mlsanityData to 14 Oct 2026

KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation

arXiv 2505.13315 ↗First posted 19 May 2025cs.LG cs.AI cs.MScited by 5

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Abstract (arXiv)

Contemporary models of high dimensional physical systems are constrained by the curse of dimensionality and a reliance on dense data. We introduce KHRONOS (Kernel Expansion Hierarchy for Reduced Order, Neural Optimized Surrogates), an AI framework for model based, model free and model inversion tasks. KHRONOS constructs continuously differentiable target fields with a hierarchical composition of per-dimension kernel expansions, which are tensorized into modes and then superposed. We evaluate KHRONOS on a canonical 2D, Poisson equation benchmark: across 16 to 512 degrees of freedom (DoFs), it obtained L_2-square errors of 5e-4 down to 6e-11. This represents a greater than 100-fold gain over Kolmogorov Arnold Networks (which itself reports a 100 times improvement on MLPs/PINNs with 100 times fewer parameters) when controlling for the number of parameters. This also represents a 1e6-fold improvement in L_2-square error compared to standard linear FEM at comparable DoFs. Inference complexity is dominated by inner products, yielding sub-millisecond full-field predictions that scale to an arbitrary resolution. For inverse problems, KHRONOS facilitates rapid, iterative level set recovery in only a few forward evaluations, with sub-microsecond per sample latency. KHRONOS's scalability, expressivity, and interpretability open new avenues in constrained edge computing, online control, computer vision, and beyond.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 9 of its 23 references that are in the map. First posted on arXiv 19 May 2025.

Builds on

9 of 23 references.

References · 9

  1. 2017Attention Is All You Needcited by 60,361
  2. 2016XGBoost: A Scalable Tree Boosting Systemcited by 5,166
  3. 2019Green AIcited by 627
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  5. 2020When Do Neural Networks Outperform Kernel Methods?cited by 150
  6. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  7. 2022Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initializationcited by 30
  8. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 13
  9. 2024Interpolating neural network: A novel unification of machine learning and interpolation theorycited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 2.

5 papers.

  1. 2025A Kernel-based Resource-efficient Neural Surrogate for Multi-fidelity Prediction of Aerodynamic Fieldcited by 3
  2. 2025A Unified Generative-Predictive Framework for Deterministic Inverse Designcited by 3
  3. 2025Explainable Hierarchical Deep Learning Neural Networks (Ex-HiDeNN)cited by 2
  4. 2026Agile Reinforcement Learning through Separable Neural Architecture and Applicationscited by 2
  5. 2026Separable neural architectures as a primitive for unified predictive and generative intelligencecited by 0