JFlow: Model-Independent Spherical Jeans Analysis using Equivariant Continuous Normalizing Flows

The kinematics of stars in dwarf spheroidal galaxies have been studied to understand the structure of dark matter halos. However, the kinematic information of these stars is often limited to celestial positions and line-of-sight velocities, making full phase space analysis challenging. Conventional methods rely on projected analytic phase space density models with several parameters and infer dark matter halo structures by solving the spherical Jeans equation. In this paper, we introduce an unsupervised machine learning method for solving the spherical Jeans equation in a model-independent way as a first step toward model-independent analysis of dwarf spheroidal galaxies. Using equivariant continuous normalizing flows, we demonstrate that spherically symmetric stellar phase space densities and velocity dispersions can be estimated without model assumptions. As a proof of concept, we apply our method to Gaia challenge datasets for spherical models and measure dark matter mass densities given velocity anisotropy profiles. Our method can identify halo structures accurately, even with a small number of tracer stars.

Artificial Wrestling: A Dynamical Formulation of Autonomous Agents Fighting in a Coupled Inverted Pendula Framework

We develop autonomous agents fighting with each other, inspired by human wrestling. For this purpose, we propose a coupled inverted pendula (CIP) framework in which: 1) tips of two inverted pendulums are linked by a connection rod, 2) each pendulum is primarily stabilized by a PD-controller, 3) and is additionally equipped with an intelligent controller. Based on this framework, we dynamically formulate an intelligent controller designed to store dynamical correspondence from initial states to final states of the CIP model, to receive state vectors of the model, and to output impulsive control forces to produce desired final states of the model. Developing a quantized and reduced order design of this controller, we have a practical control procedure based on an off-line learning method. We then conduct numerical simulations to investigate individual performance of the intelligent controller, showing that the performance can be improved by adding a delay element into the intelligent controller. The result shows that the performance depends not only on quantization resolutions of learning data but also on delay time of the delay element. Finally, we install the intelligent controllers into both pendulums in the proposed framework to demonstrate autonomous competitive behavior between inverted pendulums.