Regularised Iterative Generalised Least Squares with Optimal Selection of the Hyper-Parameter for Identifying Nonlinear Phenomenological Models

• URL: http://arxiv.org/abs/2608.18742v1
• Date: Wed, 19 Aug 2026 09:50:46 GMT
• Title: Regularised Iterative Generalised Least Squares with Optimal Selection of the Hyper-Parameter for Identifying Nonlinear Phenomenological Models
• Abstract summary: In some fields, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models contain parameters to be estimated from experimental data.<n>We introduce a ridge regression scheme to preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem.<n>An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper- parameter at each iteration.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In some fields currently dominated by empirical approaches, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models motivated by quasi-physical thinking contain parameters to be estimated from experimental data. Often the structure of such models yields fully or partially confounded parameters, which are difficult or even impossible to estimate reliably. To preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem we introduce a ridge regression scheme. An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper-parameter at each iteration. The formulae presented require fixed point iteration to solve for the hyper-parameter. Given a suitable starting value, analysis demonstrates convergence is very rapid. The optimal hyper-parameter selection mechanism is incorporated within an efficient regularised iterative generalised least squares mechanism, capable of fitting both heteroscedastic and serially correlated data as required. Simulation confirms the efficacy of the overall method.

Related papers

• A Quantum Optimization Framework for Data-Assimilation-Augmented Parameter Estimation [0.0]
  We investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems.<n>We develop a framework that reformulates a data-assimilation-augmented parameter estimation problem as a optimization task.<n>We apply the framework to SIS and SIR epidemic models, and a high-dimensional two-layer Lorenz-96 system.
  arXiv  Detail & Related papers  (2026-08-12T19:12:19Z)
• Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics [42.58292307702424]
  We propose a hybrid Neural Ordinary Differential Equation framework for data-efficient modeling of free-radical polymerization.<n>The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions.<n>In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model.
  arXiv  Detail & Related papers  (2026-06-01T12:10:48Z)
• Joint Model and Data Sparsification via the Marginal Likelihood [53.29070892356214]
  We propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification.<n>This symmetric pruning of model and data offers a natural extension that preserves conjugacy.<n> Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
  arXiv  Detail & Related papers  (2026-05-28T13:26:53Z)
• Bayesian Calibration and Model Assessment of Cell Migration Dynamics with Surrogate Model Integration [0.0]
  We systematically evaluate parameter probability distributions in cell migration models using Bayesian calibration.<n>This approach enables joint analysis of parameter uncertainty, predictive performance, and interpretability.
  arXiv  Detail & Related papers  (2025-09-23T13:45:16Z)
• Multi-fidelity Parameter Estimation Using Conditional Diffusion Models [6.934199382834925]
  We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems.<n>We use conditional generative models trained to sample the target conditional distribution.<n>We demonstrate the effectiveness of the proposed method on several numerical examples.
  arXiv  Detail & Related papers  (2025-04-02T16:54:47Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression [47.1405366895538]
  Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization algorithm.
  arXiv  Detail & Related papers  (2023-09-15T22:06:29Z)
• Conditional Korhunen-Lo\'{e}ve regression model with Basis Adaptation for high-dimensional problems: uncertainty quantification and inverse modeling [62.997667081978825]
  We propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems. We apply the proposed methodology to constructing surrogate models via the Basis Adaptation (BA) method of the stationary hydraulic head response.
  arXiv  Detail & Related papers  (2023-07-05T18:14:38Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• HyperImpute: Generalized Iterative Imputation with Automatic Model Selection [77.86861638371926]
  We propose a generalized iterative imputation framework for adaptively and automatically configuring column-wise models. We provide a concrete implementation with out-of-the-box learners, simulators, and interfaces.
  arXiv  Detail & Related papers  (2022-06-15T19:10:35Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Surrogate Models for Optimization of Dynamical Systems [0.0]
  This paper provides a smart data driven mechanism to construct low dimensional surrogate models. These surrogate models reduce the computational time for solution of the complex optimization problems.
  arXiv  Detail & Related papers  (2021-01-22T14:09:30Z)

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.