{ "cells": [ { "cell_type": "markdown", "id": "801cc87e", "metadata": {}, "source": [ "# Neural Hamiltonian ODEs\n", "Where we define a perturbation to the hamiltonian mechanics parametrized by a FFNN. This is different, but also obviously connected, from what was briefly studied in the paper:\n", "\n", "*Greydanus, S., Dzamba, M., & Yosinski, J.* (2019). Hamiltonian Neural Networks. Advances in neural information processing systems, 32.\n", "\n", "in that only the perturbation of the Hamiltonian is parametrized by a network. Let us consider the same system as [in the previous example](./NeuralODEs_I.ipynb), but this time using the Hamiltonian formalism. We will shortly summarize, in what follows, the obvious as to show later how to obtain the same symbolically and using *heyoka*.\n", "\n", "Let us first introduce our Lagrangian coordinates $\\mathbf q = [x, y]$ and their derivatives: $\\dot{\\mathbf q} = [v_x, v_y]$. Under this choice we may compute the kinetic energy of the system as:\n", "\n", "$$\n", "T = \\frac 12 (v_x^2 + v_y^2)\n", "$$\n", "\n", "its potential energy as:\n", "\n", "$$\n", "U = \\frac 12 k_x x^2 + \\frac 12 k_y y^2\n", "$$\n", "\n", "and thus its Lagrangian as:\n", "\n", "$$\n", "\\left(\\mathbf q, \\dot{\\mathbf q}\\right) = T - U\n", "$$\n", "\n", "We can then compute the trivial *canonical momenta* $\\mathbf p=[p_x, p_y]$ as:\n", "\n", "$$\n", "\\begin{array}{l}\n", "p_x = \\frac{\\partial {\\mathcal L}}{\\partial v_x} = v_x \\\\\n", "p_y = \\frac{\\partial {\\mathcal L}}{\\partial v_y} = v_y \\\\\n", "\\end{array}\n", "$$\n", "\n", "And the Hamiltonian as:\n", "\n", "$$\n", "\\mathcal H = \\sum_{i=1}^2 p_i \\dot q_i - \\mathcal L = T + U\n", "$$\n", "\n", "... a complicated, albeit very generic, way to show that the system energy is the Hamiltonian!" ] }, { "cell_type": "code", "execution_count": 1, "id": "7030234e", "metadata": {}, "outputs": [], "source": [ "# The usual main imports\n", "import heyoka as hy\n", "import numpy as np\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "b9b57295", "metadata": {}, "outputs": [], "source": [ "x, y, px, py = hy.make_vars(\"x\",\"y\",\"px\",\"py\")\n", "H = 0.5 * px**2 + 0.5 * py**2 + 0.5 * hy.par[0] * x**2 + 0.5 * hy.par[1] * y**2" ] }, { "cell_type": "markdown", "id": "c8515952", "metadata": {}, "source": [ "Now, let us define a perturbation to this Hamiltonian, one parametrised by a FFNN:\n", "\n", "$$\n", "\\mathcal H_\\theta(\\mathbf p, \\mathbf q) = \\mathcal H + \\epsilon \\mathcal N_\\theta(\\mathbf p, \\mathbf q)\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "8901c175", "metadata": {}, "outputs": [], "source": [ "# Network parameters (play around)\n", "nn_hidden = [10, 10]\n", "activations = [hy.tanh, hy.tanh, hy.tanh] # the output will be in [-1,1]\n", "n_inputs = 4\n", "n_outputs = 1\n", "nn_layers = [n_inputs] + nn_hidden + [n_outputs]\n", "\n", "# Weight matrices\n", "Ws = []\n", "for i in range(0, len(activations)):\n", " Ws.append(0.5 - np.random.random((nn_layers[i], nn_layers[i+1])))\n", "# Bias vectors\n", "bs = []\n", "for i in range(0, len(activations)):\n", " bs.append(np.random.random((nn_layers[i+1],1)))\n", "# Flatten everything\n", "flattened_nw = np.concatenate([it.flatten() for it in Ws] + [it.flatten() for it in bs])\n", "\n", "# Calling the ffnn factory\n", "ffnn = hy.model.ffnn(inputs = [x, y, px, py], nn_hidden = nn_hidden, n_out = n_outputs, activations = activations, nn_wb = flattened_nw)\n", "\n", "# Perturbing the Hamiltonian\n", "H = H + hy.par[2] * ffnn[0]" ] }, { "cell_type": "markdown", "id": "3b3808d3", "metadata": {}, "source": [ "And we may now compute the equations of motion:\n", "\n", "$$\n", "\\begin{array}{l}\n", "\\dot{\\mathbf q} = \\frac{\\partial \\mathcal H}{\\partial\\mathbf p} \\\\\n", "\\dot{\\mathbf p} = - \\frac{\\partial \\mathcal H}{\\partial\\mathbf q}\n", "\\end{array}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "93c264f5", "metadata": {}, "outputs": [], "source": [ "dynamics = [(x, hy.diff(H, px)), (y, hy.diff(H, py)), (px, -hy.diff(H, x)), (py, -hy.diff(H, y))]" ] }, { "cell_type": "markdown", "id": "efdbcaeb", "metadata": {}, "source": [ "And define our numerical integrator ... guess ... yes a Taylor integration scheme!" ] }, { "cell_type": "code", "execution_count": 5, "id": "5ac54bc7", "metadata": {}, "outputs": [], "source": [ "taH = hy.taylor_adaptive(\n", " # The ODEs.\n", " dynamics,\n", " # The initial conditions.\n", " [0., 1., 1., 0.],\n", " tol = 1e-16,\n", " compact_mode = True\n", ")" ] }, { "cell_type": "code", "execution_count": 6, "id": "f2368fe7", "metadata": {}, "outputs": [], "source": [ "taH.state[:] = [0., 1., 1., 0.]\n", "taH.time = 0\n", "taH.pars[:] = [1,1,0.0]\n", "tgrid = np.linspace(0,40,1000)\n", "sol = taH.propagate_grid(tgrid)" ] }, { "cell_type": "code", "execution_count": 7, "id": "6500272a", "metadata": {}, "outputs": [], "source": [ "taH.state[:] = [0., 1., 1., 0.]\n", "taH.time = 0\n", "taH.pars[:] = [1,1,5.3]\n", "tgrid = np.linspace(0,40,1000)\n", "sol_pert = taH.propagate_grid(tgrid)" ] }, { "cell_type": "code", "execution_count": 8, "id": "4b1521d0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(sol[5][:,0], sol[5][:,1])\n", "plt.plot(sol_pert[5][:,0], sol_pert[5][:,1], 'r')" ] }, { "cell_type": "markdown", "id": "f6c11db9", "metadata": {}, "source": [ "Clearly, the power and interest of this technique, applied to Hamiltonian systems, lies in the possibility to define some good training for the FFNN weights and biases so that the final system converges to something useful \n", "\n", "\n", "... and that IS all!" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }