# Approximation of Optimal Control Surfaces for 2× 2 Skew-Symmetric Evolutionary Game Dynamics

arXiv: https://arxiv.org/abs/2207.07167 · HTML: https://mlsanity.com/paper/2207.07167/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2022.

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

- [Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learning](https://mlsanity.com/paper/2509.08759/) (2025)

## Abstract (arXiv)

In this paper we study the problem of approximating the general solution to an optimal control problem whose dynamics arise from a 2× 2 skew-symmetric evolutionary game with arbitrary initial condition. Our approach uses a Fourier approximation method and generalizes prior work in the use of orthogonal function approximation for optimal control. At the same time we cast the fitting problem in the context of a non-standard feedforward neural network and derive the back-propagation operator in this context. An example of the efficacy of this approach is provided and generalizations are discussed.