2025
PINNs are a class of deep learning models that solve complex, data-driven differential equations by incorporating known physical laws, such as PDEs, directly into the training loss function. Particularly useful with sparse, noisy data. The studies conducted demonstrate the capabilities and limitations of PINNs (Physics-Informed Neural Networks) in solving ordinary differential equations, particularly in the context of stiff systems like the ROBER problem. Vanilla PINNs can effectively solve non-stiff and mildly stiff ODEs, but their performance degrades significantly with increasing stiffness. This is improved via a gradual iterative training procedure of the PINN on systems of increasing stiffness. Overall, PINNs show potential as a flexible tool for solving complex ODEs and inverse problems, but further research is needed to improve their robustness, especially in handling stiffness and noise.
