Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F23%3A00371319" target="_blank" >RIV/68407700:21730/23:00371319 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1109/ACCESS.2023.3287397" target="_blank" >https://doi.org/10.1109/ACCESS.2023.3287397</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/ACCESS.2023.3287397" target="_blank" >10.1109/ACCESS.2023.3287397</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression

Popis výsledku v původním jazyce

Many real-world systems can be described by mathematical models that are humancomprehensible, easy to analyze and help explain the system’s behavior. Symbolic regression is a method that can automatically generate such models from data. Historically, symbolic regression has been predominantly realized by genetic programming, a method that evolves populations of candidate solutions that are subsequently modified by genetic operators crossover and mutation. However, this approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data – models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic model, i.e., its structure and the coefficients, using gradient-based optimization algorithms. This paper proposes a novel neural network-based symbolic regression method that constructs physically plausible models based on even very small training data sets and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all the models generated throughout the whole learning process. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system. The results clearly show the potential of the method to find parsimonious models that comply with the prior knowledge provided.

Název v anglickém jazyce

Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression

Popis výsledku anglicky

Many real-world systems can be described by mathematical models that are humancomprehensible, easy to analyze and help explain the system’s behavior. Symbolic regression is a method that can automatically generate such models from data. Historically, symbolic regression has been predominantly realized by genetic programming, a method that evolves populations of candidate solutions that are subsequently modified by genetic operators crossover and mutation. However, this approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data – models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic model, i.e., its structure and the coefficients, using gradient-based optimization algorithms. This paper proposes a novel neural network-based symbolic regression method that constructs physically plausible models based on even very small training data sets and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all the models generated throughout the whole learning process. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system. The results clearly show the potential of the method to find parsimonious models that comply with the prior knowledge provided.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF15_003%2F0000470" target="_blank" >EF15_003/0000470: Robotika pro Průmysl 4.0</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Access

ISSN

2169-3536

e-ISSN

2169-3536

Svazek periodika

11

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

61481-61501

Kód UT WoS článku

001018635000001

EID výsledku v databázi Scopus

2-s2.0-85162778412