XNODE: A XAI suite to understand neural ordinary differential equations

Coelho, Cecília; Costa, M. Fernanda P.; Ferrás, Luís L.

doi:10.3390/ai6050105

XNODE: A XAI suite to understand neural ordinary differential equations

Publication date

2025-05-20

Document type

Forschungsartikel

Author

Coelho, Cecília

Costa, M. Fernanda P.

Ferrás, Luís L.

Organisational unit

Informatik im Maschinenbau

DTEC.bw

DOI

10.3390/ai6050105

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/23051

Project

Intelligente Brandgefahrenanalyse für Gebäude und Schutz der Rettungskräfte durch Künstliche Intelligenz und Digitale Brandgebäudezwillinge

Publisher

MDPI

Series or journal

AI

ISSN

2673-2688

Periodical volume

6

Periodical issue

5

Article ID

105

Peer-reviewed

✅

Part of the university bibliography

✅

Language

English

Keyword

dtec.bw

Abstract

Neural Ordinary Differential Equations (Neural ODEs) have emerged as a promising approach for learning the continuous-time behaviour of dynamical systems from data. However, Neural ODEs are black-box models, posing challenges in interpreting and understanding their decision-making processes. This raises concerns about their application in critical domains such as healthcare and autonomous systems. To address this challenge and provide insight into the decision-making process of Neural ODEs, we introduce the eXplainable Neural ODE (XNODE) framework, a suite of eXplainable Artificial Intelligence (XAI) techniques specifically designed for Neural ODEs. Drawing inspiration from classical visualisation methods for differential equations, including time series, state space, and vector field plots, XNODE aims to offer intuitive insights into model behaviour. Although relatively simple, these techniques are intended to furnish researchers with a deeper understanding of the underlying mathematical tools, thereby serving as a practical guide for interpreting results obtained with Neural ODEs. The effectiveness of XNODE is verified through case studies involving a Resistor–Capacitor (RC) circuit, the Lotka–Volterra predator-prey dynamics, and a chemical reaction. The proposed XNODE suite offers a more nuanced perspective for cases where low Mean Squared Error values are obtained, which initially suggests successful learning of the data dynamics. This reveals that a low training error does not necessarily equate to comprehensive understanding or accurate modelling of the underlying data dynamics.

Description

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Version

Published version

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