Applying machine learning to improve simulations of a chaotic dynamical system using empirical error correction

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models still show many differences compared with observations. Machine learning has been applied to solve certain prediction problems with great success, and recently it's been proposed that this could replace the role of physically-derived dynamical weather and climate models to give better quality simulations. Here, instead, a framework using machine learning together with physically-derived models is tested, in which it is learnt how to correct the errors of the latter from timestep to timestep. This maintains the physical understanding built into the models, whilst allowing performance improvements, and also requires much simpler algorithms and less training data. This is tested in the context of simulating the chaotic Lorenz '96 system, and it is shown that the approach yields models that are stable and that give both improved skill in initialised predictions and better long-term climate statistics. Improvements in long-term statistics are smaller than for single time-step tendencies, however, indicating that it would be valuable to develop methods that target improvements on longer time scales. Future strategies for the development of this approach and possible applications to making progress on important scientific problems are discussed.Comment: 26p, 7 figures To be published in Journal of Advances in Modeling Earth System

Developing an embodied gait on a compliant quadrupedal robot

Incorporating the body dynamics of compliant robots into their controller architectures can drastically reduce the complexity of locomotion control. An extreme version of this embodied control principle was demonstrated in highly compliant tensegrity robots, for which stable gait generation was achieved by using only optimized linear feedback from the robot's sensors to its actuators. The morphology of quadrupedal robots has previously been used for sensing and for control of a compliant spine, but never for gait generation. In this paper, we successfully apply embodied control to the compliant, quadrupedal Oncilla robot. As initial experiments indicated that mere linear feedback does not suffice, we explore the minimal requirements for robust gait generation in terms of memory and nonlinear complexity. Our results show that a memory-less feedback controller can generate a stable trot by learning the desired nonlinear relation between the input and the output signals. We believe this method can provide a very useful tool for transferring knowledge from open loop to closed loop control on compliant robots

An Energy-based Approach to Ensure the Stability of Learned Dynamical Systems

Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been proposed to learn stable and accurate motions from demonstration. Some approaches work by separating accuracy and stability into two learning problems, which increases the number of open parameters and the overall training time. Alternative solutions exploit single-step learning but restrict the applicability to one regression technique. This paper presents a single-step approach to learn stable and accurate motions that work with any regression technique. The approach makes energy considerations on the learned dynamics to stabilize the system at run-time while introducing small deviations from the demonstrated motion. Since the initial value of the energy injected into the system affects the reproduction accuracy, it is estimated from training data using an efficient procedure. Experiments on a real robot and a comparison on a public benchmark shows the effectiveness of the proposed approach.Comment: Accepted at the International Conference on Robotics and Automation 202

Invariant Manifolds and Rate Constants in Driven Chemical Reactions

Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets, and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability.Comment: 28 pages, 13 figures, table of contents figur

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks