Astrocytes are the largest subset of glial cells and perform structural, metabolic, and regulatory functions. They are directly involved in the communication at neuronal synapses and the maintenance of brain homeostasis. Several disorders, such as Alzheimer's, epilepsy, and schizophrenia, have been associated with astrocyte dysfunction. Computational models on various spatial levels have been proposed to aid in the understanding and research of astrocytes. The difficulty of computational astrocyte models is to fastly and precisely infer parameters. Physics informed neural networks (PINNs) use the underlying physics to infer parameters and, if necessary, dynamics that can not be observed. We have applied PINNs to estimate parameters for a computational model of an astrocytic compartment. The addition of two techniques helped with the gradient pathologies of the PINNS, the dynamic weighting of various loss components and the addition of Transformers. To overcome the issue that the neural network only learned the time dependence but did not know about eventual changes of the input stimulation to the astrocyte model, we followed an adaptation of PINNs from control theory (PINCs). In the end, we were able to infer parameters from artificial, noisy data, with stable results for the computational astrocyte model.
Keywords: astrocyte; computational model; parameter inference; physics informed neural networks; physics informed neural-net control.