Pressio: Enabling projection-based model reduction for large-scale nonlinear dynamical systems

Abstract

This work introducesPressio, an open-source project aimed at enabling leadingedge projection-based reduced order models (ROMs) for large-scale nonlinear dynamical systems in science and engineering. Pressio provides model-reduction methods that can reduce both the number of spatial and temporal degrees of freedom for any dynamical system expressible as a system of parameterized ordinary differential equations (ODEs). We leverage this simple, expressive mathematical framework as a pivotal design choice to enable a minimal application programming interface (API) that is natural to dynamical systems. The core component of Pressio is a C++11 header-only library that leverages generic programming to support applications with arbitrary data types and arbitrarily complex programming models. This is complemented with Python bindings to expose these C++ functionalities to Python users with negligible overhead and no user-required binding code. We discuss the distinguishing characteristics of Pressio relative to existing model-reduction libraries, outline its key design features, describe how the user interacts with it, and present two test cases-including one with over 20 million degrees of freedom-that highlight the performance results of Pressio and illustrate the breath of problems that can be addressed with it.

Model reduction methods for nuclear emulators

“…For example, E has better convergence properties than |ψ in the eigenvalue problem; the RB literature discusses the improvements of focusing on compliant quantities of interest [30,47]. MATLAB mpi-magdeburg.mpg.de/projects/morlab MOR of dynamical systems based on the solution of matrix equations using spectral projection methods modred [92] Python modred.readthedocs.io Library for computing modal decompositions and ROMs, including POD, DMD, and Petrov-Galerkin projection pyROM [93] Python github.com/CurtinIC/pyROM Framework that employs Python visualisation tools; includes POD and DMD pressio [94] C ++ pressio.github.io Minimally-intrusive interface for MOR routines, including Galerkin projections a See also the website of the Model Reduction for Parametrized Systems (MoRePaS) collaboration: morepas.org.…”

Model reduction methods for nuclear emulators

“…Beyond the considerations of emulator quality, building an intrusive emulator for complex systems can be a challenge. There has been great progress in building general software tools for practitioners in reduced-order modeling [47,63,84,85]. Continuing to develop and publicize such tools will permit greater acceptance of these powerful methods in nuclear physics.…”

PERFORM: A Python package for developing reduced-order models for reacting fluid flows

“…Some open-source projects provide implementations of standard ROM methods within a specific flow solver (Grunloh et al, 2021;Hess & Rozza, 2020;Hesthaven et al, 2016;Stabile et al, 2017;Stabile & Rozza, 2018). Other libraries have been developed to provide generic interfaces with dynamical system solvers and supply ROM capabilities, most notably Pressio (Rizzi et al, 2020) and pyMOR (Milk et al, 2016). These libraries allow CFD practitioners to test a suite of standard ROM methods with an existing CFD solver.…”