# Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applications

arXiv: https://arxiv.org/abs/2606.05202 · HTML: https://mlsanity.com/paper/2606.05202/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 12 of 12)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Physics informed WNO](https://mlsanity.com/paper/2302.05925/) (2023)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Multi-fidelity reduced-order surrogate modeling](https://mlsanity.com/paper/2309.00325/) (2023)
- [A DeepONet multi-fidelity approach for residual learning in reduced order modeling](https://mlsanity.com/paper/2302.12682/) (2023)
- [Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction](https://mlsanity.com/paper/2307.11793/) (2023)
- [From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility](https://mlsanity.com/paper/2503.08907/) (2025)
- [Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2503.08904/) (2025)
- [Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling](https://mlsanity.com/paper/2503.17941/) (2025)
- [Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models](https://mlsanity.com/paper/2410.13376/) (2024)
- [Application of parametric Shallow Recurrent Decoder Network to magnetohydrodynamic flows in liquid metal blankets of fusion reactors](https://mlsanity.com/paper/2604.02139/) (2026)
- [Surrogate models for nuclear fusion with parametric Shallow Recurrent Decoder Networks: applications to magnetohydrodynamics](https://mlsanity.com/paper/2603.10678/) (2026)

## Abstract (arXiv)

In reactor physics, neutronics and multi-physics phenomena can be modelled at different fidelity levels. High-fidelity models based on the Boltzmann transport equation, multi-group diffusion, or computational fluid dynamics are computationally demanding, whereas simplified models, such as zero-dimensional lumped formulations, can be evaluated efficiently at the cost of neglecting spatial details. The computational intractability of detailed models translates into a scarcity of high-fidelity data and an abundance of low-fidelity data, motivating the development of multi-fidelity (MF) learning strategies able to map between the two. This work extends Shallow Recurrent Decoders (SHRED), a machine learning architecture that reconstructs high-dimensional fields from time-series measurements, to multi-fidelity reduced-order modelling, in which the input trajectories are provided by a low-fidelity model. The resulting MF-SHRED is assessed on three benchmark problems: (i) a two-group point-kinetics-to-diffusion; (ii) a non-linear reaction-advection-diffusion system of six chemical species; and (iii) the coupled neutronics-thermal-hydraulics multi-physics model of the Molten Salt Fast Reactor (MSFR). Across all three cases, MF-SHRED reconstructs the high-fidelity fields with relative errors below a few percent, closely approaching the truncation error of the underlying proper orthogonal decomposition, while reducing the computational cost by three orders of magnitude relative to the corresponding high-fidelity solver. MF-SHRED performs comparably to the original sparse-sensor SHRED formulation. These results support the use of MF-SHRED as a non-intrusive reduced-order modelling strategy for reactor physics and multi-physics applications, particularly for design and safety analysis tasks that must be carried out before a facility is even built.