Optimization of Physics-Informed Neural Networks for Efficient Surrogate Modeling of Huxley's Muscle Model in Multi-Scale Finite Element Simulations

Huxley's muscle model, originally devised for modeling non-uniform contractions, possesses a noteworthy drawback rooted in its substantial computational demands, particularly evident in the context of multi-scale finite element simulations. In order to address this limitation, we have created surrogate models of Huxley's muscle model. These surrogate models emulate the behavior of the original model while reducing the computational demands in terms of execution time. In this paper, we present the construction of surrogate models using physics-informed neural networks. Besides the precision of neural network predictions, it is also important for the neural network to have a small number of weights in order to be computationally efficient. To optimize the size of the neural network along with the precision of its predictions, we performed Bayesian Optimization. Our physics-informed neural network predicts the probabilities of cross-bridge formation, based on which, force and stiffness can be calculated and used during finite element analysis. In our work, we also present the procedure to integrate a physics-informed neural network into the finite element analysis framework at the micro-level of multi-scale simulation.