Reinforcement learning-based estimation for spatio-temporal systems.

State estimators such as Kalman filters compute an estimate of the instantaneous state of a dynamical system from sparse sensor measurements. For spatio-temporal systems, whose dynamics are governed by partial differential equations (PDEs), state estimators are typically designed based on a reduced-order model (ROM) that projects the original high-dimensional PDE onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials.

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows.