AstroAI Lunch Talks - June 23, 2025 - Luca Gómez Bachar
23 Jun 2025 - Joshua Wing
The video can be found here: https://www.youtube.com/watch?v=qj12C6a9lXk
Speaker: Luca Gómez Bachar (ITeDA, Harvard University)
Title: Evolution of linear matter perturbations with error-bounded bundle physics-informed neural networks
Abstract: The Physics-Informed Neural Network (PINN) bundle method provides a significant reduction in the computational time required for the inference process when the problem is computationally demanding to integrate. However, it is still necessary to rely on numerical solutions to assess the precision of the results, even though these numerical solutions are not used by the PINN bundle method to solve the differential system. This approach is required because the PINN bundle method does not yet provide an error bound for its solutions, regardless of the type of differential equation. Error bounds have only been developed for linear ODEs, certain nonlinear ODEs, and a specific kind of first-order linear PDEs. Recently, we have also developed an exact bound for a family of nonlinear first-order ODEs, of which, after some variable changes, the matter perturbation equation is a particular case. In this work, we use these results to calculate an error bound on the theoretical prediction of fσ₈(z) obtained using the PINN bundle method without relying on the numerical solution. This allows us to use the PINN-based solutions to perform a statistical analysis. Finally, the use of an updated data set, developed by ourselves, allows us to obtain more stringent constraints on the Ωₘ − σ₈ plane than previous works.