82,381 research outputs found
How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equations
We present a framework and algorithms to learn controlled dynamics models
using neural stochastic differential equations (SDEs) -- SDEs whose drift and
diffusion terms are both parametrized by neural networks. We construct the
drift term to leverage a priori physics knowledge as inductive bias, and we
design the diffusion term to represent a distance-aware estimate of the
uncertainty in the learned model's predictions -- it matches the system's
underlying stochasticity when evaluated on states near those from the training
dataset, and it predicts highly stochastic dynamics when evaluated on states
beyond the training regime. The proposed neural SDEs can be evaluated quickly
enough for use in model predictive control algorithms, or they can be used as
simulators for model-based reinforcement learning. Furthermore, they make
accurate predictions over long time horizons, even when trained on small
datasets that cover limited regions of the state space. We demonstrate these
capabilities through experiments on simulated robotic systems, as well as by
using them to model and control a hexacopter's flight dynamics: A neural SDE
trained using only three minutes of manually collected flight data results in a
model-based control policy that accurately tracks aggressive trajectories that
push the hexacopter's velocity and Euler angles to nearly double the maximum
values observed in the training dataset.Comment: Final submission to CoRL 202
State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: The discrete-time case
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes
Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective
On metrics of density and power efficiency, neuromorphic technologies have
the potential to surpass mainstream computing technologies in tasks where
real-time functionality, adaptability, and autonomy are essential. While
algorithmic advances in neuromorphic computing are proceeding successfully, the
potential of memristors to improve neuromorphic computing have not yet born
fruit, primarily because they are often used as a drop-in replacement to
conventional memory. However, interdisciplinary approaches anchored in machine
learning theory suggest that multifactor plasticity rules matching neural and
synaptic dynamics to the device capabilities can take better advantage of
memristor dynamics and its stochasticity. Furthermore, such plasticity rules
generally show much higher performance than that of classical Spike Time
Dependent Plasticity (STDP) rules. This chapter reviews the recent development
in learning with spiking neural network models and their possible
implementation with memristor-based hardware
Channel noise effects on neural synchronization
Synchronization in neural networks is strongly tied to the implementation of
cognitive processes, but abnormal neuronal synchronization has been linked to a
number of brain disorders such as epilepsy and schizophrenia. Here we examine
the effects of channel noise on the synchronization of small Hodgkin-Huxley
neuronal networks. The principal feature of a Hodgkin-Huxley neuron is the
existence of protein channels that transition between open and closed states
with voltage dependent rate constants. The Hodgkin-Huxley model assumes
infinitely many channels, so fluctuations in the number of open channels do not
affect the voltage. However, real neurons have finitely many channels which
lead to fluctuations in the membrane voltage and modify the timing of the
spikes, which may in turn lead to large changes in the degree of
synchronization. We demonstrate that under mild conditions, neurons in the
network reach a steady state synchronization level that depends only on the
number of neurons in the network. The channel noise only affects the time it
takes to reach the steady state synchronization level.Comment: 7 Figure
Deterministic networks for probabilistic computing
Neural-network models of high-level brain functions such as memory recall and
reasoning often rely on the presence of stochasticity. The majority of these
models assumes that each neuron in the functional network is equipped with its
own private source of randomness, often in the form of uncorrelated external
noise. However, both in vivo and in silico, the number of noise sources is
limited due to space and bandwidth constraints. Hence, neurons in large
networks usually need to share noise sources. Here, we show that the resulting
shared-noise correlations can significantly impair the performance of
stochastic network models. We demonstrate that this problem can be overcome by
using deterministic recurrent neural networks as sources of uncorrelated noise,
exploiting the decorrelating effect of inhibitory feedback. Consequently, even
a single recurrent network of a few hundred neurons can serve as a natural
noise source for large ensembles of functional networks, each comprising
thousands of units. We successfully apply the proposed framework to a diverse
set of binary-unit networks with different dimensionalities and entropies, as
well as to a network reproducing handwritten digits with distinct predefined
frequencies. Finally, we show that the same design transfers to functional
networks of spiking neurons.Comment: 22 pages, 11 figure
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