SciML Symbolic-Numeric Computing Projects – Google Summer of Code

Automated Model Order Reduction

Model order reduction is a technique for automatically finding a small model which approximates the large model but is computationally much cheaper. We plan to use the infrastructure built by ModelingToolkit.jl to implement a litany of methods and find out the best way to accelerate differential equation solves.

Recommended Skills: A basic background in differential equations and the ability to use numerical ODE solver libraries. Background in the numerical analysis of differential equation solvers is not required.

Expected Results: Efficient and high-quality implementations of model order reduction methods.

Mentors: Chris Rackauckas

Expected Project Size: 350 hour.

Difficulty: Medium to Hard depending on the chosen subtasks.

Automated symbolic manipulations of differential equation systems

Numerically solving a differential equation can be difficult, and thus it can be helpful for users to simplify their model before handing it to the solver. Alas this takes time... so let's automate it! ModelingToolkit.jl is a project for automating the model transformation process. Various parts of the library are still open, such as:

Recommended Skills: A basic background in differential equations and the ability to use numerical ODE solver libraries. Background in the numerical analysis of differential equation solvers is not required.

Expected Results: Efficient and high-quality implementations of model transformation methods.

Mentors: Chris Rackauckas and Yingbo Ma

Expected Project Size: 175 hour or 350 hour depending on the chosen subtasks.

Difficulty: Medium to Hard depending on the chosen subtasks.

Symbolic chemistry and calculating reaction rate coefficients

Catalyst is a great tool to model chemical reactions, but often reaction rate coefficients are usually suspect. There are well established methods to calculate what these coefficients should be given the activation energy of a reaction. We want to automate part of this modeling, allowing the user to provide atom-bond graphs and have coefficients determined for free.

Recommended Skills: Strong understanding of chemistry and Julia open-source programming, particularly Symbolics.jl and ModelingToolkit.jl.

Expected Results: Define an interface for providing a Symbolics.jl object that contains relevant metadata for calculating activation energy and reaction rate coefficients using the Arrhenius equation.

Mentors: Chris Rackauckas, Anand Jain and Samuel Isaacson

Expected Project Size: 175 hour or 350 hour depending on the chosen subtasks.

Difficulty: Easy to Medium depending on the chosen subtasks.

Symbolic Analysis and Transformations of Chemical Reaction Networks

Catalyst.jl provides the ability to create symbolic models of chemical reaction networks, generate symbolic differential equation and stochastic process models from them, and offers some limited ability to analyze the symbolic chemical reaction networks. There are a variety of ways Catalyst.jl's core capabilities could be expanded, including adding

Recommended Skills: Strong understanding of ODE models for chemical systems and Julia open-source programming, particularly Symbolics.jl and ModelingToolkit.jl.

Expected Results: Extend Catalyst with one or more of the preceding features, with corresponding ModelingToolkit updates, enabling users to build, analyze, and simulate Catalyst-derived models incorporating the new components.

Mentors: Samuel Isaacson and Chris Rackauckas.

Expected Project Size: 175 hour or 350 hour depending on the chosen subtasks.

Difficulty: Easy to Hard depending on the chosen subtasks.