mlsanityData to 14 Oct 2026

Towards General Neural Surrogate Solvers with Specialized Neural Accelerators

arXiv 2405.02351 ↗First posted 2 May 2024cs.LG cs.AI cs.DCcited by 9

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Abstract (arXiv)

Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary conditions. We propose Specialized Neural Accelerator-Powered Domain Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which subdomain problems containing arbitrary boundary conditions and geometric parameters are accurately solved using an ensemble of specialized neural operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems and show how innovations in network architecture and loss function engineering can produce specialized surrogate subdomain solvers with near unity accuracy. We utilize these solvers with standard DDM algorithms to accurately solve freeform electromagnetics and fluids problems featuring a wide range of domain sizes.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 23 of its 54 references that are in the map. First posted on arXiv 2 May 2024.

Builds on

23 of 54 references.

References · 23

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11 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 4.

9 papers.

  1. 2025A multi-agentic framework for real-time, autonomous freeform metasurface designcited by 14
  2. 2025Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solvingcited by 6
  3. 2025Accurate and scalable deep Maxwell solvers using multilevel iterative methodscited by 5
  4. 2025GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equationscited by 2
  5. 2024Generalizing Deep Surrogate Solvers for Broadband Electromagnetic Field Prediction at Unseen Wavelengthscited by 0
  6. 2026A Differentiable Ray-Wave Framework for Hybrid Refractive-Diffractive System Modeling and Optimizationcited by 0
  7. 2026Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problemscited by 0
  8. 2026Learnable composition for neural operatorscited by 0
  9. 2026A Composable AI-Accelerated Iterative Solver for 3D-IC Thermal Modelingcited by 0