Xref: utzoo comp.ai.neural-nets:693 sci.chem:244 Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!rutgers!cmcl2!lanl!opus!ted From: ted@nmsu.edu (Ted Dunning) Newsgroups: comp.ai.neural-nets,sci.chem Subject: Re: Neural Net Applications in Chemistry Message-ID: Date: 11 May 89 20:15:34 GMT References: <1989May10.095408.5836@gpu.utcs.utoronto.ca> <201@bach.nsc.com> Sender: news@nmsu.edu Followup-To: comp.ai.neural-nets Distribution: na Organization: NMSU Computer Science Lines: 61 In-reply-to: andrew@berlioz's message of 11 May 89 01:47:22 GMT In article <201@bach.nsc.com> andrew@berlioz (Lord Snooty @ The Giant Poisoned Electric Head) writes: In article , ted@nmsu.edu (Ted Dunning) writes: > much of the work at lanl using neural net methods has been supplanted > by doyne farmers local approximation method which (for many problems) ... This is very interesting, Ted. Could you post some references to the net on Doyne Farmer's method, and perhaps a brief resume of his approach? the best reference is the los alamos tech report LA-UR-88-901. i asssume that this is available from lanl, somehow (i got mine by hand). (interestingly, on the last page i not a us gov printing office number: 1988-0-573-034/80049). (you might also try doyne whose net address is jdf@lanl.gov) an extract of the abstract follows: Exploiting Chaos to Predict the Future and Reduce Noise J. Doyne Farmer and John J. Sidorowich We discuss new approaches to forecasting, noise reduction, and the analysis of experimental data. The basic idea is to embed the data in a state space and then use straightforward numerical techniques to build a nonlinear dynamical model. We pick an ad hoc nonlinear representation, and fit it to the data. For higher dimensional problems we find that breaking the domain into neighborhoods using local approxiamtion is usually better than using an arbitrary global representation. When random behavior is caused by low dimensional chaos our short term forecasts can be several orders of magnitude better than thos of standard linear methods. We derive error estimates for the accuracy of approximatin in terms of attractor dimension and Lyapunov exponents, the number of data points, and the extrapolation time. We demonstrate that for a given extrapolation time T iterating a short-term estimate is superior to computing an estimate for T directly. ... We propose a nonlinear averaging scheme for separating noise from deterministic dynamics. For chaotic time series the noise reduction possible depends exponentially on the length of the time series, whereas for non-chaotic behavior it is proportional to the square root. WHen the equations of motion are known exactly, we can achieve noise reductions of more than ten orders of magnitude. Wehn the equations are not known the limitation comes from predication error, but for low dimensional systems noise reductions of several orders of magnitude are still possible. The basic principles underlying our methods are similar to those of neural nets, but are more straightforward. For forecasting, we get equivalent or better results with vastly less computer time. We suggest that these ideas can be applied to a much larger class of problems. ---------------- hope that this helps.