All workPython
Research2026
Physics-Informed Neural Networks for the Matrix mKdV System
A two-input/two-output PINN framework for reconstructing complex soliton solutions and recovering unknown system parameters.
7.4×10⁻⁴
relative L2 error
10⁻³
parameter accuracy
2×2
input–output system
Case study 05
Jan – Jun 2026
7.4×10⁻⁴
relative L2 error
10⁻³
parameter accuracy
2×2
input–output system
01 / Context
The problem
Oscillatory and high-gradient regions are difficult for conventional PINN training, particularly when observations are limited. The dissertation also required simultaneous recovery of system parameters rather than only solution reconstruction.
02 / Approach
What I did
- Built a two-input/two-output PINNs framework with differentiated modelling strategies for dark-bright, breather and third-order pole soliton solutions.
- Introduced Fourier feature mapping, structure-aware dense sampling and weighted losses to improve reconstruction.
- Recovered the system parameters λ1 and λ2 from limited observations as part of the training objective.
03 / Outcome
What came out of it
- Reduced relative L2 reconstruction error to 7.4 × 10⁻⁴ under limited observations.
- Recovered system parameters λ1 and λ2 to 10⁻³ accuracy.
- Extended the modelling treatment across multiple soliton-solution families.