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  5. Efficient Reduced-Order Models for Multi-Physics Simulations

Efficient Reduced-Order Models for Multi-Physics Simulations

Youngsoo Choi | 21-FS-042

Project Overview

The reduced order model team at Lawrence Livermore National Laboratory (LLNL) has developed several efficient algorithms that accurately accelerate single physical simulations, such as Lagrangian hydrodynamics and particle transport simulations. However, the speed-up and accuracy initially was not satisfactory for some applications, e.g., only providing a speedup of a factor of two with a relative error around 4% with respect to the corresponding full order model solutions. Furthermore, many LLNL critical missions require fast and accurate multi-physics simulations. Therefore, the reduced order model team wanted to check the feasibility of further improving the accuracy and speedup of both single- and multi-physics model calculations. Also, the team wanted to develop the feasibility of non-intrusive reduced order models by using the dynamics identification algorithm, which does not require a priori knowledge of the numerical methods and implementation of the full order model physics solver.

We take two basic approaches to accomplish the goals above: (1) physics-constrained data-driven approach and (2) non-intrusive data and dynamics identification-driven approach. For the first approach, we have improved the accuracy and speed-up of the single physics solver tremendously by intelligently choosing the simulation data. It was vital to carefully investigate the numerical path that the full order model physics solver takes each time step. Additionally, we have identified that the nonlinear behavior, determining the time derivative behavior in the first principles of the underlying physics, which can be efficiently represented by a mathematical modification of the solution dynamics. These two steps enabled us to improve the accuracy of the single physics Lagrangian hydrodynamics simulation from 2% to 0.04% relative error. At the same time, we were able to improve the speedup from around 2x to 26x for the Sedov blast problem and around 9x to 75x for the Triple-point problem. For the multi-physics problems, we developed a physics-constrained data-driven reduced order models. We have implemented the reduced order model capability for rad-hydro multi-physics problems in MARBL (i.e., a Weapons Simulation and Computing (WSC) physics code developed by LLNL). The reduced order model was able to achieve a speedup of 9x with a relative error of 0.1%. Furthermore, we also demonstrated that the physics-constrained approach shows robustness in extrapolation, which is not possible for purely data-driven machine learning-based method. For Sedov blast problems, the local reduced order model, which was built using only one initial blast energy parameter point, i.e., 0.25, was able to maintain the relative error of around 1% for the initial blast energy from 0.1 to 0.4. For the non-intrusive dynamics identification-based approach, we have developed the LAtent Space Dynamics Identification (LaSDI) method. In the LaSDI method, we compressed the full order model simulation data into reduced space data. The dynamics in the reduced space is often simpler than the dynamics in the full space. We applied the dynamics identification regression techniques to the reduced space data. The identified dynamics equation played the role of predicting a new reduced space solution, which is in turn decompressed into the full space solution. Furthermore, we adopted the automatic greedy algorithm with the LaSDI method to apply physics-informed sampling procedure. We call the method gLaSDI, short for the "greedy LaSDI method." We have applied the gLaSDI method to a benchmark problem, i.e., advection dominated 1D Burgers equations. The gLaSDI method was able to achieve a relative error of 4% with a speed-up of 8x.

Mission Impact

Although there are many sophisticated physics solvers producing high accuracy solutions with high resolution, one of the main bottlenecks hindering the next breakthrough in several LLNL mission areas is the expensive computational cost for one forward simulation. It is too expensive to be practically used in multi-query applications, such as design optimization, uncertainty quantification, and inverse problems. Our reduced order model development, i.e., data-driven physics-constrained physical simulation tool, provides a broadly applicable framework, in which physicists and analysts can do fast physics calculation accurately without losing resolution so that they can achieve breakthrough scientific discovery and innovative design in almost every LLNL mission, including, but not limited to, space science and security, quantum science and technology, nuclear weapons science, high explosive physics, chemistry, and material science, nuclear threat reduction, and hypersonics.

Publications, Presentations, and Patents

Hoang, Chi, Youngsoo Choi, and Kevin Carlberg. 2021. "Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction." Computer methods in applied mechanics and engineering, 384.

Kim, Youngkyu, Karen Wang, and Youngsoo Choi. 2021. "Efficient space-time reduced order model for linear dynamical systems in Python using less than 120 lines of code." Mathematics, 9(14).

McBane, Sean and Youngsoo Choi. 2021. "Component-wise reduced order model lattice-type structure design." Computer Methods in Applied Mechanics and Engineering, 381.

Choi, Youngsoo. "Why efficient nonlinear manifold reduced order models" at mini-symposium (MS 4-9) of "Advances in reduced order modeling of solids, fluids, and porous media," MMLDT-CSET, September 26-29, 2021.

Choi, Youngsoo. "Physics-constrained data-driven methods of accurately accelerating simulations and their applications," at PhIML Seminar, Pacific Northwest National Laboratory, August 16, 2021.

Choi, Youngsoo. "Efficient nonlinear manifold reduced order model," at mini-symposium of "Model Order Reduction for Physical Simulations," 16th U.S. National Congress on Computational Mechanics, July 25-29, 2021.

Copeland, Dylan. "Accelerating Lagrangian Hydrodynamics Simulation with Space-time Reduced Order Models," at mini-symposium of "Model Order Reduction for Physical Simulations," 16th U.S. National Congress on Computational Mechanics, July 25-29, 2021.

Cheung, Siu Wun. "Reduced-order modeling for hydrodynamics simulation of the Rayleigh-Taylor instability," at mini-symposium of "Model Order Reduction for Physical Simulations," 16th U.S. National Congress on Computational Mechanics, July 25-29, 2021.

Choi, Youngsoo. "Accelerating design optimization using reduced order models," at WCSMO-14, June 13-18, 2021.

Choi, Youngsoo. "Machine learning powered nonlinear manifold reduced order model," at Computational Science and AI in Industry, ECCOMAS Thematic Conference, June 7-9, 2021.

Choi, Youngsoo. "Data-driven methods of accelerating physical simulations and their applications," at Machine Learning + X seminar, CRUNCH group, Brown University, June 4, 2021.

Choi, Youngsoo. "Nonlinear manifold reduced order model for hydrodynamics," at IOP Institute of Physics, PETER 2021, May 25-27, 2021.

Cheung, Siu Wun. "Reduced-order modeling for hydrodynamics simulation of the Rayleigh-Taylor instability," at IOP Institute of Physics, PETER 2021, May 25-27, 2021.

Copeland, Dylan. "Accelerating Lagrangian hydrodynamics simulation with reduced order models," at IOP Institute of Physics, PETER 2021, May 25-27, 2021.

Choi, Youngsoo. "Data-driven methods of accelerating physical simulations and their applications," at the Applied Mathematics Colloquium in the Institute of Analysis and Numerics, University of Muenster, May 19, 2021.

Choi, Youngsoo. "Where are we with data-driven surrogate modeling for various physical simulations," at CMAI Colloquium, April 16, 2021.

Choi, Youngsoo"Where are we with data-driven surrogate modeling for various physical simulations," at AJS - Analysis Junior Seminars, March 19, 2021.

Choi, Youngsoo. "A fast and accurate neural network reduced order model for advection-dominated physical simulations," at SIAM conference on Computational Science and Engineering (CSE21), March 1-5, 2021.

Copeland, Dylan. "Accelerating Lagrangian hydrodynamics simulation with reduced order models," at SIAM conference on Computational Science and Engineering (CSE21), March 1-5, 2021.

Choi, Youngsoo. "Where are we with data-driven surrogate modeling for various physical simulations," at MAE Spring 2021 Seminar Series, Cornell University, February 16, 2021.

Choi, Youngsoo. "Where are we with data-driven surrogate modeling for various physical simulations," at MEMS Seminar, Duke University, February 3, 2021.

Choi, Youngsoo. "Component-wise reduced order model lattice design," at 14th World Congress in Computational Mechanics and ECCOMAS Congress, January 11-15, 2021.

Choi, Youngsoo. "Efficient nonlinear manifold reduced order model," at Machine Learning for Engineering Modeling, Simulation, and Design, Workshop at Neural Information Processing Systems, December 12, 2020.