Seminar by Irina Tezaur

Speaker

Irina Tezaur (Sandia National Laboratories)

Title

Rigorous component-based coupling of first-principles and data-driven models

Date

  • April 30, 2024 16:00 CEST+0200 (Europe/Rome)

  • April 30, 2024 10:00 EDT-0400 (US/Eastern)

  • April 30, 2024 09:00 CDT-0500 (US/Central)

  • April 30, 2024 07:00 PDT-0700 (US/Pacific)

Abstract

This talk will describe several recent advancements in developing a rigorous mathematical framework for the domain decomposition-based coupling of arbitrary combinations of first-principles numerical methods with data-driven models under the flexible Heterogeneous Numerical Methods (fHNM) project at Sandia National Laboratories. After giving a high-level overview of this project and its research vision, we will take you on a deep dive into two of the coupling methods pursued under fHNM as they relate to the coupling of projection-based reduced order models (ROMs) with each other and with conventional full order models (FOMs): (1) alternating Schwarz-based coupling, and (2) coupling via generalized mortar methods (GMMs).

In the first part of the talk, we will discuss a recent extension of the Schwarz alternating method (Mota, Tezaur, and Alleman 2017; Mota, Tezaur, and Phlipot 2022) that enables the creation of FOM-ROM and ROM-ROM couplings from nonlinear monolithic problems. This method works by performing an overlapping or non-overlapping domain decomposition (DD) of the physical domain, and solving a sequence of problems on these subdomains, with information propagating through carefully-constructed transmission conditions on the subdomain boundaries (Barnett, Tezaur, and Mota 2022). We will showcase recent results obtained by implementing this method in the open-source Pressio demo-apps library. Time-permitting, we will summarize our experience in applying the method to couple subdomain-local Physics-Informed Neural Networks (PINNs) with each other and with FOMs (Snyder, Tezaur, and Wentland 2023).

In the second part of the talk, we will present a new partitioned method that enables FOM-ROM and ROM-ROM coupling following a non-overlapping DD of the physical domain. At the crux of this method is a dual Schur complement system, which implicitly expresses a Lagrange multiplier, representing the interfacial flux, in terms of the state variables (de Castro et al. 2023). The solution of the Schur complement system and the application of an explicit time-stepping scheme allow for the subdomain equations to be decoupled and independently solved at each time step. Time-permitting, we will briefly mention some recent work that mitigates the cost of solving the required Schur complement problem by replacing it with a pre-trained Dynamic Mode Decomposition (DMD) or neural ODE (nODE) model.

We evaluate the new coupling methods on canonical test cases from several applications. Our results demonstrate that the proposed coupling methodologies are computationally efficient and capable of coupling disparate models without introducing numerical artifacts into the solution. Importantly, our results suggest that FOM-ROM and ROM-ROM couplings of the sort considered have the potential of improving the predictive viability of projection-based ROMs, by enabling the spatial localization of ROMs (via domain decomposition) and the online integration of high-fidelity information into these models (via FOM coupling). Sandia National Laboratories is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. This work is in collaboration with Chris Wentland (Sandia National Laboratories), Francesco Rizzi (NexGen Analytics), Joshua Barnett (Cadence Design Systems), Alejandro Mota (Sandia National Laboratories), Amy de Castro (Clemson University), Pavel Bochev (Sandia National Laboratories).

Barnett, Joshua, Irina Tezaur, and Alejandro Mota. 2022. “The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models.” In Computer Science Research Institute Summer Proceedings 2022, s. Seritan and j. Smith, Eds.

de Castro, Amy, Pavel Bochev, Paul Kuberry, and Irina Tezaur. 2023. “Explicit Synchronous Partitioned Scheme for Coupled Reduced Order Models Based on Composite Reduced Bases.” Computer Methods in Applied Mechanics and Engineering 417: 116398. https://doi.org/10.1016/j.cma.2023.116398.

Mota, Alejandro, Irina Tezaur, and Coleman Alleman. 2017. “The Schwarz Alternating Method in Solid Mechanics.” Computer Methods in Applied Mechanics and Engineering 319: 19–51. https://doi.org/https://doi.org/10.1016/j.cma.2017.02.006.

Mota, Alejandro, Irina Tezaur, and Gregory Phlipot. 2022. “The Schwarz Alternating Method for Transient Solid Dynamics.” International Journal for Numerical Methods in Engineering 123 (21): 5036–71. https://doi.org/10.1002/nme.6982.

Snyder, Will, Irina Tezaur, and Christopher Wentland. 2023. “Domain Decomposition-Based Coupling of Physics-Informed Neural Networks via the Schwarz Alternating Method.” In Computer Science Research Institute Summer Proceedings 2023, s. Seritan and b. Reuter, Eds.

Recording

Watch the recording on our YouTube channel.