently, minimizing an empirical Kullback-Leibler loss) or a penalized version thereof. We establish concentration inequalities for a general class of penalized measure transport estimators, by combining techniques from M-estimation with analytical properties of the transport-based density representation. We then demonstrate the implications of our theory for the case of triangular Knothe-Rosenblatt (KR) transports on the d-dimensional unit cube, and show that both penalized and unpenalized versions of such estimators achieve minimax optimal convergence rates over Hölder classes of densities. Specifically, we establish optimal rates for unpenalized nonparametric maximum likelihood estimation over bounded Hölder-type balls, and then for certain Sobolev-penalized estimators and sieved wavelet estimators.

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Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport

Cited by 2 publications

References 0 publications

Perspective: New directions in dynamical density functional theory

Perspective: New directions in dynamical density functional theory

On minimax density estimation via measure transport

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