1,479 research outputs found
RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator
This paper addresses a neural network-based surrogate model that provides a
structure-preserving approximation for the fivefold collision integral. The
notion originates from the similarity in structure between the BGK-type
relaxation model and residual neural network (ResNet) when a particle
distribution function is treated as the input to the neural network function.
We extend the ResNet architecture and construct what we call the relaxation
neural network (RelaxNet). Specifically, two feed-forward neural networks with
physics-informed connections and activations are introduced as building blocks
in RelaxNet, which provide bounded and physically realizable approximations of
the equilibrium distribution and velocity-dependent relaxation time
respectively. The evaluation of the collision term is significantly accelerated
since the convolution in the fivefold integral is replaced by tensor
multiplication in the neural network. We fuse the mechanical advection operator
and the RelaxNet-based collision operator into a unified model named the
universal Boltzmann equation (UBE). We prove that UBE preserves the key
structural properties in a many-particle system, i.e., positivity,
conservation, invariance, and H-theorem. These properties promise that RelaxNet
is superior to strategies that naively approximate the right-hand side of the
Boltzmann equation using a machine learning model. The construction of the
RelaxNet-based UBE and its solution algorithm are presented in detail. Several
numerical experiments are investigated. The capability of the current approach
for simulating non-equilibrium flow physics is validated through excellent in-
and out-of-distribution performance.Comment: 44 pages, 27 figures, 11 table
Adaptive and learning-based formation control of swarm robots
Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation
A program for the Bayesian Neural Network in the ROOT framework
We present a Bayesian Neural Network algorithm implemented in the TMVA
package, within the ROOT framework. Comparing to the conventional utilization
of Neural Network as discriminator, this new implementation has more advantages
as a non-parametric regression tool, particularly for fitting probabilities. It
provides functionalities including cost function selection, complexity control
and uncertainty estimation. An example of such application in High Energy
Physics is shown. The algorithm is available with ROOT release later than 5.29.Comment: 12 pages, 6 figure
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