Progressive multi-fidelity learning with neural networks for physical system predictions
(2026) In Computer Methods in Applied Mechanics and Engineering 455.- Abstract
Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and in real-time. Even building sufficiently accurate surrogate models can be extremely challenging with limited high-fidelity data. Conversely, less expensive, low-fidelity data can be computed more easily and encompass a broader range of scenarios. By leveraging multi-fidelity information, prediction capabilities of surrogates can be improved. However, in practical situations, data may be different in types, come from sources of different modalities, and not be concurrently available, further... (More)
Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and in real-time. Even building sufficiently accurate surrogate models can be extremely challenging with limited high-fidelity data. Conversely, less expensive, low-fidelity data can be computed more easily and encompass a broader range of scenarios. By leveraging multi-fidelity information, prediction capabilities of surrogates can be improved. However, in practical situations, data may be different in types, come from sources of different modalities, and not be concurrently available, further complicating the modeling process. To address these challenges, we introduce a progressive multi-fidelity surrogate model. This model can sequentially incorporate diverse data types using tailored encoders. Multi-fidelity regression from the encoded inputs to the target quantities of interest is then performed using neural networks. Input information progressively flows from lower to higher fidelity levels through two sets of connections: concatenations among all the encoded inputs, and additive connections among the final outputs. This dual connection system enables the model to exploit correlations among different datasets while ensuring that each level makes an additive correction to the previous level without altering it. This approach prevents performance degradation as new input data are integrated into the model and automatically adapts predictions based on the available inputs. We demonstrate the effectiveness of the approach on numerical benchmarks and a real-world air pollution case study, showing that it reliably integrates multi-modal data, mitigates low-fidelity imperfections, and provides accurate predictions, while maintaining performance when generalizing across time and parameter variations.
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- author
- Conti, Paolo ; Guo, Mengwu LU ; Frangi, Attilio and Manzoni, Andrea
- organization
- publishing date
- 2026-06-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Data fusion, Multi-fidelity, Neural networks, Progressive learning, Scientific machine learning, Surrogate model
- in
- Computer Methods in Applied Mechanics and Engineering
- volume
- 455
- article number
- 118881
- publisher
- Elsevier
- external identifiers
-
- scopus:105034259800
- ISSN
- 0045-7825
- DOI
- 10.1016/j.cma.2026.118881
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. http://creativecommons.org/licenses/by/4.0/
- id
- b3c51334-f59f-4b5b-a6b0-e990407e36aa
- date added to LUP
- 2026-04-21 18:41:00
- date last changed
- 2026-08-17 11:58:31
@article{b3c51334-f59f-4b5b-a6b0-e990407e36aa,
abstract = {{<p>Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and in real-time. Even building sufficiently accurate surrogate models can be extremely challenging with limited high-fidelity data. Conversely, less expensive, low-fidelity data can be computed more easily and encompass a broader range of scenarios. By leveraging multi-fidelity information, prediction capabilities of surrogates can be improved. However, in practical situations, data may be different in types, come from sources of different modalities, and not be concurrently available, further complicating the modeling process. To address these challenges, we introduce a progressive multi-fidelity surrogate model. This model can sequentially incorporate diverse data types using tailored encoders. Multi-fidelity regression from the encoded inputs to the target quantities of interest is then performed using neural networks. Input information progressively flows from lower to higher fidelity levels through two sets of connections: concatenations among all the encoded inputs, and additive connections among the final outputs. This dual connection system enables the model to exploit correlations among different datasets while ensuring that each level makes an additive correction to the previous level without altering it. This approach prevents performance degradation as new input data are integrated into the model and automatically adapts predictions based on the available inputs. We demonstrate the effectiveness of the approach on numerical benchmarks and a real-world air pollution case study, showing that it reliably integrates multi-modal data, mitigates low-fidelity imperfections, and provides accurate predictions, while maintaining performance when generalizing across time and parameter variations.</p>}},
author = {{Conti, Paolo and Guo, Mengwu and Frangi, Attilio and Manzoni, Andrea}},
issn = {{0045-7825}},
keywords = {{Data fusion; Multi-fidelity; Neural networks; Progressive learning; Scientific machine learning; Surrogate model}},
language = {{eng}},
month = {{06}},
publisher = {{Elsevier}},
series = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{Progressive multi-fidelity learning with neural networks for physical system predictions}},
url = {{http://dx.doi.org/10.1016/j.cma.2026.118881}},
doi = {{10.1016/j.cma.2026.118881}},
volume = {{455}},
year = {{2026}},
}