mlsanityData to 14 Oct 2026

Rethinking materials simulations: Blending direct numerical simulations with neural operators

arXiv 2312.05410 ↗First posted 8 Dec 2023cs.LG physics.comp-phcited by 25

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Abstract (arXiv)

Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolution equations, the nature of multiscale spatio-temporal interactions, and the need to reach long-time integration. We develop a new method that blends numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism that enables accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this framework on simulations of microstructure evolution during physical vapor deposition modeled via the phase-field method. Such simulations exhibit high spatial gradients due to the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with up to 16.5× speed-up compared to DNS. This methodology is generalizable to a broad range of evolutionary models, from solid mechanics, to fluid dynamics, geophysics, climate, and more.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). Builds on 33 of its 89 references that are in the map. First posted on arXiv 8 Dec 2023.

Builds on

33 of 89 references.

References · 33

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  4. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
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  9. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  10. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  11. 2022U-NO: U-shaped Neural Operatorscited by 230
  12. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
21 more
  1. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  2. 2016A guide to convolution arithmetic for deep learningcited by 185
  3. 2020Transformer Networks for Trajectory Forecastingcited by 181
  4. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  5. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  6. 2023Residual-based attention in physics-informed neural networkscited by 72
  7. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  8. 2022Generic bounds on the approximation error for physics-informed (and) operator learningcited by 65
  9. 2020Multi-fidelity Bayesian Neural Networks: Algorithms and Applicationscited by 59
  10. 2023LNO: Laplace Neural Operator for Solving Differential Equationscited by 47
  11. 2021Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural networkcited by 35
  12. 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
  13. 2023On the training and generalization of deep operator networkscited by 31
  14. 2023Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoilscited by 19
  15. 2023A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Datacited by 18
  16. 2023Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)cited by 16
  17. 2023Learning bias corrections for climate models using deep neural operatorscited by 9
  18. 2022An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operatorcited by 7
  19. 2022Adaptive physics-informed neural operator for coarse-grained non-equilibrium flowscited by 7
  20. 2023Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processescited by 4
  21. 2023Prediction of Diblock Copolymer Morphology via Machine Learningcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 5; 2025: 14; 2026: 6.

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  1. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modelingcited by 36
  2. 2025Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systemscited by 31
  3. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  4. 2024Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbonecited by 10
  5. 2024Ensemble and Mixture-of-Experts DeepONets For Operator Learningcited by 9
  6. 2025Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modelingcited by 8
  7. 2025Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learningcited by 7
  8. 2025A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometriescited by 5
  9. 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inferencecited by 5
  10. 2025Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Modelcited by 4
  11. 2025Continuum Transformers Perform In-Context Learning by Operator Gradient Descentcited by 3
  12. 2025Scaling Kinetic Monte-Carlo Simulations of Grain Growth with Combined Convolutional and Graph Neural Networkscited by 2
13 more
  1. 2026Autoregression-Free Neural Operators for Time-Dependent PDEscited by 2
  2. 2024Physics-informed Partitioned Coupled Neural Operator for Complex Networkscited by 1
  3. 2025Thompson Sampling in Function Spaces via Neural Operatorscited by 1
  4. 2025Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operatorscited by 1
  5. 2025Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injurycited by 1
  6. 2025Latent Representation Learning of Multi-scale Thermophysics: Application to Dynamics in Shocked Porous Energetic Materialcited by 0
  7. 2025Unified machine-learning framework for property prediction and time-evolution simulation of strained alloy microstructurecited by 0
  8. 2025Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networkscited by 0
  9. 2025Neural surrogates for designing gravitational wave detectorscited by 0
  10. 2026Towards Spatio-Temporal Extrapolation of Phase-Field Simulations with Convolution-Only Neural Networkscited by 0
  11. 2026NewPINNs: Physics-Informing Neural Networks Using Conventional Solvers for Partial Differential Equationscited by 0
  12. 2026DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splittingcited by 0
  13. 2026Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solverscited by 0