2025-10-02 –, Jean-Baptiste Say Amphitheater
Language: English
Universal Differential Equations (or UDEs for short) have emerged as a novel way to integrate information
from experimental data into mechanistic models. In this talk I will present ModelingToolkitNeuralNets, a package intended to help with embedding neural networks inside ModelingToolkit models.
In this talk we will discuss about how to augment acasual models in the ModelingToolkit framework and about how does the architecture impact the kind of corrections we can make.
The initial paper on UDEs [1], a methodology is described for systems of differential equations, but in the context of acasual models we start with sets of differential algebraic equations (DAEs) for each component and then a simplification algorithm condenses them in a final system of DAEs that will be solved.
This two stage nature of the process naturally divides the possible UDE architectures in two: before structural simplification, where we have we deal with individual components and after simplification where we only have the final simplified system without a direct link to the individual components. We will call these component level UDEs and system level UDEs. In this talk I will mainly focus on component level UDEs.
The ModelingToolkitNeuralNets.jl package provides a block component that abstracts a Lux.jl neural network. This block component can be then used as any other component from the ModelingToolkitStandardLibrary. Besides that, we also have a function based interface with the SymbolicNeuralNetwork API.
In this talk I will present how to use the package and explore some applications for UDEs in the context of component based models.
[1] C. Rackauckas et al., “Universal Differential Equations for Scientific Machine Learning,” arXiv:2001.04385 [cs, math, q-bio, stat], Jan. 2020, Accessed: Feb. 09, 2020. [Online]. Available: http://arxiv.org/abs/2001.04385
