Recent advances in high-resolution CT-imaging technology are creating a new class of ultra-high resolved microstructural datasets that challenge the limits of traditional homogenization approaches. While state-of-the-art FFT-based homogenization techniques remain effective for moderate datasets, their memory footprint and computational cost grow rapidly with increasing resolution, making them progressively inefficient for industrial-scale problems. To address these challenges, the recently developed Superfast-Fourier Transform (SFFT)-based homogenization algorithm leverages the memory-efficient low-rank representations of Tensor Trains (TTs), which reduce the storage and computational requirements of large-scale homogenization problems. Developed for CPU usage, SFFT-based Homogenization efficiently handles high-resolution datasets, assuming the underlying data is well-behaved.In this work, we investigate the performance of fundamental TT operations on modern hardware accelerators using the JAX framework. A benchmarking study across CPUs, GPUs, and TPUs evaluates execution times and computational efficiency, highlighting the strengths and limitations of TT operations on different architectures and motivating future hybrid approaches. Building on these insights, we adapt the SFFT-based homogenization algorithm for accelerator execution, enabling homogenization at high resolutions ranging from 300 million to 70 billion grid points, which are infeasible for the best available GPU-based FFT reference implementation. While the observed scaling behavior is geometry-dependent, the results demonstrate the potential of accelerator-based quantum-inspired homogenization for high-performance multiscale simulations.

Recent reinforcement learning (RL) methods have achieved success in various domains. However, multi-agent RL (MARL) remains a challenge in terms of decentralization, partial observability and scalability to many agents. Meanwhile, collective behavior requires resolution of the aforementioned challenges, and remains of importance to many state-of-the-art applications such as active matter physics, self-organizing systems, opinion dynamics, and biological or robotic swarms. Here, MARL via mean field control (MFC) offers a potential solution to scalability, but fails to consider decentralized and partially observable systems. In this paper, we enable decentralized behavior of agents under partial information by proposing novel models for decentralized partially observable MFC (Dec-POMFC), a broad class of problems with permutation-invariant agents allowing for reduction to tractable single-agent Markov decision processes (MDP) with single-agent RL solution. We provide rigorous theoretical results, including a dynamic programming principle, together with optimality guarantees for Dec-POMFC solutions applied to finite swarms of interest. Algorithmically, we propose Dec-POMFC-based policy gradient methods for MARL via centralized training and decentralized execution, together with policy gradient approximation guarantees. In addition, we improve upon state-of-the-art histogram-based MFC by kernel methods, which is of separate interest also for fully observable MFC. We evaluate numerically on representative collective behavior tasks such as adapted Kuramoto and Vicsek swarming models, being on par with state-of-the-art MARL. Overall, our framework takes a step towards RL-based engineering of artificial collective behavior via MFC.