| Deep learning is widely considered to be an extremely representative research in the field of machine learning or artificial intelligence today.This paper mainly studies two types of problems: one is the reconstruction of compressed sensing magnetic resonance imaging(CS-MRI),and the other is to solve the nonlinear Biot problems.In terms of CS-MRI image reconstruction,this paper combines traditional model-driven compressed sensing reconstruction algorithms with data-driven deep learning methods to propose a new algorithm—ADMM-CNN.This proposed algorithm solves one sub-problem in the alternating direction multiplier method(ADMM)using convolutional neural networks,and then constructs a loss function to optimize the penalty parameters and Lagrange multiplier update rates in ADMM using gradient descent,thus obtaining a trained ADMM model that can effectively reconstruct magnetic resonance imaging signal from compressed sensing measurements.On the other hand,the paper systematically studies the numerical solution of quasi-static Biot model,including the numerical solution of linear and nonlinear Biot model forward and inverse problems in two and three dimensions by designing physics-informed neural networks and self-adaptive physics-informed neural networks.We study the solution performance of PINNs when → ∞,and the self-adaptive PINNs algorithm is proposed to simulate solutions with high spatiotemporal complexity comparing with the original PINNs.In addition,the self-adaptive PINNs is applied to simulate brain pressure distribution,demonstrating its ability to solve irregular boundary and practical problems.The results show that physics-informed neural networks have good precision in solving nonlinear problems,forward and inverse problems and high-dimensional problems. |
