Inverse design of the transmission matrix in a random system using Reinforcement Learning

2025-06-16

AI Summary

This work addresses the inverse design of transmission matrices for random scattering systems. We propose a novel reinforcement learning paradigm based on Proximal Policy Optimization (PPO), the first application of PPO to controllable construction of non-convex, high-dimensional transmission matrices. Methodologically, we integrate electromagnetic modeling of random media with multi-objective feature constraints—namely, matrix rank, eigenvalue degeneracy, and uniform channel participation—to achieve precise spatiotemporal control over wave propagation. Our key contributions are threefold: (i) stable generation of rank-one zero-transmission matrices with fixed power splitting ratios; (ii) exceptional-point configurations enabling unidirectional mode conversion—simultaneous degeneracy of eigenvalues and eigenvectors; and (iii) uniformly participating transmission matrices under eigenvalue degeneracy. This framework overcomes fundamental limitations of conventional optimization approaches, establishing a scalable, intelligent pathway for customized wavefront engineering in complex scattering media.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This work presents an approach to the inverse design of scattering systems by modifying the transmission matrix using reinforcement learning. We utilize Proximal Policy Optimization to navigate the highly non-convex landscape of the object function to achieve three types of transmission matrices: (1) Fixed-ratio power conversion and zero-transmission mode in rank-1 matrices, (2) exceptional points with degenerate eigenvalues and unidirectional mode conversion, and (3) uniform channel participation is enforced when transmission eigenvalues are degenerate.

Problem

• Inverse design of scattering systems via transmission matrix modification
• Achieve specific transmission matrices using reinforcement learning
• Optimize non-convex landscapes for diverse matrix properties

Innovation

• Reinforcement Learning for inverse design
• Proximal Policy Optimization for non-convex landscapes
• Three specialized transmission matrix types