mlsanityData to 7 Oct 2026

AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields

arXiv 2406.02176 ↗First posted 4 Jun 2024cs.LGcited by 38

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Abstract (arXiv)

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 24 of its 33 references that are in the map. First posted on arXiv 4 Jun 2024.

Builds on

24 of 33 references.

References · 24

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2022Scalable Diffusion Models with Transformerscited by 5,931
  4. 2017Neural Discrete Representation Learningcited by 4,650
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  8. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  9. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  10. 2022Message Passing Neural PDE Solverscited by 368
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  12. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
12 more
  1. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  2. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
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  4. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 137
  5. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 105
  6. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
  7. 2018Variational Autoencoders Pursue PCA Directions (by Accident)cited by 84
  8. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 12; 2026: 24.

38 papers.

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  1. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 49
  2. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
  3. 2024Zebra: In-Context Generative Pretraining for Solving Parametric PDEscited by 14
  4. 2025Transolver is a Linear Transformer: Revisiting Physics-Attention through the Lens of Linear Attentioncited by 11
  5. 2025Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solvingcited by 6
  6. 2025Geometry aware inference of steady state PDEs using Equivariant Neural Fields representationscited by 5
  7. 2026Structure-Preserving Learning Improves Geometry Generalization in Neural PDEscited by 5
  8. 2026Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computingcited by 4
  9. 2025SCENT: Robust Spatiotemporal Learning for Continuous Scientific Data via Scalable Conditioned Neural Fieldscited by 3
  10. 2026SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Modelcited by 3
  11. 2025Point-wise Diffusion Models for Physical Systems with Shape Variations: Application to Spatio-temporal and Large-scale systemcited by 2
  12. 2025Reframing Generative Models for Physical Systems using Stochastic Interpolantscited by 2
26 more
  1. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  2. 2026Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentationcited by 2
  3. 2026From Basis to Basis: Gaussian Particle Representation for Interpretable PDE Operatorscited by 2
  4. 2026TS-ICL: A Flexible Time-Indexed Foundation Model for Time Series via In-Context Learningcited by 2
  5. 2025From Cheap Geometry to Expensive Physics: Elevating Neural Operators via Latent Shape Pretrainingcited by 1
  6. 2026Learning geometry-dependent lead-field operators for forward ECG modelingcited by 1
  7. 2026A meshfree exterior calculus for generalizable and data-efficient learning of physics from point cloudscited by 1
  8. 2026Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagatorscited by 1
  9. 2026Neural Field Tokenizations with Hierarchy and Spatial Locality Priorscited by 1
  10. 2026Zero-shot generalization of transformer neural operators to larger domainscited by 1
  11. 2025DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecastingcited by 0
  12. 2025GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometriescited by 0
  13. 2025PIBNet: a Physics-Inspired Boundary Network for Multiple Scattering Simulationscited by 0
  14. 2026LASER: Learning Active Sensing for Continuum Field Reconstructioncited by 0
  15. 2026QuadNorm: Resolution-Robust Normalization for Neural Operatorscited by 0
  16. 2026MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functionscited by 0
  17. 2026Data-Efficient Neural Operator Training via Physics-Based Active Learningcited by 0
  18. 2026Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decompositioncited by 0
  19. 2026LEIA: Learned Environment for Interactive Architected Materialscited by 0
  20. 2026Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidancecited by 0
  21. 2026No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Studycited by 0
  22. 2026MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometriescited by 0
  23. 2026Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processingcited by 0
  24. 2026HiLNO: A Hierarchical Latent Neural Operator with Multi-Scale Supervision for PDEs on General Geometriescited by 0
  25. 2026ScaGNN: a Graph Neural Network for Multiple Scattering Simulationscited by 0
  26. 2026Function-Space Transformer with Adaptive Anchorscited by 0