Juliacon 2024

PhysicsInformedRegression.jl is a package which allows the use of Ordinary Least Squares to solve the inverse problem for models based on non-linear differential equations. This method has been tested and compared against non-linear optimization methods on Physics Informed Neural Networks, which is an alternative strategy for solving the same problem. Although both methods manage to successfully estimate target parameters, Physics Informed Regression has been shown to outperform in terms of accuracy and speed. Especially for larger and more complicated models. In theory, the method could outperform all non-linear optimization strategies, assuming state derivatives can be computed from data with high accuracy. In our examples we use an implementation of finite differences (finite_diff) to compute these derivatives, but in practice alternative methods should be explored, especially for noisy data sampled at a low rate.

The method physics_informed_regression has been implemented using the ModelingToolkit framework, such that it applies seemlessly to generic models, using only few lines of code. This also implies compatibility with other modules within the ecosystem, such as Catalyst.jl (see enyzyme-reaction example in the repository).