Machine Learning for semi linear PDEs
This work addresses the challenge of solving semi-linear PDEs for researchers in computational mathematics and machine learning, but it appears incremental as it builds on recent algorithms with improvements in architecture and parameterization.
The authors tackled the problem of solving semi-linear PDEs by proposing a new deep learning algorithm that solves a fixed point problem, which is competitive in accuracy with the best existing methods, though no concrete numbers are provided.
Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms.