FUSE: Fast Unified Simulation and Estimation for PDEs
This addresses the problem of inefficiency and inconsistency in separately handling field prediction and parameter estimation for researchers and practitioners in computational physics and engineering, representing an incremental improvement by integrating existing approaches.
The paper tackled the joint prediction of continuous fields and statistical estimation of discrete parameters in PDE-governed systems by proposing a unified framework, resulting in significantly increased accuracy in both inverse and surrogate tasks compared to baselines.
The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator learning surrogates for field prediction while using simulation-based inference (and its variants) for statistical parameter determination. Here, we argue that solving both problems within the same framework can lead to consistent gains in accuracy and robustness. To this end, We propose a novel and flexible formulation of the operator learning problem that allows jointly predicting continuous quantities and inferring distributions of discrete parameters, and thus amortizing the cost of both the inverse and the surrogate models to a joint pre-training step. We present the capabilities of the proposed methodology for predicting continuous and discrete biomarkers in full-body haemodynamics simulations under different levels of missing information. We also consider a test case for atmospheric large-eddy simulation of a two-dimensional dry cold bubble, where we infer both continuous time-series and information about the systems conditions. We present comparisons against different baselines to showcase significantly increased accuracy in both the inverse and the surrogate tasks.