Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)

• URL: http://arxiv.org/abs/2512.05306v2
• Date: Tue, 09 Dec 2025 18:44:00 GMT
• Title: Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
• Authors: Y. Sungtaek Ju,
• Abstract summary: Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons.<n>We present a framework integrating sparse variational Gaussian process inference with the Kolmogorov-Arnold topology.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific applications. We present a framework integrating sparse variational Gaussian process inference with the Kolmogorov-Arnold topology, enabling scalable Bayesian inference with computational complexity quasi-linear in sample size. Through analytic moment matching, we propagate uncertainty through deep additive structures while maintaining interpretability. We use three example studies to demonstrate the framework's ability to distinguish aleatoric from epistemic uncertainty: calibration of heteroscedastic measurement noise in fluid flow reconstruction, quantification of prediction confidence degradation in multi-step forecasting of advection-diffusion dynamics, and out-of-distribution detection in convolutional autoencoders. These results suggest Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KANs) is a promising architecture for uncertainty-aware learning in scientific machine learning.

Related papers

• Scalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN) [0.0]
  Kolmogorov-Arnold Networks (KANs) offer a promising alternative to Multi-Layer Perceptron (MLP)<n>KANs lack probabilistic outputs, limiting their utility in applications requiring uncertainty quantification.<n>We introduce the Sparse Variational GP-KAN, an architecture that integrates sparse variational inference with the KAN topology.
  arXiv  Detail & Related papers  (2025-11-29T00:48:55Z)
• Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed [0.0]
  We present a framework for training neural networks with a multidimensional Gaussian loss.<n>This framework generates closed-form predictive distributions over outputs with non-identically distributed and heteroscedastic structure.<n>We discuss its broader applicability to uncertainty-aware prediction in scientific models.
  arXiv  Detail & Related papers  (2025-08-21T18:22:44Z)
• Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantification [0.0]
  We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) By incorporating Bayesian neural networks as the building blocks for the branch and trunk networks, our framework endows DeepONet with uncertainty quantification. We demonstrate that modifying the variational objective function yields superior results in terms of minimising the mean squared error.
  arXiv  Detail & Related papers  (2024-08-01T16:22:03Z)
• Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning [12.947265104477237]
  Pursuing causality from data is a fundamental problem in scientific discovery, treatment intervention, and transfer learning.<n>This paper introduces a novel algorithmic method for addressing nonparametric invariance and causality learning in regression models across multiple environments.<n>The proposed Focused Adrial Invariant Regularization framework utilizes an innovative minimax optimization approach that drives regression models toward prediction-invariant solutions through adversarial testing.
  arXiv  Detail & Related papers  (2024-05-07T23:37:40Z)
• An Analytic Solution to Covariance Propagation in Neural Networks [10.013553984400488]
  This paper presents a sample-free moment propagation technique to accurately characterize the input-output distributions of neural networks. A key enabler of our technique is an analytic solution for the covariance of random variables passed through nonlinear activation functions. The wide applicability and merits of the proposed technique are shown in experiments analyzing the input-output distributions of trained neural networks and training Bayesian neural networks.
  arXiv  Detail & Related papers  (2024-03-24T14:08:24Z)
• DiffHybrid-UQ: Uncertainty Quantification for Differentiable Hybrid Neural Modeling [4.76185521514135]
  We introduce a novel method, DiffHybrid-UQ, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity.
  arXiv  Detail & Related papers  (2023-12-30T07:40:47Z)
• GIT: Detecting Uncertainty, Out-Of-Distribution and Adversarial Samples using Gradients and Invariance Transformations [77.34726150561087]
  We propose a holistic approach for the detection of generalization errors in deep neural networks. GIT combines the usage of gradient information and invariance transformations. Our experiments demonstrate the superior performance of GIT compared to the state-of-the-art on a variety of network architectures.
  arXiv  Detail & Related papers  (2023-07-05T22:04:38Z)
• Variational Neural Networks [88.24021148516319]
  We propose a method for uncertainty estimation in neural networks called Variational Neural Network (VNN) VNN generates parameters for the output distribution of a layer by transforming its inputs with learnable sub-layers. In uncertainty quality estimation experiments, we show that VNNs achieve better uncertainty quality than Monte Carlo Dropout or Bayes By Backpropagation methods.
  arXiv  Detail & Related papers  (2022-07-04T15:41:02Z)
• NUQ: Nonparametric Uncertainty Quantification for Deterministic Neural Networks [151.03112356092575]
  We show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. We demonstrate the strong performance of the method in uncertainty estimation tasks on a variety of real-world image datasets.
  arXiv  Detail & Related papers  (2022-02-07T12:30:45Z)
• A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures [68.8204255655161]
  It is shown that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches. It is shown, that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches.
  arXiv  Detail & Related papers  (2021-10-26T07:02:14Z)
• Multivariate Deep Evidential Regression [77.34726150561087]
  A new approach with uncertainty-aware neural networks shows promise over traditional deterministic methods. We discuss three issues with a proposed solution to extract aleatoric and epistemic uncertainties from regression-based neural networks.
  arXiv  Detail & Related papers  (2021-04-13T12:20:18Z)
• Sampling-free Variational Inference for Neural Networks with Multiplicative Activation Noise [51.080620762639434]
  We propose a more efficient parameterization of the posterior approximation for sampling-free variational inference. Our approach yields competitive results for standard regression problems and scales well to large-scale image classification tasks.
  arXiv  Detail & Related papers  (2021-03-15T16:16:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.