Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling

• URL: http://arxiv.org/abs/2507.13416v1
• Date: Thu, 17 Jul 2025 12:45:10 GMT
• Title: Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling
• Authors: Jiaxiang Yi, Bernardo P. Ferreira, Miguel A. Bessa,
• Abstract summary: Data-driven learning is generalized to consider history-dependent multifidelity data, while quantifying uncertainty and disentangling it from data noise (aleatoric uncertainty)<n>The versatility and generality of the proposed methodology are demonstrated by applying it to different Bayesian data-driven modeling scenarios that include multiple fidelities with and without aleatoric uncertainty (noise)<n>This opens opportunities for future real-world applications in diverse scientific and engineering domains.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data-driven learning is generalized to consider history-dependent multi-fidelity data, while quantifying epistemic uncertainty and disentangling it from data noise (aleatoric uncertainty). This generalization is hierarchical and adapts to different learning scenarios: from training the simplest single-fidelity deterministic neural networks up to the proposed multi-fidelity variance estimation Bayesian recurrent neural networks. The versatility and generality of the proposed methodology are demonstrated by applying it to different data-driven constitutive modeling scenarios that include multiple fidelities with and without aleatoric uncertainty (noise). The method accurately predicts the response and quantifies model error while also discovering the noise distribution (when present). This opens opportunities for future real-world applications in diverse scientific and engineering domains; especially, the most challenging cases involving design and analysis under uncertainty.

Related papers

• Cooperative Bayesian and variance networks disentangle aleatoric and epistemic uncertainties [0.0]
  Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process.<n>Mean variance estimation (MVE) networks can learn this type of uncertainty but require ad-hoc regularization strategies to avoid overfitting.<n>We propose to train a variance network with a Bayesian neural network and demonstrate that the resulting model disentangles aleatoric and epistemic uncertainties while improving the mean estimation.
  arXiv  Detail & Related papers  (2025-05-05T15:50:52Z)
• Contextual Similarity Distillation: Ensemble Uncertainties with a Single Model [5.624791703748109]
  Uncertainty quantification is a critical aspect of reinforcement learning and deep learning.<n>We propose contextual similarity distillation, a novel approach that explicitly estimates the variance of an ensemble of deep neural networks with a single model.<n>We empirically validate our method across a variety of out-of-distribution detection benchmarks and sparse-reward reinforcement learning environments.
  arXiv  Detail & Related papers  (2025-03-14T12:09:58Z)
• One step closer to unbiased aleatoric uncertainty estimation [71.55174353766289]
  We propose a new estimation method by actively de-noising the observed data. By conducting a broad range of experiments, we demonstrate that our proposed approach provides a much closer approximation to the actual data uncertainty than the standard method.
  arXiv  Detail & Related papers  (2023-12-16T14:59:11Z)
• Towards stable real-world equation discovery with assessing differentiating quality influence [52.2980614912553]
  We propose alternatives to the commonly used finite differences-based method. We evaluate these methods in terms of applicability to problems, similar to the real ones, and their ability to ensure the convergence of equation discovery algorithms.
  arXiv  Detail & Related papers  (2023-11-09T23:32:06Z)
• Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification [0.0]
  This paper presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime.
  arXiv  Detail & Related papers  (2023-04-13T08:57:33Z)
• How to Combine Variational Bayesian Networks in Federated Learning [0.0]
  Federated learning enables multiple data centers to train a central model collaboratively without exposing any confidential data. deterministic models are capable of performing high prediction accuracy, their lack of calibration and capability to quantify uncertainty is problematic for safety-critical applications. We study the effects of various aggregation schemes for variational Bayesian neural networks.
  arXiv  Detail & Related papers  (2022-06-22T07:53:12Z)
• FiLM-Ensemble: Probabilistic Deep Learning via Feature-wise Linear Modulation [69.34011200590817]
  We introduce FiLM-Ensemble, a deep, implicit ensemble method based on the concept of Feature-wise Linear Modulation. By modulating the network activations of a single deep network with FiLM, one obtains a model ensemble with high diversity. We show that FiLM-Ensemble outperforms other implicit ensemble methods, and it comes very close to the upper bound of an explicit ensemble of networks.
  arXiv  Detail & Related papers  (2022-05-31T18:33:15Z)
• Uncertainty Modeling for Out-of-Distribution Generalization [56.957731893992495]
  We argue that the feature statistics can be properly manipulated to improve the generalization ability of deep learning models. Common methods often consider the feature statistics as deterministic values measured from the learned features. We improve the network generalization ability by modeling the uncertainty of domain shifts with synthesized feature statistics during training.
  arXiv  Detail & Related papers  (2022-02-08T16:09:12Z)
• 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)
• Quantifying Uncertainty in Deep Spatiotemporal Forecasting [67.77102283276409]
  We describe two types of forecasting problems: regular grid-based and graph-based. We analyze UQ methods from both the Bayesian and the frequentist point view, casting in a unified framework via statistical decision theory. Through extensive experiments on real-world road network traffic, epidemics, and air quality forecasting tasks, we reveal the statistical computational trade-offs for different UQ methods.
  arXiv  Detail & Related papers  (2021-05-25T14:35:46Z)
• Aleatoric uncertainty for Errors-in-Variables models in deep regression [0.48733623015338234]
  We show how the concept of Errors-in-Variables can be used in Bayesian deep regression. We discuss the approach along various simulated and real examples.
  arXiv  Detail & Related papers  (2021-05-19T12:37:02Z)
• 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)
• Dropout Strikes Back: Improved Uncertainty Estimation via Diversity Sampling [3.077929914199468]
  We show that modifying the sampling distributions for dropout layers in neural networks improves the quality of uncertainty estimation. Our main idea consists of two main steps: computing data-driven correlations between neurons and generating samples, which include maximally diverse neurons.
  arXiv  Detail & Related papers  (2020-03-06T15:20:04Z)

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.