ModelOrderReduction.jl -- Symbolic-Enhanced Model Simplification

We present ModelOrderReduction.jl -- a Julia package for the automatic simplification of scientific models by way of symbolic computation. As such, ModelOrderReduction.jl enables modelers without detailed knowledge of the domain of model order reduction to automatically generate simplified models that approximate the dominant behavior of otherwise too complex ones.

The computational analysis of complex physicochemical phenomena or networked systems relies commonly on the simulation of detailed large-scale models. The computational burden imposed by simulating such large-scale models, however, is frequently found to render a range of scientific and engineering tasks like design, control or uncertainty quantification prohibitively expensive. To recover the tractability of such tasks in this setting, it is customary to build a compact, cheap-to-evaluate proxy for the original large-scale model which captures its dominant behaviors accurately, i.e, a reduced order model. And while there exists a wide range of systematic techniques to build such reduced order models, it typically remains a tedious, error-prone and often ad hoc process that frequently requires substantial intrusion into the original model. With ModelOrderReduction.jl we set out to streamline and largely automate this process, keeping active intrusion into the model by the user to a minimum. To that end, we rely on a symbolic representation of the original model specified via ModelingToolkit.jl. The reduction task is then performed on the symbolic representation using the tools provided by Symbolics.jl.

For those who are non-technical, we will discuss how this approach fits into the paradigm of symbolic-numeric computing and as such applies automatic code transformations beyond automatic differentiation that benefit greatly from the features of the Julia programming language.

For modelers, we will show with scientific PDE and ODE models from the realms of chemical engineering and neuroscience how ModelOrderReduction.jl can help you reduce your models and speed up your computations.

For those who are technical, we will dive into greater mathematical detail about the model order reduction techniques that are supported in ModelOrderReduction.jl and why they lend themselves to being automated by way of symbolic computation. We will specifically focus on the automatic generation of efficient discrete empirical interpolators and polynomial chaos expansions as well as the associated reduced order models obtained from Petrov-Galerkin projection.