# Progressive multi-fidelity learning with neural networks for physical system predictions

arXiv: https://arxiv.org/abs/2510.13762 · HTML: https://mlsanity.com/paper/2510.13762/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 16 of 16)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Scaling Wearable Foundation Models](https://mlsanity.com/paper/2410.13638/) (2024)
- [Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities](https://mlsanity.com/paper/2102.13403/) (2021)
- [Multi-fidelity Generative Deep Learning Turbulent Flows](https://mlsanity.com/paper/2006.04731/) (2020)
- [Multi-fidelity surrogate modeling using long short-term memory networks](https://mlsanity.com/paper/2208.03115/) (2022)
- [Multi-fidelity reduced-order surrogate modeling](https://mlsanity.com/paper/2309.00325/) (2023)
- [Multi-fidelity Hierarchical Neural Processes](https://mlsanity.com/paper/2206.04872/) (2022)
- [Multi-fidelity Reinforcement Learning Control for Complex Dynamical Systems](https://mlsanity.com/paper/2504.05588/) (2025)

## Built on by (most cited first, 2 of 2)

- [Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networks](https://mlsanity.com/paper/2512.16430/) (2025)
- [Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements](https://mlsanity.com/paper/2606.15690/) (2026)

## Abstract (arXiv)

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 case study, showing that it reliably integrates multi-modal data and provides accurate predictions, maintaining performance when generalizing across time and parameter variations.