TY - JOUR
T1 - Black and gray box learning of amplitude equations
T2 - Application to phase field systems
AU - Kemeth, Felix P.
AU - Alonso, Sergio
AU - Echebarria, Blas
AU - Moldenhawer, Ted
AU - Beta, Carsten
AU - Kevrekidis, Ioannis G.
N1 - Funding Information:
The work of F.P.K. and I.G.K. was partially supported by the U.S. Department of Energy, Grant No. SA22-0052-S001 and the U.S. Air Force Office of Scientific Research, Grant No. A9550-21-1-0317. T.M. and C.B. acknowledge financial support from the Deutsche Forschungsgemeinschaft Project No. 318763901–SFB1294. B.E. acknowledges financial support from MICINN/AEI through research Grant No. PID2020-116927RB-C22.
Publisher Copyright:
© 2023 American Physical Society.
PY - 2023/2
Y1 - 2023/2
N2 - We present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.
AB - We present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.
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U2 - 10.1103/PhysRevE.107.025305
DO - 10.1103/PhysRevE.107.025305
M3 - Article
C2 - 36932491
AN - SCOPUS:85149569644
SN - 2470-0045
VL - 107
JO - Physical Review E
JF - Physical Review E
IS - 2
M1 - 025305
ER -