no code implementations • 24 Oct 2021 • Zitong Zhou, Nicholas Zabaras, Daniel M. Tartakovsky
We use a convolutional adversarial autoencoder (CAAE) for the parameterization of the heterogeneous non-Gaussian conductivity field with a low-dimensional latent representation.
no code implementations • 17 Aug 2021 • Sayan Ghosh, Govinda A. Padmanabha, Cheng Peng, Steven Atkinson, Valeria Andreoli, Piyush Pandita, Thomas Vandeputte, Nicholas Zabaras, Liping Wang
One of the critical components in Industrial Gas Turbines (IGT) is the turbine blade.
1 code implementation • 8 Mar 2021 • Govinda Anantha Padmanabha, Nicholas Zabaras
In addition, it is challenging to develop accurate surrogate and uncertainty quantification models for high-dimensional problems governed by stochastic multiscale PDEs using limited training data.
2 code implementations • 4 Feb 2021 • Yingzhi Xia, Nicholas Zabaras
In this way, the global features are identified in the coarse-scale with inference of low-dimensional variables and inexpensive forward computation, and the local features are refined and corrected in the fine-scale.
2 code implementations • 4 Oct 2020 • Nicholas Geneva, Nicholas Zabaras
Transformers are widely used in natural language processing due to their ability to model longer-term dependencies in text.
1 code implementation • 29 Sep 2020 • Navid Shervani-Tabar, Nicholas Zabaras
In this work, we assess the predictive capabilities of a molecular generative model developed based on variational inference and graph theory in the small data regime.
1 code implementation • 31 Jul 2020 • Govinda Anantha Padmanabha, Nicholas Zabaras
In this work, we construct a two- and three-dimensional inverse surrogate models consisting of an invertible and a conditional neural network trained in an end-to-end fashion with limited training data.
1 code implementation • 8 Jun 2020 • Nicholas Geneva, Nicholas Zabaras
The resulting surrogate is able to generate physically accurate turbulent realizations at a computational cost magnitudes lower than that of a high-fidelity simulation.
no code implementations • 24 Feb 2020 • Markus Schöberl, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis
Rather than separating model learning from the data-generation procedure - the latter relies on simulating atomistic motions governed by force fields - we query the atomistic force field at sample configurations proposed by the predictive coarse-grained model.
1 code implementation • 26 Jun 2019 • Shaoxing Mo, Nicholas Zabaras, Xiaoqing Shi, Jichun Wu
In addition, a deep residual dense convolutional network (DRDCN) is proposed for surrogate modeling of forward models with high-dimensional and highly-complex mappings.
1 code implementation • 13 Jun 2019 • Nicholas Geneva, Nicholas Zabaras
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems.
1 code implementation • 18 Jan 2019 • Yinhao Zhu, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis, Paris Perdikaris
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training.
1 code implementation • 22 Dec 2018 • Shaoxing Mo, Nicholas Zabaras, Xiaoqing Shi, Jichun Wu
Results indicate that, with relatively limited training data, the deep autoregressive neural network consisting of 27 convolutional layers is capable of providing an accurate approximation for the high-dimensional model input-output relationship.
1 code implementation • 18 Sep 2018 • Markus Schöberl, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis
In this work, we formulate the discovery of CVs as a Bayesian inference problem and consider the CVs as hidden generators of the full-atomistic trajectory.
1 code implementation • 11 Jul 2018 • Steven Atkinson, Nicholas Zabaras
A structured Bayesian Gaussian process latent variable model is used both to construct a low-dimensional generative model of the sample-based stochastic prior as well as a surrogate for the forward evaluation.
1 code implementation • 8 Jul 2018 • Nicholas Geneva, Nicholas Zabaras
Uncertainty quantification for such data-driven models is essential since their predictive capability rapidly declines as they are tested for flow physics that deviate from that in the training data.
1 code implementation • 2 Jul 2018 • Shaoxing Mo, Yinhao Zhu, Nicholas Zabaras, Xiaoqing Shi, Jichun Wu
A training strategy combining a regression loss and a segmentation loss is proposed in order to better approximate the discontinuous saturation field.
no code implementations • 22 May 2018 • Steven Atkinson, Nicholas Zabaras
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for computational tractability.
no code implementations • 21 Jan 2018 • Yinhao Zhu, Nicholas Zabaras
We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered in deep learning for image-to-image regression tasks.
no code implementations • 26 May 2016 • Markus Schöberl, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics.
2 code implementations • 21 Oct 2014 • Panagiotis Tsilifis, Ilias Bilionis, Ioannis Katsounaros, Nicholas Zabaras
The classical approach to inverse problems is based on the optimization of a misfit function.