TY - GEN
T1 - The Uniqueness Problem of Physical Law Learning
AU - Scholl, Philipp
AU - Bacho, Aras
AU - Boche, Holger
AU - Kutyniok, Gitta
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - Physical law learning is the ambiguous attempt at automating the derivation of governing equations with the use of machine learning techniques. This paper shall serve as a first step to build a comprehensive theoretical framework for learning physical laws, aiming to provide reliability to according algorithms. One key problem consists in the fact that the governing equations might not be uniquely determined by the given data. We will study this problem in the common situation that a physical law is described by an ordinary or partial differential equation. For various different classes of differential equations, we provide both necessary and sufficient conditions for a function from a given function class to uniquely determine the differential equation which is governing the phenomenon. We then use our results to determine in extensive numerical experiments whether a function solves a differential equation uniquely.
AB - Physical law learning is the ambiguous attempt at automating the derivation of governing equations with the use of machine learning techniques. This paper shall serve as a first step to build a comprehensive theoretical framework for learning physical laws, aiming to provide reliability to according algorithms. One key problem consists in the fact that the governing equations might not be uniquely determined by the given data. We will study this problem in the common situation that a physical law is described by an ordinary or partial differential equation. For various different classes of differential equations, we provide both necessary and sufficient conditions for a function from a given function class to uniquely determine the differential equation which is governing the phenomenon. We then use our results to determine in extensive numerical experiments whether a function solves a differential equation uniquely.
KW - learning differential equations
KW - machine learning This conference paper displays the most important results from the longer version [1]
KW - physical law learning
KW - the proofs can also be found in [1]
UR - http://www.scopus.com/inward/record.url?scp=85177553538&partnerID=8YFLogxK
U2 - 10.1109/ICASSP49357.2023.10095017
DO - 10.1109/ICASSP49357.2023.10095017
M3 - Conference contribution
AN - SCOPUS:85177553538
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
BT - ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing, Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023
Y2 - 4 June 2023 through 10 June 2023
ER -