4. Conclusion

The goal of this project was to implement and test a novel mathematics-informed PINN method to solve the decay equation. In the end we were able to solve the decay equation with both decay and burnup matrices, for matrices with stiffnesses up to about $\kappa(A) = 10^{19}$ and matrices of any size. The latter claim was tested on a burnup matrix of size 442. PINN method is faster than CRAM for matrices with stiffness below $10^{16}$, with relative final error compared to CRAM of around $10^{-5}$. CRAM is more accurate than PINN. But if we compare the PINN method to a general purpose PINN, such as presented in, the method performs better both in terms of accuracy and computation time. It is also able to solve bigger and stiffer problems compared to general purpose PINNs, which were tested on matrices of size 3 and stiffness up to 500.

In future research, there are three main areas of focus to enhance the existing work. Firstly improving performance at higher stiffness levels, secondly on decreasing the use of memory for better efficiency when dealing with bigger matrices, and thirdly on finding an optimal way of setting the weight ratio. It is also necessary to perform further analysis with the burnup method to test its performance limitations.