mlsanityData to 14 Oct 2026

BubbleOKAN: A Physics-Informed Interpretable Neural Operator for High-Frequency Bubble Dynamics

arXiv 2508.03965 ↗First posted 5 Aug 2025cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

In this work, we employ physics-informed neural operators to map pressure profiles from an input function space to the corresponding bubble radius responses. Our approach employs a two-step DeepONet architecture. To address the intrinsic spectral bias of deep learning models, our model incorporates the Rowdy adaptive activation function, enhancing the representation of high-frequency features. Moreover, we introduce the Kolmogorov-Arnold network (KAN) based two-step DeepOKAN model, which enhances interpretability (often lacking in conventional multilayer perceptron architectures) while efficiently capturing high-frequency bubble dynamics without explicit utilization of activation functions in any form. We particularly investigate the use of spline basis functions in combination with radial basis functions (RBF) within our architecture, as they demonstrate superior performance in constructing a universal basis for approximating high-frequency bubble dynamics compared to alternative formulations. Furthermore, we emphasize on the performance bottleneck of RBF while learning the high frequency bubble dynamics and showcase the advantage of using spline basis function for the trunk network in overcoming this inherent spectral bias. The model is systematically evaluated across three representative scenarios: (1) bubble dynamics governed by the Rayleigh-Plesset equation with a single initial radius, (2) bubble dynamics governed by the Keller-Miksis equation with a single initial radius, and (3) Keller-Miksis dynamics with multiple initial radii. We also compare our results with state-of-the-art neural operators, including Fourier Neural Operators, Wavelet Neural Operators, OFormer, and Convolutional Neural Operators. Our findings demonstrate that the two-step DeepOKAN accurately captures both low- and high-frequency behaviors, and offers a promising alternative to conventional numerical solvers.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 29 of its 63 references that are in the map. First posted on arXiv 5 Aug 2025.

Builds on

29 of 63 references.

References · 29

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2018On the Spectral Bias of Neural Networkscited by 1,341
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  5. 2022Transformer for Partial Differential Equations' Operator Learningcited by 283
  6. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 262
  7. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  8. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 174
  9. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  10. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  11. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  12. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 79
17 more
  1. 2022Physics-informed neural networks for inverse problems in supersonic flowscited by 76
  2. 2022Error estimates for physics informed neural networks approximating the Navier-Stokes equationscited by 63
  3. 2021When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?cited by 58
  4. 2016Noisy Activation Functionscited by 53
  5. 2021Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functionscited by 49
  6. 2023A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionscited by 48
  7. 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 44
  8. 2020Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networkscited by 42
  9. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 38
  10. 2023On the training and generalization of deep operator networkscited by 31
  11. 2023Learning stiff chemical kinetics using extended deep neural operatorscited by 30
  12. 2022How important are activation functions in regression and classification? A survey, performance comparison, and future directionscited by 29
  13. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  14. 2019ProbAct: A Probabilistic Activation Function for Deep Neural Networkscited by 12
  15. 2025Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Studycited by 11
  16. 2025Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEscited by 11
  17. 2025An Approximation Theory Perspective on Machine Learningcited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026FEKAN: Feature-Enriched Kolmogorov-Arnold Networkscited by 5
  2. 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accuratecited by 3
  3. 2026Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradientscited by 2
  4. 2026In Transformer We Trust? A Perspective on Transformer Architecture Failure Modescited by 1
  5. 2026GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Modelcited by 1