CDSE Project

Major Goals of the Project

Our objective in this proposal is to develop an integrated research program that addresses data management and data analytics challenges arising from observations and simulations in UQ and complex inverse problems.

Aim 1: Developing scalable algorithms for managing large simulation data.

One of the main bottlenecks to data scalability of existing inverse/UQ approaches is the amount of simulated data being generated and the associated costs of accessing this data. We shall develop innovative algorithms to overcome this bottleneck by minimizing the amount of simulation data and at the same time hiding the cost of data-movement by overlapping data-access with computation.

Projects

• Deep learning enhanced reduced order models
• Managing big simulation data for inverse problems with autoencoders
• Deep-learning-enhanced POD method
• Model-constrained Deep Learning Approaches for Inverse Problems
• A Model-Constrained Tangent Manifold Learning Approach for Dynamical Systems
• Model-Constrained Bayesian Neural Networks for Uncertainty Quantification

Aim 2: Creating strategies to tackle large observation data.

While more observation data generally leads to less uncertain predictions, it makes the task of inversion and UQ more expensive. We shall develop iterative inversion/UQ methods that utilize only a manageable subset of data during each iteration. This is further enhanced by a streaming computational model that we will create to ensure data scalability while minimizing overall computation.

Projects

• On unifying randomized approaches in inverse problems
• A new look at the Ensemble Kalman Filter
• New approach for DNN architecture design
• Variational inference with UQ-VAEs
• Neural Networks and Active Subspaces
• DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems

Publications

[1] Sheroze Sheriffdeen, Jean C.. (2019). Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models. https://arxiv.org/abs/1912.08864

[2] Goh, H.. (2020). Solving Forward and Inverse Problems Using Autoencoders. https://arxiv.org/abs/1912.04212v3

[3] Nguyen, H., and Bui-Thanh, T., Model-Constrained Deep Learning Approaches for Inverse Problems, SIAM Journal of Scientific Computing, In Production, 2023. https://arxiv.org/abs/2105.12033. Status = ACCEPTED.

[4]Nguyen, Hai V. and Bui-Thanh, Tan. (2022). A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems. International Journal of Computational Fluid Dynamics. 36 (7) 655 to 685. Status = Added in NSF-PAR doi: https://doi.org/10.1080/10618562.2022.2146677

[5] Nguyen, Hai and Wittmer, Jonathan and Bui-Thanh, Tan. (2022). DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems. Computation. 10 (3) 38. Status = Added in NSF-PAR doi: https://doi.org/10.3390/computation10030038

[6] Lee, Jeonghun J. and Bui-Thanh, Tan and Villa, Umberto and Ghattas, Omar. (2022). Forward and inverse modeling of fault transmissibility in subsurface flows. Computers & Mathematics with Applications. 128 (C) 354 to 367. Status = Added in NSF-PAR doi: https://doi.org/10.1016/j.camwa.2022.09.013

[7] Steins, Ella and Bui‐Thanh, Tan and Herty, Michael and Müller, Siegfried. (2022). Probabilistic constrained Bayesian inversion for transpiration cooling. International Journal for Numerical Methods in Fluids. 94 (12) 2020 to 2039. Status = Added in NSF-PAR doi: https://doi.org/10.1002/fld.5135

[8] Muralikrishnan, Sriramkrishnan and Shannon, Stephen and Bui-Thanh, Tan and Shadid, John N. (2023). A multilevel block preconditioner for the HDG trace system applied to incompressible resistive MHD. Computer Methods in Applied Mechanics and Engineering. 404 (C) 115775. Status = Added in NSF-PAR doi: https://doi.org/10.1016/j.cma.2022.115775

[9] Ambartsumyan, Ilona and Boukaram, Wajih and Bui-Thanh, Tan and Ghattas, Omar and Keyes, David and Stadler, Georg and Turkiyyah, George and Zampini, Stefano. (2020). Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs. SIAM Journal on Scientific Computing. 42 (5) A3397 to A3426. Status = Added in NSF-PAR doi: https://doi.org/10.1137/19M1270367

[10] Kang, Shinhoo and Bui-Thanh, Tan. (2021). A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations. Computer Methods in Applied Mechanics and Engineering. 385 (C) 114031. Status = Added in NSF-PAR doi: https://doi.org/10.1016/j.cma.2021.114031

[11] Myers, Aaron and Thiéry, Alexandre H. and Wang, Kainan and Bui-Thanh, Tan. (2021). Sequential ensemble transform for Bayesian inverse problems. Journal of Computational Physics. 427 (C) 110055. Status = Added in NSF-PAR doi: https://doi.org/10.1016/j.jcp.2020.110055

[12] Zhang, Wenbo and Rossini, Giovanni and Kamensky, David and Bui‐Thanh, Tan and Sacks, Michael S.. (2021). Isogeometric finite element‐based simulation of the aortic heart valve: Integration of neural network structural material model and structural tensor fiber architecture representations. International Journal for Numerical Methods in Biomedical Engineering. 37 (4). Status = Added in NSF-PAR doi: https://doi.org/10.1002/cnm.3438

[13] Bui-Thanh, T.. (2021). The Optimality of Bayes’ Theorem. SIAM news. 54 (6). Status = Added in NSF-PAR

[14] Goh, H.. (2021). Solving Bayesian Inverse Problems via Variational Autoencoders. Proceeding of Machine Learning Research, 2nd Annual Conference on Mathematical and Scientific Machine Learning. 145. Status = Added in NSF-PAR

Licenses

Other Conference Presentations / Papers

[1] Russell Philley, Hai V. Nguyen, and Tan Bui-Thanh (2023). Model-constrained uncertainty quantification for scientific deep learning of inverse solutions. the XLIV Iberto-Latin American Congress on Computational Mechanics in Engineering, Refereed proceeding. Porto, Portugal. Status = PUBLISHED;

Other Products

Other Publications

Patent Applications

Technologies or Techniques

Thesis/Dissertations

[1] Wittmer, Jonathan. Accelerating inverse solutions with machine learning and randomization. (2023). The University of Texas at Austin.