mlsanityData to 7 Oct 2026

Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations

arXiv 2303.11577 ↗First posted 21 Mar 2023cs.LG cs.NA math.NAcited by 8

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Abstract (arXiv)

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to generate. To reduce or even eliminate the dependency on high-fidelity data, we propose a novel multi-fidelity architecture which is based on a feature space shared by the low- and high-fidelity solutions. In the feature space, the projections of the low-fidelity and high-fidelity solutions are adjacent by constraining their relative distance. The feature space is represented with an encoder and its mapping to the original solution space is effected through a decoder. The proposed multi-fidelity approach is validated on forward and inverse problems for steady and unsteady problems described by partial differential equations.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 26 of its 53 references that are in the map. First posted on arXiv 21 Mar 2023.

Builds on

26 of 53 references.

References · 26

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14 more
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Cited by year

Citing papers per year: 2023: 2; 2024: 3; 2025: 3.

8 papers.

  1. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  2. 2024Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networkscited by 20
  3. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  4. 2023Bi-fidelity Variational Auto-encoder for Uncertainty Quantificationcited by 8
  5. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 5
  6. 2024Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modelingcited by 3
  7. 2025PC-SRGAN: Physically Consistent Super-Resolution Generative Adversarial Network for General Transient Simulationscited by 2
  8. 2025Bridging quantum and classical computing for partial differential equations through multifidelity machine learningcited by 1