Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Yang, Yibo; Perdikaris, Paris

doi:10.1007/s00466-019-01718-y

Title: Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Abstract

Here, we present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a statistical inference framework that enables the end-to-end training of surrogate models on paired input–output observations that may be stochastic in nature, originate from different information sources of variable fidelity, or be corrupted by complex noise processes. The resulting surrogates can accommodate high-dimensional inputs and outputs and are able to return predictions with quantified uncertainty. Furthermore, the effectiveness our approach is demonstrated through a series of canonical studies, including the regression of noisy data, multi-fidelity modeling of stochastic processes, and uncertainty propagation in high-dimensional dynamical systems.

Authors:

Yang, Yibo ^[1];

^[1]

Univ. of Pennsylvania, Philadelphia, PA (United States)

Publication Date:: Tue May 21 00:00:00 EDT 2019

Research Org.:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1595804

Grant/Contract Number:: SC0019116; HR00111890034

Resource Type:: Accepted Manuscript

Journal Name:: Computational Mechanics

Additional Journal Information:: Journal Volume: 64; Journal Issue: 2; Related Information: https://github.com/PredictiveIntelligenceLab/CADGMs; Journal ID: ISSN 0178-7675

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Probabilistic deep learning; Generative adversarial networks; Variational inference; Multi- delity modeling; Data-driven surrogates

Citation Formats


                    Yang, Yibo, and Perdikaris, Paris. Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems.  United States: N. p., 2019. 
Web.  doi:10.1007/s00466-019-01718-y.

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                    Yang, Yibo, & Perdikaris, Paris. Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems.  United States.  https://doi.org/10.1007/s00466-019-01718-y

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                    Yang, Yibo, and Perdikaris, Paris. Tue .  
"Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems".  United States.  https://doi.org/10.1007/s00466-019-01718-y.  https://www.osti.gov/servlets/purl/1595804.

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@article{osti_1595804,

  title        = {Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems},

  author       = {Yang, Yibo and Perdikaris, Paris},

  abstractNote = {Here, we present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a statistical inference framework that enables the end-to-end training of surrogate models on paired input–output observations that may be stochastic in nature, originate from different information sources of variable fidelity, or be corrupted by complex noise processes. The resulting surrogates can accommodate high-dimensional inputs and outputs and are able to return predictions with quantified uncertainty. Furthermore, the effectiveness our approach is demonstrated through a series of canonical studies, including the regression of noisy data, multi-fidelity modeling of stochastic processes, and uncertainty propagation in high-dimensional dynamical systems.},

  doi          = {10.1007/s00466-019-01718-y},

  journal      = {Computational Mechanics},

  number       = 2,

  volume       = 64,

  place        = {United States},

  year         = {Tue May 21 00:00:00 EDT 2019},

  month        = {Tue May 21 00:00:00 EDT 2019}

}

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Title: Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Abstract

Citation Formats

Multi-fidelity Gaussian process regression for prediction of random fields journal, May 2017

Multi-fidelity Gaussian process regression for prediction of random fields journal, May 2017

Active Learning with Statistical Models journal, January 1996

DDDAS-based multi-fidelity simulation framework for supply chain systems journal, February 2010

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping journal, November 2008

Deep learning journal, May 2015

Bayesian inference with optimal maps journal, October 2012

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets journal, January 2016

Information Theory and an Extension of the Maximum Likelihood Principle book, January 1998

Deep Learning text, January 2018

Multi-Fidelity Uncertainty Quantification: Application to a Vertical Axis Wind Turbine Under an Extreme Gust conference, June 2014

Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules. text, January 2018

Predictive collective variable discovery with deep Bayesian models journal, January 2019

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond journal, May 2016

A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime journal, November 2019

Understanding deep convolutional networks journal, April 2016

Variational Inference: A Review for Statisticians journal, July 2016

Active Learning with Statistical Models text, January 1996

Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules journal, January 2018

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping journal, November 2008

Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification conference, June 2012

A Stochastic Collocation Algorithm with Multifidelity Models journal, January 2014

Optimal Model Management for Multifidelity Monte Carlo Estimation journal, January 2016

Multifidelity importance sampling journal, March 2016

Multi-fidelity optimization via surrogate modelling journal, September 2007

Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme journal, September 2014

A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials journal, September 2010

Taking the Human Out of the Loop: A Review of Bayesian Optimization journal, January 2016

Graphical Models, Exponential Families, and Variational Inference journal, January 2007

Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models journal, November 2001

Computational Aspects of Stochastic Collocation with Multifidelity Models journal, January 2014

Extracting and composing robust features with denoising autoencoders conference, January 2008

Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification journal, May 2013

Variational Inference: A Review for Statisticians text, January 2016

Multi-fidelity optimization for sheet metal forming process journal, December 2010

Design of efficient molecular organic light-emitting diodes by a high-throughput virtual screening and experimental approach journal, August 2016

Variational Inference: A Review for Statisticians text, January 2017

A deep generative model for single-cell RNA sequencing with application to detecting differentially expressed genes preprint, January 2017

Data-Driven Parallel Scientific Computing: Multi-Fidelity Information Fusion Algorithms and Applications to Physical and Biological Systems text, January 2015

Variational Inference: A Review for Statisticians journal, July 2016

Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks preprint, January 2017

Active Learning with Statistical Models text, January 1996

Predicting the output from a complex computer code when fast approximations are available journal, March 2000

Variational Inference: A Review for Statisticians text, January 2017

Enabling Dark Energy Science with Deep Generative Models of Galaxy Images journal, February 2017

Multi-fidelity Gaussian process regression for prediction of random fields
journal, May 2017

Multi-fidelity Gaussian process regression for prediction of random fields
journal, May 2017

Active Learning with Statistical Models
journal, January 1996

DDDAS-based multi-fidelity simulation framework for supply chain systems
journal, February 2010

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping
journal, November 2008

Deep learning
journal, May 2015

Bayesian inference with optimal maps
journal, October 2012

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets
journal, January 2016

Information Theory and an Extension of the Maximum Likelihood Principle
book, January 1998

Deep Learning
text, January 2018

Multi-Fidelity Uncertainty Quantification: Application to a Vertical Axis Wind Turbine Under an Extreme Gust
conference, June 2014

Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules.
text, January 2018

Predictive collective variable discovery with deep Bayesian models
journal, January 2019

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond
journal, May 2016

A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime
journal, November 2019

Understanding deep convolutional networks
journal, April 2016

Variational Inference: A Review for Statisticians
journal, July 2016

Active Learning with Statistical Models
text, January 1996

Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules
journal, January 2018

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping
journal, November 2008

Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification
conference, June 2012

A Stochastic Collocation Algorithm with Multifidelity Models
journal, January 2014

Optimal Model Management for Multifidelity Monte Carlo Estimation
journal, January 2016

Multifidelity importance sampling
journal, March 2016

Multi-fidelity optimization via surrogate modelling
journal, September 2007

Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme
journal, September 2014

A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials
journal, September 2010

Taking the Human Out of the Loop: A Review of Bayesian Optimization
journal, January 2016

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journal, January 2007

Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models
journal, November 2001

Computational Aspects of Stochastic Collocation with Multifidelity Models
journal, January 2014

Extracting and composing robust features with denoising autoencoders
conference, January 2008

Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification
journal, May 2013

Variational Inference: A Review for Statisticians
text, January 2016

Multi-fidelity optimization for sheet metal forming process
journal, December 2010

Design of efficient molecular organic light-emitting diodes by a high-throughput virtual screening and experimental approach
journal, August 2016

Variational Inference: A Review for Statisticians
text, January 2017

A deep generative model for single-cell RNA sequencing with application to detecting differentially expressed genes
preprint, January 2017

Data-Driven Parallel Scientific Computing: Multi-Fidelity Information Fusion Algorithms and Applications to Physical and Biological Systems
text, January 2015

Variational Inference: A Review for Statisticians
journal, July 2016

Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks
preprint, January 2017

Active Learning with Statistical Models
text, January 1996

Predicting the output from a complex computer code when fast approximations are available
journal, March 2000

Variational Inference: A Review for Statisticians
text, January 2017

Enabling Dark Energy Science with Deep Generative Models of Galaxy Images
journal, February 2017