mlsanityData to 7 Oct 2026

Challenges and opportunities for machine learning in multiscale computational modeling

arXiv 2303.12261 ↗First posted 22 Mar 2023cs.LG cs.CEcited by 6

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Abstract (arXiv)

Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional numerical methods. Pioneering work has demonstrated that ML provides solutions to governing systems of equations with comparable accuracy to those obtained using direct numerical methods, but with significantly faster computational speed. These high-speed, high-fidelity estimations can facilitate the solving of complex multiscale systems by providing a better initial solution to traditional solvers. This paper provides a perspective on the opportunities and challenges of using ML for complex multiscale modeling and simulation. We first outline the current state-of-the-art ML approaches for simulating multiscale systems and highlight some of the landmark developments. Next, we discuss current challenges for ML in multiscale computational modeling, such as the data and discretization dependence, interpretability, and data sharing and collaborative platform development. Finally, we suggest several potential research directions for the future.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 24 of its 76 references that are in the map. First posted on arXiv 22 Mar 2023.

Builds on

24 of 76 references.

References · 24

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2014OpenML: networked science in machine learningcited by 523
  3. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  4. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  5. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  6. 2019Machine Learning for Fluid Mechanicscited by 380
  7. 2022U-NO: U-shaped Neural Operatorscited by 219
  8. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 156
  9. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  10. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  11. 2018Deep Fluids: A Generative Network for Parameterized Fluid Simulationscited by 121
  12. 2020Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systemscited by 51
12 more
  1. 2022Generative Adversarial Neural Operatorscited by 51
  2. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 44
  3. 2021Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNscited by 38
  4. 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
  5. 2022On the use of Artificial Neural Networks in Topology Optimisationcited by 35
  6. 2021Stress field prediction in fiber-reinforced composite materials using a deep learning approachcited by 22
  7. 2020METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Designcited by 15
  8. 2022Deep transfer learning for image classification: a surveycited by 13
  9. 2022PARC: Physics-Aware Recurrent Convolutional Neural Networks to Assimilate Meso-scale Reactive Mechanics of Energetic Materialscited by 11
  10. 2018ZerNet: Convolutional Neural Networks on Arbitrary Surfaces via Zernike Local Tangent Space Estimationcited by 8
  11. 2022A physics-aware deep learning model for energy localization in multiscale shock-to-detonation simulations of heterogeneous energetic materialscited by 7
  12. 2021MaterialsAtlas.org: A Materials Informatics Web App Platform for Materials Discovery and Survey of State-of-the-Artcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 2.

6 papers.