Speaker
Description
The characterization of tumor evolution through partial differential equations (PDEs), ranging from reaction-diffusion systems to moving-interface models, provides essential insights into cancer progression. However, utilizing these high-dimensional frameworks in inverse settings to recover patient-specific biophysical properties is often computationally prohibitive due to the requirement for repeated forward evaluations.
We propose a novel framework for fast, grounded inversion by leveraging Latent Dynamics Networks (LDNets), introduced by Regazzoni et al. (2024), as consistent, causal surrogates. Rather than operating in high-dimensional discretized spaces, this architecture discovers a low-dimensional manifold to represent complex spatio-temporal dynamics. The architecture employs two neural components: $\mathcal{NN}_{dyn}$, which learns the intrinsic evolution of a latent state $s(t)$, and $\mathcal{NN}_{rec}$, a meshless reconstruction network mapping the latent state and spatial coordinates $x$ to the output field $\tilde{y}(x,t)$. This approach exploits the low intrinsic dimensionality of tumor growth dynamics. By leveraging the manifold hypothesis, we utilize the biophysiological regularity of tumor expansion as an inductive bias, allowing us to compress complex spatio-temporal evolution into a compact, low-dimensional latent space.
Because the surrogate is fully differentiable, it enables rapid parameter recovery even in non-ideal clinical scenarios. This includes inversion from noisy data or "non-rest" conditions where the initial state and timing of the tumor are unknown. Finally, the efficiency of this surrogate approach facilitates robust Uncertainty Quantification. By enabling rapid sampling methods, the framework provides a principled approach to estimating parameter posterior distributions, offering a more reliable foundation for predictive modeling in oncology