# DeepONet-accelerated Bayesian inversion for moving boundary problems

arXiv: https://arxiv.org/abs/2512.20268 · HTML: https://mlsanity.com/paper/2512.20268/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Dimension-independent likelihood-informed MCMC](https://mlsanity.com/paper/1411.3688/) (2014)
- [Semi-supervised Invertible Neural Operators for Bayesian Inverse Problems](https://mlsanity.com/paper/2209.02772/) (2022)
- [Geometric Operator Learning with Optimal Transport](https://mlsanity.com/paper/2507.20065/) (2025)
- [A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems](https://mlsanity.com/paper/1505.03876/) (2015)
- [Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2403.08220/) (2024)
- [Point-DeepONet: Predicting Nonlinear Fields on Non-Parametric Geometries under Variable Load Conditions](https://mlsanity.com/paper/2412.18362/) (2024)
- [Iterative Updating of Model Error for Bayesian Inversion](https://mlsanity.com/paper/1707.04246/) (2017)
- [Adaptive regularisation for ensemble Kalman inversion](https://mlsanity.com/paper/2006.14980/) (2020)

## Abstract (arXiv)

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep Operator Network (DeepONet) architecture is employed to construct an efficient surrogate model for moving boundary problems in single-phase Darcy flow through porous media. The surrogate enables rapid and accurate approximation of complex flow dynamics and is coupled with an Ensemble Kalman Inversion (EKI) algorithm to solve Bayesian inverse problems. The proposed inversion framework is demonstrated by estimating the permeability and porosity of fibre reinforcements for composite materials manufactured via the Resin Transfer Moulding (RTM) process. Using both synthetic and experimental in-process data, the DeepONet surrogate accelerates inversion by several orders of magnitude compared with full-model EKI. This computational efficiency enables real-time, accurate, high-resolution estimation of local variations in permeability, porosity, and other parameters, thereby supporting effective monitoring and control of RTM processes, as well as other applications involving moving boundary flows. Unlike prior approaches for RTM inversion that learn mesh-dependent mappings, the proposed neural operator generalises across spatial and temporal domains, enabling evaluation at arbitrary sensor configurations without retraining, and represents a significant step toward practical industrial deployment of digital twins.