scholarly journals Eigencages: Learning a Latent Space of Porous Cage Molecules

2018 ◽  
Author(s):  
Arni Sturluson ◽  
Melanie T. Huynh ◽  
Arthur H. P. York ◽  
Cory Simon
Keyword(s):  
Dimensional Subspace ◽  
Singular Value ◽  
Adsorption Properties ◽  
3D Image ◽  
Latent Space ◽  
Cage Molecules ◽  
Gas Molecules ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Lower Dimensional

<div>Porous organic cage molecules harbor nano-sized cavities that can selectively adsorb gas molecules, lending them applications in separations and sensing. The geometry of the cavity strongly influences adsorptive selectivity.</div><div><br></div><div>For comparing cages and predicting their adsorption properties, we embed/encode the cavities of a set of 74 porous organic cage molecules into a low-dimensional, latent "cage space".</div><div><br></div><div>We first scan the cavity of each cage to generate a 3D image of its porosity. Leveraging the singular value decomposition, in an unsupervised manner, we then learn across all cages an approximate, lower-dimensional subspace in which the 3D cage cavity images lay. The "eigencages" are the set of characteristic 3D cage cavity images that span this lower-dimensional subspace. A latent representation/encoding of each cage then follows from expressing it as a combination of the eigencages.</div><div><br></div><div>We show that the learned encoding captures salient features of the cavities of porous cages and is predictive of properties of the cages that arise from cavity shape.</div>

scholarly journals Eigencages: Learning a Latent Space of Porous Cage Molecules

2018 ◽  
Author(s):  
Arni Sturluson ◽  
Melanie T. Huynh ◽  
Arthur H. P. York ◽  
Cory Simon
Keyword(s):  
Dimensional Subspace ◽  
Singular Value ◽  
Adsorption Properties ◽  
3D Image ◽  
Latent Space ◽  
Cage Molecules ◽  
Gas Molecules ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Lower Dimensional

<div>Porous organic cage molecules harbor nano-sized cavities that can selectively adsorb gas molecules, lending them applications in separations and sensing. The geometry of</div><div>the cavity strongly influences their adsorptive selectivity. </div><div><br></div><div>For comparing cages and predicting their adsorption properties, we embed/encode a set of 74 porous organic</div><div>cage molecules into a low-dimensional, latent “cage space” on the basis of their intrinsic porosity. </div><div><br></div><div>We first computationally scan each cage to generate a 3D image of its porosity. Leveraging the singular value decomposition, in an unsupervised manner, we then learn across all cages an approximate, lower-dimensional subspace in which the 3D porosity images lay. The “eigencages” are the set of orthogonal characteristic 3D porosity images that span this lower-dimensional subspace, ordered in terms of importance. A latent representation/encoding of each cage follows from expressing it as a combination of the eigencages. </div><div><br></div><div>We show that the learned encoding captures salient features of the cavities of porous cages and is predictive of properties of the cages that arise from cavity shape.</div>

scholarly journals Eigencages: Learning a Latent Space of Porous Cage Molecules

2018 ◽  
Author(s):  
Arni Sturluson ◽  
Melanie T. Huynh ◽  
Arthur H. P. York ◽  
Cory Simon
Keyword(s):  
Dimensional Subspace ◽  
Singular Value ◽  
Adsorption Properties ◽  
3D Image ◽  
Latent Space ◽  
Cage Molecules ◽  
Gas Molecules ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Lower Dimensional

<div>Porous organic cage molecules harbor nano-sized cavities that can selectively adsorb gas molecules, lending them applications in separations and sensing. The geometry of</div><div>the cavity strongly influences their adsorptive selectivity. </div><div><br></div><div>For comparing cages and predicting their adsorption properties, we embed/encode a set of 74 porous organic</div><div>cage molecules into a low-dimensional, latent “cage space” on the basis of their intrinsic porosity. </div><div><br></div><div>We first computationally scan each cage to generate a 3D image of its porosity. Leveraging the singular value decomposition, in an unsupervised manner, we then learn across all cages an approximate, lower-dimensional subspace in which the 3D porosity images lay. The “eigencages” are the set of orthogonal characteristic 3D porosity images that span this lower-dimensional subspace, ordered in terms of importance. A latent representation/encoding of each cage follows from expressing it as a combination of the eigencages. </div><div><br></div><div>We show that the learned encoding captures salient features of the cavities of porous cages and is predictive of properties of the cages that arise from cavity shape.</div>

scholarly journals Eigencages: Learning a Latent Space of Porous Cage Molecules

2018 ◽  
Author(s):  
Arni Sturluson ◽  
Melanie T. Huynh ◽  
Arthur H. P. York ◽  
Cory Simon
Keyword(s):  
Dimensional Subspace ◽  
Singular Value ◽  
Adsorption Properties ◽  
3D Image ◽  
Latent Space ◽  
Cage Molecules ◽  
Gas Molecules ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Lower Dimensional

<div>Porous organic cage molecules harbor nano-sized cavities that can selectively adsorb gas molecules, lending them applications in separations and sensing. The geometry of the cavity strongly influences adsorptive selectivity.</div><div><br></div><div>For comparing cages and predicting their adsorption properties, we embed/encode the cavities of a set of 74 porous organic cage molecules into a low-dimensional, latent "cage space".</div><div><br></div><div>We first scan the cavity of each cage to generate a 3D image of its porosity. Leveraging the singular value decomposition, in an unsupervised manner, we then learn across all cages an approximate, lower-dimensional subspace in which the 3D cage cavity images lay. The "eigencages" are the set of characteristic 3D cage cavity images that span this lower-dimensional subspace. A latent representation/encoding of each cage then follows from expressing it as a combination of the eigencages.</div><div><br></div><div>We show that the learned encoding captures salient features of the cavities of porous cages and is predictive of properties of the cages that arise from cavity shape.</div>

scholarly journals Wavelet filtering of chaotic data

2000 ◽  
Vol 7 (1/2) ◽  
pp. 111-116 ◽  
Author(s):  
M. Grzesiak
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Finite Impulse Response ◽  
Gaussian White Noise ◽  
Noisy Data ◽  
Singular Value ◽  
Filter Methods ◽  
Satisfactory Method ◽  
Low Dimensional ◽  
Value Decomposition

Abstract. Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.

scholarly journals High-dimensional Bayesian optimization using low-dimensional feature spaces

2020 ◽  
Vol 109 (9-10) ◽  
pp. 1925-1943 ◽  
Author(s):  
Riccardo Moriconi ◽  
Marc Peter Deisenroth ◽  
K. S. Sesh Kumar
Keyword(s):  
Optimization Problem ◽  
Feature Space ◽  
Dimensional Subspace ◽  
Global Optimum ◽  
Black Box ◽  
Fine Tuning ◽  
Bayesian Optimization ◽  
Feature Spaces ◽  
Low Dimensional ◽  
Lower Dimensional

Abstract Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to optimizing 10–20 parameters. To scale BO to high dimensions, we usually make structural assumptions on the decomposition of the objective and/or exploit the intrinsic lower dimensionality of the problem, e.g. by using linear projections. We could achieve a higher compression rate with nonlinear projections, but learning these nonlinear embeddings typically requires much data. This contradicts the BO objective of a relatively small evaluation budget. To address this challenge, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Our approach allows for optimization of BO’s acquisition function in the lower-dimensional subspace, which significantly simplifies the optimization problem. We reconstruct the original parameter space from the lower-dimensional subspace for evaluating the black-box function. For meaningful exploration, we solve a constrained optimization problem.

scholarly journals Analysis of the 2D complex Ginzburg-Landau Equation using Singular Value Decomposition

2021 ◽  
Author(s):  
Emily Gottry ◽  
Edwin Ding
Keyword(s):  
Singular Value Decomposition ◽  
Landau Equation ◽  
Singular Value ◽  
Optical Systems ◽  
Qualitative Behavior ◽  
Dimensional Model ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Low Dimensional ◽  
Value Decomposition

The cubic-quintic Ginzburg-Landau equation (CQGLE) governs the dynamics of solitons in lasers and many optical systems. Using data obtained from the simulations of the CQGLE, we performed a singular value decomposition (SVD) to create a low dimensional model that qualitatively predicts the stability of the solitons as a function of the energy gain constant. It was found both in the full simulations and in the low dimensional model that the soliton becomes unstable when the gain exceeds a certain threshold value. Both the low dimensional model and the full simulation demonstrated the same qualitative behavior when the soliton loses stability.

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