  Inverse problems in granular flows, such as landslides and debris flows,
involve estimating material parameters or boundary conditions based on target
runout profile. Traditional high-fidelity simulators for these inverse problems
are computationally demanding, restricting the number of simulations possible.
Additionally, their non-differentiable nature makes gradient-based optimization
methods, known for their efficiency in high-dimensional problems, inapplicable.
While machine learning-based surrogate models offer computational efficiency
and differentiability, they often struggle to generalize beyond their training
data due to their reliance on low-dimensional input-output mappings that fail
to capture the complete physics of granular flows. We propose a novel
differentiable graph neural network simulator (GNS) by combining reverse mode
automatic differentiation of graph neural networks with gradient-based
optimization for solving inverse problems. GNS learns the dynamics of granular
flow by representing the system as a graph and predicts the evolution of the
graph at the next time step, given the current state. The differentiable GNS
shows optimization capabilities beyond the training data. We demonstrate the
effectiveness of our method for inverse estimation across single and
multi-parameter optimization problems, including evaluating material properties
and boundary conditions for a target runout distance and designing baffle
locations to limit a landslide runout. Our proposed differentiable GNS
framework offers an orders of magnitude faster solution to these inverse
problems than the conventional finite difference approach to gradient-based
optimization.
