47,105 research outputs found
Learning Dynamic Boltzmann Distributions as Reduced Models of Spatial Chemical Kinetics
Finding reduced models of spatially-distributed chemical reaction networks
requires an estimation of which effective dynamics are relevant. We propose a
machine learning approach to this coarse graining problem, where a maximum
entropy approximation is constructed that evolves slowly in time. The dynamical
model governing the approximation is expressed as a functional, allowing a
general treatment of spatial interactions. In contrast to typical machine
learning approaches which estimate the interaction parameters of a graphical
model, we derive Boltzmann-machine like learning algorithms to estimate
directly the functionals dictating the time evolution of these parameters. By
incorporating analytic solutions from simple reaction motifs, an efficient
simulation method is demonstrated for systems ranging from toy problems to
basic biologically relevant networks. The broadly applicable nature of our
approach to learning spatial dynamics suggests promising applications to
multiscale methods for spatial networks, as well as to further problems in
machine learning
Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes
A method is provided for designing and training noise-driven recurrent neural
networks as models of stochastic processes. The method unifies and generalizes
two known separate modeling approaches, Echo State Networks (ESN) and Linear
Inverse Modeling (LIM), under the common principle of relative entropy
minimization. The power of the new method is demonstrated on a stochastic
approximation of the El Nino phenomenon studied in climate research
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