# Multi-level Optimal Control with Neural Surrogate Models

arXiv: https://arxiv.org/abs/2402.07763 · HTML: https://mlsanity.com/paper/2402.07763/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 6 of 6)

- [Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations](https://mlsanity.com/paper/1907.05317/) (2019)
- [Trends in Consensus-based optimization](https://mlsanity.com/paper/2104.01383/) (2021)
- [Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equations](https://mlsanity.com/paper/2103.04091/) (2021)
- [Consensus-Based Optimization for Saddle Point Problems](https://mlsanity.com/paper/2212.12334/) (2022)
- [Actuator design for parabolic distributed parameter systems with the moment method](https://mlsanity.com/paper/1701.02191/) (2017)
- [Optimal actuator design based on shape calculus](https://mlsanity.com/paper/1711.01183/) (2017)

## Built on by (most cited first, 1 of 1)

- [Nuclear Microreactor Control with Deep Reinforcement Learning](https://mlsanity.com/paper/2504.00156/) (2025)

## Abstract (arXiv)

Optimal actuator and control design is studied as a multi-level optimisation problem, where the actuator design is evaluated based on the performance of the associated optimal closed loop. The evaluation of the optimal closed loop for a given actuator realisation is a computationally demanding task, for which the use of a neural network surrogate is proposed. The use of neural network surrogates to replace the lower level of the optimisation hierarchy enables the use of fast gradient-based and gradient-free consensus-based optimisation methods to determine the optimal actuator design. The effectiveness of the proposed surrogate models and optimisation methods is assessed in a test related to optimal actuator location for heat control.