# MFNets: Data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

arXiv: https://arxiv.org/abs/2008.02672 · HTML: https://mlsanity.com/paper/2008.02672/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2020.

## Built on by (most cited first, 10 of 10)

- [Probabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets](https://mlsanity.com/paper/2301.13271/) (2023)
- [Verification and Validation for Trustworthy Scientific Machine Learning](https://mlsanity.com/paper/2502.15496/) (2025)
- [Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification](https://mlsanity.com/paper/2211.10835/) (2022)
- [Multifidelity linear regression for scientific machine learning from scarce data](https://mlsanity.com/paper/2403.08627/) (2024)
- [Assessing the performance of correlation-based multi-fidelity neural emulators](https://mlsanity.com/paper/2512.02868/) (2025)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [General multi-fidelity surrogate models: Framework and active learning strategies for efficient rare event simulation](https://mlsanity.com/paper/2212.03375/) (2022)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfer](https://mlsanity.com/paper/2310.03770/) (2023)
- [Multifidelity Formulations for Triangular Transport](https://mlsanity.com/paper/2610.00698/) (2026)

## Abstract (arXiv)

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data -- we can combine noisy, non-nested evaluations of the information sources. Numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.