Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Journal Article · 14 January 2025 · SIAM Journal on Scientific Computing

DOI: https://doi.org/10.1137/23m1625366 · OSTI ID:2506988

Maltba, Tyler E.  ^[1]; Zhao, Hongli  ^[2]; Maldonado, Daniel Adrian ^[3]

---

1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. Univ. of Chicago, IL (United States)
3. Argonne National Laboratory (ANL), Argonne, IL (United States)

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: 89233218CNA000001; AC02-06CH11357
• OSTI ID: 2506988
• Report Number(s): LA-UR--23-34004; 185381
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 47; ISSN 1064-8275; ISSN 1095-7197
• Publisher: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
• Country of Publication: United States
• Language: English