mlsanityData to 7 Oct 2026

Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models

arXiv 2409.05709 ↗First posted 9 Sep 2024math.OC cs.LG cs.NAcited by 4

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Abstract (arXiv)

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical system to be controlled. Moreover, the control action needs to be updated whenever the underlying scenario undergoes variations. Full-order models based on, e.g., the Finite Element Method, do not meet these requirements due to the computational burden they usually entail. On the other hand, conventional reduced order modeling techniques such as the Reduced Basis method, are intrusive, rely on a linear superimposition of modes, and lack of efficiency when addressing nonlinear time-dependent dynamics. In this work, we propose a non-intrusive Deep Learning-based Reduced Order Modeling (DL-ROM) technique for the rapid control of systems described in terms of parametrized PDEs in multiple scenarios. In particular, optimal full-order snapshots are generated and properly reduced by either Proper Orthogonal Decomposition or deep autoencoders (or a combination thereof) while feedforward neural networks are exploited to learn the map from scenario parameters to reduced optimal solutions. Nonlinear dimensionality reduction therefore allows us to consider state variables and control actions that are both low-dimensional and distributed. After (i) data generation, (ii) dimensionality reduction, and (iii) neural networks training in the offline phase, optimal control strategies can be rapidly retrieved in an online phase for any scenario of interest. The computational speedup and the high accuracy obtained with the proposed approach are assessed on different PDE-constrained optimization problems, ranging from the minimization of energy dissipation in incompressible flows modelled through Navier-Stokes equations to the thermal active cooling in heat transfer.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 56 of its 120 references that are in the map. First posted on arXiv 9 Sep 2024.

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56 of 120 references.

References · 56

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38 more
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50 most cited of 56 All 56 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026On the training of physics-informed neural operators for solving parametric partial differential equationscited by 1
  2. 2025Employing Deep Neural Operators for PDE control by decoupling training and optimizationcited by 0
  3. 2026Real-time optimal control with shallow recurrent decoder networkscited by 0
  4. 2026Variational Parameter Calibration with Physics-Aware Latent-Space Surrogatescited by 0