Rapid advances in both computing capabilities and efficient algorithms make it possible to carry out simulations of physics-based models of increasing size and complexity. In some situations, however, the primary requirement is providing very fast turnaround of solutions or ensembles of solutions, as in design optimization, real-time control, and on-demand disaster modeling, rather than maximizing the fidelity of the model. In these cases, model reduction provides an alternative and efficient process that combines methods from physics-based simulation, data science, and data compression, trading generality for an orders-of-magnitude reduction in computing costs.
Our project advanced reduced-order modeling technology as applied to a suite of models based on partial differential equations relevant to Lawrence Livermore National Laboratory. We focused on the Laboratory's ARDRA linear transport code and the radiation diffusion capability in the BLAST code as platforms for model reduction research and targets for implementation of model reduction features. Our work provided 1) the algorithmic and high-performance computing (HPC) capabilities necessary to compute the largest known, proper orthogonal decomposition based model reduction, using the ARDRA code, 2) space-time reduced order model (ROM) algorithms applicable to the ARDRA code, 3) nonlinear ROM capabilities applied to 2T radiation diffusion using hyper-reduction methods in the BLAST code, and 4) the development of an open-source software infrastructure for projection-based model reduction, libROM, that can be applied across linear and nonlinear simulation codes. We have validated that nonlinear ROMs utilizing hyper-reduction are a credible technology for very fast model evaluations in "outer-loop" applications such as design optimization or parameter studies.
Our algorithms and code advanced the Laboratory's HPC, simulation, and data science core competencies. We created first-of-their-kind, projection-based, reduced-order model capabilities and demonstrated them in two important laboratory simulation codes, ARDRA and BLAST. Our approach can be implemented in Livermore's MFEM, a core component of multiple mission-related codes. We also created an open-source library that enables further ROM development work in laboratory codes.
Choi, Y. 2018. "ST-GNAT and SNS: Model Order Reduction Techniques for Nonlinear Dynamical Systems." Linear Algebra and Optimization Seminar, Stanford, CA, October 2018. LLNL-PRES-758124.
Choi, Y. and B. Arrighi. 2018. "Space-Time Reduced Order Model for Dynamical Systems." Data Science Workshop, Livermore, CA, August 2018. LLNL-POST-753977.
Choi, Y. and K. Carlberg. 2018. "Space-Time Least-Squares Petrov-Galerkin Nonlinear Model Reduction." West Coast ROM Workshop, Berkeley, CA, November 2017. LLNL-PRES-728809.
Kostova-Vassilevskaa, T. and G. M. Oxberry. 2017. "Model Reduction of Dynamical Systems by Proper Orthogonal Decomposition: Error Bounds and Comparison of Methods Using Snapshots from the Solution and the Time Derivatives - ScienceDirect." Journal of Computational and Applied Mathematics, 330:553-573. doi: 10.1016/j.cam.2017.09.001. LLNL-JRNL-720257.
Oxberry, G., et al. 2017. "libROM: A Distributed-Memory Adaptive Incremental Proper Orthogonal Decomposition." LLNL-PRES-725445.
——— . 2018. "Laser-Assisted Advanced Manufacturing." 10th CIRP Conference on Photonic Technologies, Furth, Germany, September 2018. LLNL-PRES-751323.
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