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Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks

Journal Article · · Foundations of Data Science
DOI:https://doi.org/10.3934/fods.2024029· OSTI ID:2507166
 [1];  [2];  [1];  [3]
  1. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
  2. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Univ. of North Carolina, Charlotte, NC (United States)
  3. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Univ. of Washington, Seattle, WA (United States); Brown Univ., Providence, RI (United States)

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can happen to be difficult or impossible to train accurately. Here, we present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training a longer chain, gradually increasing the expressivity of the learnt model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to learn progressively features of a solution which could have been hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.

Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
Grant/Contract Number:
AC05-76RL01830
OSTI ID:
2507166
Report Number(s):
PNNL-SA-192288
Journal Information:
Foundations of Data Science, Vol. 7, Issue 1; ISSN 2639-8001
Publisher:
AIMSCopyright Statement
Country of Publication:
United States
Language:
English

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