Aggregate Loss Data Assimilation (ALDA) for Supersonic BOS

Experimental measurements of practical flows are needed to develop and validate numerical models for design. However, real fluid measurements exhibit limited resolution and often provide path-integrated or bulk information. We explore a new aggregate loss (AL) approach to data assimilation (DA): ALDA. The method is applied to high-speed flow using background-oriented schlieren data. CFD solvers often incorporate measurements using computationally-intensive DA techniques such as Kalman filter, state observer, and adjoint–variational methods. Physics-informed neural networks (PINNs) were proposed as a low-cost DA tool, but PINNs implicitly filter the flow and considerable effort is required to optimize their architecture. For complex flows, an expensive domain decomposition technique must be employed to capture the dynamically relevant scales. ALDA uses the same optimization tools as a PINN to quickly solve for flow fields that roughly satisfy the governing equations and match experimental data. However, the flow is parameterized as integral quantities in finite volumes (voxels) and the physics loss is evaluated using discrete numerical operators. The result is a more scalable and interpretable model with well-known and controllable numerical filtering properties.