Rapidly accelerated numerical solvers using operator networks for performing laser-tissue optothermal simulations

To numerically characterize optothermal interactions at the laser-tissue interface during tissue imaging or surgery, the bioheat transfer partial differential equation (PDE) must be solved using a laser excitation source function. Given the range of possible experimental scenarios, the PDEs become parametric and must be solved for multiple optical and laser parameters. Due to constraints such as solver stability and domain size, classical numerical techniques used for performing such simulations are often computationally taxing and time consuming. To overcome these challenges, we propose to learn the mapping between infinite dimensional function spaces of the parameterized laser source functions and the solutions of the parametric bioheat transfer PDEs. In this work, we introduce Res-DeepONet, a new neural network architecture leveraging deep operator networks for rapidly accelerating PDE inferences. We train our operator network using synthetic laser heating source functions consisting of Gaussian beam profiles. The proposed neural network architecture demonstrates excellent generalization performance on unseen Gaussian source functions, achieving a 30× speedup over the classical finite difference method. With the introduction of Res-DeepONets, we aim to bring a paradigm shift in performing bioheat transfer simulations in the realm of laser-tissue interactions.