Real-time simulation of soft-tissue deformation is an important enabling technology for medical
applications such as surgical training, preoperative planning, and computer-assisted and robotic
surgery. While classical numerical methods, in particular finite element methods (FEM), provide
accurate solutions for hyperelastic material models, their computational cost often prevents real-time use or requires substantial model simplifications. Recently, deep learning-based surrogate models have emerged as a promising alternative, offering fast inference times. However, their applicability to realistic soft-tissue simulation remains limited, primarily due to insufficient generalization across complex geometries, boundary conditions, and material variations, as well as evaluation on overly simplified benchmark problems.
The objective of this project is to advance deep learning-based surrogate models for real-time hyperelastic soft-tissue simulation, with a particular focus on robust generalization across geometries and boundary conditions relevant to medical applications. We focus on neural operator-based approaches, which learn mappings between function spaces and are naturally suited for parametrized partial differential equations. In addition, the differentiability of these models enables their use in gradient-based downstream tasks, such as inverse problems, which are relevant for applications including tissue property estimation.