{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Estimating Friedrich's coefficients describing the deterministic dynamics of Langevin model

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Andreas W. Kempa-Liehr (Department of Engineering Science, University of Auckland)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebooks explains the friedrich_coefficient features, which has been inspired by the paper of Friedrich et al. (2000): *Extracting model equations from experimental data*. Physics Letters A 271, p. 217-222" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The general idea is to assume a Langevin model for the dynamics of the time series $x(t)$ \n", "$$\\dot{x}(t) = h(x(t)) + \\mathcal{N}(0,R)$$\n", "with $\\dot{x}(t)$ denoting the temporal derivative, $h(x(t))$ the deterministic dynamics, and $\\mathcal{N}(0,R)$ a Langevin force modelled as Gaussian white noise with standard deviation $R$.\n", "Now, an estimate $\\tilde{h}(x)$ of the deterministic dynamics can be computed by averaging $\\dot{x}(t)$ for a specific interval $x(t)\\in[x-\\epsilon,x+\\epsilon]$ with $|\\epsilon|\\ll 1$:\n", "$$\\left.\\tilde{h}(x)\\right|_{x\\in[x-\\epsilon,x+\\epsilon]} \\approx \\frac{\\sum\\limits_{x(t)\\in[x-\\epsilon,x+\\epsilon]} x(t+\\Delta_t)-x(t)}{\\Delta_t \\sum\\limits_{x(t)\\in[x-\\epsilon,x+\\epsilon]} 1}.$$\n", "Having a set of estimations $\\{\\tilde{h}(x_1),\\tilde{h}(x_2),\\ldots,\\tilde{h}(x_n)\\}$ with $x_10:\n", " active='Active'\n", " else:\n", " active=''\n", " \n", " plt.title('{} Brownian Motion (largest equilibrium velocity in red)'.format(active))\n", " plt.subplot(2,1,2)\n", " ax = plt.errorbar(result.v_mean,result.a_mean,\n", " xerr=result.v_std,fmt='o')\n", " x = np.linspace(-0.004, 0.004, 201)\n", " plt.plot(x, np.poly1d(dynamics)(x), label='estimated dynamics')\n", " plt.plot(v0,0.,'ro')\n", " plt.axvline(x=v0, color='r')\n", " plt.xlabel('mean velocity')\n", " plt.ylabel('mean acceleration')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Beyond drift-bifurcation" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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//eTnmGyu7PjXW3P5atYGXvxiCUvXFXL7f6fzzEcLmTRvE29/u4Ka2rpG4atq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\nLTtFpBy4Hvg33Pv5F+BCVW0cJNMSdc+Wn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ds = velocity(tau=3.8, delta_t=0.05, R=3e-4, seed=0)\n", "v = ds.simulate(1000000, v0=np.zeros(1))\n", "friedrich_method(v, default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Before drift-bifurcation" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ds = velocity(tau=2./0.3-3.8, delta_t=0.05, R=3e-4, seed=0)\n", "v = ds.simulate(1000000, v0=np.zeros(1))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OzoK6DgLnr9wR9r5obEUmza+73v7q59HP+LzyXe56fH4/b30V385r4/a9TJy/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\nPnmCxxY+w6Zdpc3cw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "friedrich_method(v, default)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }