A novel machine learning model is presented in this work to obtain the complex high-dimensional deformation of Multi-Walled Carbon Nanotubes (MWCNTs) containing millions of atoms. To obtain the deformation of these high dimensional systems, existing models like Atomistic, Continuum or Atomistic-Continuum models are very accurate and reliable but are computationally prohibitive for these large systems. This high computational requirement slows down the exploration of physics of these materials. To alleviate this problem, we developed a machine learning model that contains a) a novel dimensionality reduction technique which is combined with b) deep neural network based learning in the reduced dimension. The proposed non-linear dimensionality reduction technique serves as an extension of functional principal component analysis. This extension ensures that the geometric constraints of deformation are satisfied exactly and hence we termed this extension as constrained functional principal component analysis. The novelty of this technique is its ability to design a function space where all the functions satisfy the constraints exactly, not approximately. The efficient dimensionality reduction along with the exact satisfaction of the constraint bolster the deep neural network to achieve remarkable accuracy. The proposed model predicts the deformation of MWCNTs very accurately when compared with the deformation obtained through atomistic-physics-based model. To simulate the complex high-dimensional deformation the atomistic-physics-based models takes weeks high performance computing facility, whereas the proposed machine learning model can predict the deformation in seconds. This technique also extracts the universally dominant pattern of deformation in an unsupervised manner. These patterns are comprehensible to us and provides us a better explanation on the working of the model. The comprehensibility of the dominant modes of deformation yields the interpretability of the model.
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This content will become publicly available on August 1, 2024
Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow
In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.
more » « less- Award ID(s):
- 1944678
- NSF-PAR ID:
- 10489335
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Energies
- Volume:
- 16
- Issue:
- 16
- ISSN:
- 1996-1073
- Page Range / eLocation ID:
- 5913
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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