Domain-Informed Machine Learning
Many advances in signal and image processing were driven in the past years by optimization techniques, neural networks, and synergy between the two. Model-Informed ML can now combine both traditional methods and deep learning ones for enhanced performance, efficiency, and stability.
Despite that, representation at a given scale, such as grid discretization for 2D or 3D, remains essential but it has limitations, including high memory use, resolution rigidity, and inefficiency for complex structures.
Implicit neural representations and Physics-Informed Neural Networks (PINNs) offer alternatives by representing objects continuously, avoiding discretization constraints. While promising, they currently hold for specific tasks only, and an objective is to broaden their applications in information processing. We also study new neural networks architectures by imposing equivariance to the physical symmetries of the problem (e.g., geometric transformations), and investigate how these additional constraints can remove the need of ground-truth data for training.
These frameworks offer promising ways to handle large datasets without grid-discretization stage but remain specialized to very limited task in image processing such as view synthesis or simple task of inverse problems (e.g. interpolation) and thus pave the way to future research developments.