  Modeling of brain tumor dynamics has the potential to advance therapeutic
planning. Current modeling approaches resort to numerical solvers that simulate
the tumor progression according to a given differential equation. Using
highly-efficient numerical solvers, a single forward simulation takes up to a
few minutes of compute. At the same time, clinical applications of tumor
modeling often imply solving an inverse problem, requiring up to tens of
thousands forward model evaluations when used for a Bayesian model
personalization via sampling. This results in a total inference time
prohibitively expensive for clinical translation. While recent data-driven
approaches become capable of emulating physics simulation, they tend to fail in
generalizing over the variability of the boundary conditions imposed by the
patient-specific anatomy. In this paper, we propose a learnable surrogate for
simulating tumor growth which maps the biophysical model parameters directly to
simulation outputs, i.e. the local tumor cell densities, whilst respecting
patient geometry. We test the neural solver on Bayesian tumor model
personalization for a cohort of glioma patients. Bayesian inference using the
proposed surrogate yields estimates analogous to those obtained by solving the
forward model with a regular numerical solver. The near-real-time computation
cost renders the proposed method suitable for clinical settings. The code is
available at https://github.com/IvanEz/tumor-surrogate.
