Uncertainty Quantification in Data-Driven Dynamical Models via Inverse Problem Solving

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Akrout, Mohamed, Wilson, Dan
Format: Preprint
Veröffentlicht: 2026
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866908910229651456
author Akrout, Mohamed
Wilson, Dan
author_facet Akrout, Mohamed
Wilson, Dan
contents Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance with least-squares fitting, it is generally difficult to quantify the uncertainty associated with the prediction of the temporal evolution of the observables. This paper considers a general framework for uncertainty quantification in data-driven dynamical models by framing prediction error through the lens of inverse problem theory. Building on Koopman-inspired model identification strategies that are suited for nonlinear dynamical models, we consider a prediction as an approximate measurement from which the original input state can be faithfully recovered, and define the prediction error as the MSE of solving the inverse problem that would yield this prediction. We demonstrate the efficacy of this approach on both numerical models and experimental data showing that it provides a robust uncertainty measure of model performance.
format Preprint
id arxiv_https___arxiv_org_abs_2602_19889
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Uncertainty Quantification in Data-Driven Dynamical Models via Inverse Problem Solving
Akrout, Mohamed
Wilson, Dan
Dynamical Systems
Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance with least-squares fitting, it is generally difficult to quantify the uncertainty associated with the prediction of the temporal evolution of the observables. This paper considers a general framework for uncertainty quantification in data-driven dynamical models by framing prediction error through the lens of inverse problem theory. Building on Koopman-inspired model identification strategies that are suited for nonlinear dynamical models, we consider a prediction as an approximate measurement from which the original input state can be faithfully recovered, and define the prediction error as the MSE of solving the inverse problem that would yield this prediction. We demonstrate the efficacy of this approach on both numerical models and experimental data showing that it provides a robust uncertainty measure of model performance.
title Uncertainty Quantification in Data-Driven Dynamical Models via Inverse Problem Solving
topic Dynamical Systems
url https://arxiv.org/abs/2602.19889