LEAPS-MPS: Physics-oriented Numerical Solutions for Poromechanics

Poromechanics plays an important role across various disciplines, including geosciences, medicine, and biophysics. A classical and widely used poromechanics model is the Biot’s model. Multiple-network poroelastic theory (MPET) has been introduced into poromechanics as a generalization of Biot’s theory. Over the past decade, MPET has found diverse applications in medicine and biomechanics, making it an active area of research. However, the computational complexity of multiple-network poromechanics models poses challenges, particularly due to the wide-ranging variations in physical parameters encountered in practical applications. Another computational challenge in poromechanics lies in preserving fundamental physical laws such as mass conservation and constitutive laws, as well as the conservation of angular momentum in numerical solutions. This project provides excellent opportunities for graduate and underrepresented undergraduate students to gain multidisciplinary training in physics, computational mathematics, and deep learning, and to develop cutting-edge numerical algorithms for applications in science and engineering. Furthermore, the research is conducted at Missouri University of Science and Technology, contributing positively to the rural Midwest region surrounding the institute. This project is devoted to a systematic study of physics-oriented numerical solutions for poromechanics, mainly focusing on MPET model and includes: i) developing physics-oriented parameter robust and more practical numerical discretizations strongly preserving the mass conservation in poromechanics and preserving the symmetry of the tress tensor exactly in those discretizations; ii) designing physics-oriented parameter robust and ecient iterative methods for linear system arising from those discretizations including preconditioning, multigrid methods and fixed-stress methods; iii) developing physics-oriented deep learning numerical methods in the cases the physical parameters are anisotropic, discontinuous, or even perform as randomly distributed function on a domain with complex geometry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.