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Neural network approaches for parameterized optimal control

Journal Article · · Foundations of Data Science
DOI:https://doi.org/10.3934/fods.2024042· OSTI ID:2481183
 [1];  [2];  [3];  [2]
  1. Clemson Univ., SC (United States)
  2. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
  3. Emory Univ., Atlanta, GA (United States)

Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage to enable rapid decision-making and be able to react to changes in the parameter in the online stage. To tackle the curse of dimensionality arising when the state and/or parameter are high-dimensional, we represent the policy using neural networks. We compare two training paradigms: First, our model-based approach leverages the dynamics and definition of the objective function to learn the value function of the parameterized optimal control problem and obtain the policy using a feedback form. Second, we use actor-critic reinforcement learning to approximate the policy in a data-driven way. Using an example involving a two-dimensional convection-diffusion equation, which features high-dimensional state and parameter spaces, we investigate the accuracy and efficiency of both training paradigms. While both paradigms lead to a reasonable approximation of the policy, the model-based approach is more accurate and considerably reduces the number of PDE solves.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)
Grant/Contract Number:
NA0003525; 20-023231; FA9550-20-1-0372; DMS 1751636; DMS 2038118
OSTI ID:
2481183
Report Number(s):
SAND-2024-16667J
Journal Information:
Foundations of Data Science, Vol. 7, Issue 1; ISSN 2639-8001
Publisher:
AIMSCopyright Statement
Country of Publication:
United States
Language:
English