# Generative AI-enhanced Probabilistic Multi-Fidelity Surrogate Modeling Via Transfer Learning

arXiv: https://arxiv.org/abs/2602.00072 · HTML: https://mlsanity.com/paper/2602.00072/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 20 Jan 2026.

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

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [Parallel Spatio-Temporal Attention-Based TCN for Multivariate Time Series Prediction](https://mlsanity.com/paper/2203.00971/) (2022)
- [Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation](https://mlsanity.com/paper/2308.01054/) (2023)
- [Randomized Physics-Informed Neural Networks for Bayesian Data Assimilation](https://mlsanity.com/paper/2407.04617/) (2024)
- [Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling](https://mlsanity.com/paper/2503.17941/) (2025)
- [Funnels: Exact maximum likelihood with dimensionality reduction](https://mlsanity.com/paper/2112.08069/) (2021)
- [Solving High-dimensional Inverse Problems Using Amortized Likelihood-free Inference with Noisy and Incomplete Data](https://mlsanity.com/paper/2412.04565/) (2024)

## Abstract (arXiv)

The performance of machine learning surrogates is critically dependent on data quality and quantity. This presents a major challenge, as high-fidelity (HF) data is often scarce and computationally expensive to acquire, while low-fidelity (LF) data is abundant but less accurate. To address this data-scarcity problem, we propose a probabilistic multi-fidelity surrogate modeling framework that integrates transfer learning with generative modeling. We employ a normalizing flow (NF) generative model as the backbone, which is trained in two phases: (i) the NF is first pretrained on a large LF dataset to learn a probabilistic forward model; (ii) the pretrained model is then fine-tuned on a small HF dataset, allowing it to correct for LF--HF discrepancies via knowledge transfer. To relax the dimension-preserving constraint of standard bijective NFs, we integrate surjective (dimension-reducing) layers with standard coupling blocks. This architecture enables learned dimension reduction while preserving the ability to train with exact likelihoods. The resulting surrogate provides fast probabilistic predictions with quantified uncertainty and significantly outperforms LF-only baselines while using fewer HF evaluations. We validate the approach for two benchmark systems: a rail-sleeper-ballast and a reinforced concrete slab. For both applications, we combine many coarse-mesh (LF) simulations with a limited set of fine-mesh (HF) simulations. The proposed model achieves probabilistic predictions with HF accuracy, demonstrating a practical path toward data-efficient, generative AI-driven surrogates for complex engineering systems.