Physically inspired neural networks for data-driven inference of biological mechanism.

Systems biology and neurophysiology have recently emerged as powerful tools for a number of key applications in biomedical sciences. Such multiphysics and multiscale models require ad hoc computational strategies and pose extremely high computational demands. Recent developments in the field of deep neural networks have demonstrated the possibility of formulating nonlinear, universal approximators to estimate solutions to highly nonlinear and complex problems with significant speed and accuracy advantages in comparison with traditional models. Physically Constrained Neural Networks (PINN) include analytical and physical constraints in the computational graphs, generating interpretable and parsimonious solutions to complex forward and inverse problems. We will present diverse applications of PINN-based, specialized deep learning architectures, like e.g. inference of hidden neuronal dynamics from real-world data and derivation of arterial input functions from image data exclusively in quantitative PET imaging. PINN-base strategies have the potential to provide high-capacity models with physical plausibility while battling the data paucity commonly observed in biomedical applications.