Failure-averse Active Learning for Physics-constrained Systems

Active learning is a subfield of machine learning that is devised for design and modeling of systems with highly expensive sampling costs. Industrial and engineering systems are generally subject to physics constraints that may induce fatal failures when they are violated, while such constraints are frequently underestimated in active learning. In this paper, we develop a novel active learning method that avoids failures considering implicit physics constraints that govern the system. The proposed approach is driven by two tasks: the safe variance reduction explores the safe region to reduce the variance of the target model, and the safe region expansion aims to extend the explorable region exploiting the probabilistic model of constraints. The global acquisition function is devised to judiciously optimize acquisition functions of two tasks, and its theoretical properties are provided. The proposed method is applied to the composite fuselage assembly process with consideration of material failure using the Tsai-wu criterion, and it is able to achieve zero-failure without the knowledge of explicit failure regions.

[1]  H. Milton Stewart,et al.  Surrogate Model Based Control Considering Uncertainties for Composite Fuselage Assembly , 2017 .

[2]  Chao Hu,et al.  Sequential exploration-exploitation with dynamic trade-off for efficient reliability analysis of complex engineered systems , 2017 .

[3]  Duy Nguyen-Tuong,et al.  Safe Exploration for Active Learning with Gaussian Processes , 2015, ECML/PKDD.

[4]  Jianjun Shi,et al.  Virtual assembly and residual stress analysis for the composite fuselage assembly process , 2019, Journal of Manufacturing Systems.

[5]  Victor Picheny,et al.  A Stepwise uncertainty reduction approach to constrained global optimization , 2014, AISTATS.

[6]  Xiaowei Yue,et al.  Partitioned Active Learning for Heterogeneous Systems , 2021, ArXiv.

[7]  Ling Li,et al.  Sequential design of computer experiments for the estimation of a probability of failure , 2010, Statistics and Computing.

[8]  Pingfeng Wang,et al.  A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design , 2013, DAC 2013.

[9]  M. Eldred,et al.  Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions , 2008 .

[10]  Saeed Moaveni,et al.  Finite Element Analysis Theory and Application with ANSYS , 2007 .

[11]  David A. Barajas-Solano,et al.  Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence , 2018, J. Comput. Phys..

[12]  Xi Chen,et al.  Sequential design strategies for mean response surface metamodeling via stochastic kriging with adaptive exploration and exploitation , 2017, Eur. J. Oper. Res..

[13]  Jianguo Wu,et al.  Neural Network Gaussian Process Considering Input Uncertainty for Composite Structure Assembly , 2020, IEEE/ASME Transactions on Mechatronics.

[14]  S. White,et al.  Stress analysis of fiber-reinforced composite materials , 1997 .

[15]  Grace X. Gu,et al.  Generative Deep Neural Networks for Inverse Materials Design Using Backpropagation and Active Learning , 2020, Advanced science.

[16]  Joel W. Burdick,et al.  Stagewise Safe Bayesian Optimization with Gaussian Processes , 2018, ICML.

[17]  Lei Wang,et al.  REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis , 2019, Reliab. Eng. Syst. Saf..

[18]  Donald R. Jones,et al.  Global versus local search in constrained optimization of computer models , 1998 .

[19]  Jasper Snoek,et al.  Bayesian Optimization with Unknown Constraints , 2014, UAI.

[20]  Robert D. Nowak,et al.  Faster Rates in Regression via Active Learning , 2005, NIPS.

[21]  Jeffrey H. Hunt,et al.  Active Learning for Gaussian Process Considering Uncertainties With Application to Shape Control of Composite Fuselage , 2020, IEEE Transactions on Automation Science and Engineering.

[22]  Yibo Yang,et al.  Physics-Informed Neural Networks for Cardiac Activation Mapping , 2020, Frontiers in Physics.

[23]  Vipin Kumar,et al.  Integrating Physics-Based Modeling with Machine Learning: A Survey , 2020, ArXiv.

[24]  Sébastien Le Digabel,et al.  Modeling an Augmented Lagrangian for Blackbox Constrained Optimization , 2014, Technometrics.

[25]  Klaus Obermayer,et al.  Gaussian process regression: active data selection and test point rejection , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[26]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[27]  A. Basudhar,et al.  Constrained efficient global optimization with support vector machines , 2012, Structural and Multidisciplinary Optimization.

[28]  George Michailidis,et al.  Sequential Experiment Design for Contour Estimation From Complex Computer Codes , 2008, Technometrics.

[29]  Robert B. Gramacy,et al.  Optimization Under Unknown Constraints , 2010, 1004.4027.

[30]  Xiu Yang,et al.  Physics-Informed Kriging: A Physics-Informed Gaussian Process Regression Method for Data-Model Convergence , 2018, ArXiv.

[31]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[32]  F. Pfaff,et al.  Consistency of Gaussian Process Regression in Metric Spaces , 2021, J. Mach. Learn. Res..

[33]  Felix Berkenkamp,et al.  Safe Exploration for Interactive Machine Learning , 2019, NeurIPS.

[34]  Burr Settles,et al.  Active Learning Literature Survey , 2009 .

[35]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[36]  Rajitha Meka,et al.  Sequential Laplacian regularized V-optimal design of experiments for response surface modeling of expensive tests: An application in wind tunnel testing , 2019, IISE Trans..

[37]  Matthew W. Hoffman,et al.  Predictive Entropy Search for Bayesian Optimization with Unknown Constraints , 2015, ICML.

[38]  A.C.W.M. Vrouwenvelder,et al.  Reliability based structural design , 2013 .

[39]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[40]  Rodney S. Thomson,et al.  Review of methodologies for composite material modelling incorporating failure , 2008 .

[41]  David A. Cohn,et al.  Active Learning with Statistical Models , 1996, NIPS.

[42]  Deep Ray,et al.  Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks , 2020, ArXiv.

[43]  Steven G. Johnson,et al.  Active learning of deep surrogates for PDEs: application to metasurface design , 2020, npj Computational Materials.