publications

2024

1. Scaled-up prediction of steady Navier-Stokes equation with component reduced order modeling

   Seung Whan Chung, Youngsoo Choi , Pratanu Roy , and 6 more authors

   2024

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2. Scalable physics-guided data-driven component model reduction for steady Navier-Stokes flow

   Seung Whan Chung, Youngsoo Choi , Pratanu Roy , and 6 more authors

   arXiv preprint arXiv:2410.21583, 2024

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3. A time-parallel multiple-shooting method for large-scale quantum optimal control

   N Anders Petersson , Stefanie Günther , and Seung Whan Chung

   arXiv preprint arXiv:2407.13950, 2024

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4. CMAME

   Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

   Dibyajyoti Chakraborty , Seung Whan Chung, Troy Arcomano , and 1 more author

   Computer Methods in Applied Mechanics and Engineering, 2024

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   Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto–Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

5. Characterization of uncertainties in electron-argon collision cross sections under statistical principles

   Seung Whan Chung, Todd A. Oliver , Laxminarayan L. Raja , and 1 more author

   arXiv preprint arXiv:2404.00467, 2024

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6. CMAME

   Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition

   Seung Whan Chung, Youngsoo Choi , Pratanu Roy , and 7 more authors

   Computer Methods in Applied Mechanics and Engineering, 2024

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   Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ∼ 1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.

2023

1. Accelerating kinetic simulations of electrostatic plasmas with reduced-order modeling

   Ping-Hsuan Tsai , Seung Whan Chung, Debojyoti Ghosh , and 3 more authors

   arXiv preprint arXiv:2310.18493, 2023

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2022

1. JCP

   An optimization method for chaotic turbulent flow

   Seung Whan Chung, and Jonathan B. Freund

   Journal of Computational Physics, 2022

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   Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial ∆\mathbfq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of ∆\mathbfq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the temporarily increases the search scale prior to the strong ∆\mathbfq\to0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. The utility of such an optimized chaotic solution is discussed.

2020

1. JCP

   Regular sensitivity computation avoiding chaotic effects in particle-in-cell plasma methods

   Seung Whan Chung, Stephen D. Bond , Eric C. Cyr , and 1 more author

   Journal of Computational Physics, 2020

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   Particle-in-cell (PIC) simulation methods are attractive for representing species distribution functions in plasmas. However, as a model, they introduce uncertain parameters, and for quantifying their prediction uncertainty it is useful to be able to assess the sensitivity of a quantity-of-interest (QoI) to these parameters. Such sensitivity information is likewise useful for optimization. However, computing sensitivity for PIC methods is challenging due to the chaotic particle dynamics, and sensitivity techniques remain underdeveloped compared to those for Eulerian discretizations. This challenge is examined from a dual particle–continuum perspective that motivates a new sensitivity discretization. Two routes to sensitivity computation are presented and compared: a direct fully-Lagrangian particle-exact approach provides sensitivities of each particle trajectory, and a new particle-pdf discretization, which is formulated from a continuum perspective but discretized by particles to take the advantages of the same type of Lagrangian particle description leveraged by PIC methods. Since the sensitivity particles in this approach are only indirectly linked to the plasma-PIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debye shielding and sheath configurations. In essence, the continuum perspective makes implicit the distinctness of the particles, which circumvents the Lyapunov instability of the N-body PIC system. The cost of the particle-pdf approach is comparable to the baseline PIC simulation.