FUSE: Fast Unified Simulation and Estimation for PDEs

TL;DR

FUSE introduces a unified framework for simultaneously predicting continuous fields and estimating discrete parameters in PDE-governed systems, improving accuracy and robustness over traditional separate methods.

Contribution

It proposes a novel operator learning approach that jointly predicts continuous quantities and infers parameter distributions, enabling integrated and efficient PDE analysis.

Findings

Enhanced accuracy in biomarker prediction in haemodynamics simulations

Improved inference of system conditions in atmospheric simulations

Joint modeling reduces computational costs and increases robustness

Abstract

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.