{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "bb8bfde7", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:44:38.333335Z", "iopub.status.busy": "2026-10-02T14:44:38.333073Z", "iopub.status.idle": "2026-10-02T14:44:38.338580Z", "shell.execute_reply": "2026-10-02T14:44:38.337556Z" }, "papermill": { "duration": 0.008648, "end_time": "2026-10-02T14:44:38.339297+00:00", "exception": false, "start_time": "2026-10-02T14:44:38.330649+00:00", "status": "completed" }, "tags": [ "remove-input", "active-ipynb", "remove-output" ] }, "outputs": [], "source": [ "try:\n", " from openmdao.utils.notebook_utils import notebook_mode # noqa: F401\n", "except ImportError:\n", " !python -m pip install openmdao[notebooks]" ] }, { "cell_type": "markdown", "id": "b9cb7e94", "metadata": { "papermill": { "duration": 0.001248, "end_time": "2026-10-02T14:44:38.442895+00:00", "exception": false, "start_time": "2026-10-02T14:44:38.441647+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Using CSDL Components\n", "\n", "## CSDL Background\n", "\n", "CSDL is domain-specific language embedded in Python designed for solving Multidisciplinary Design Analysis and Optimization (MDAO) problems. CSDL enables complete separation between specifying a mathematical model and implementing a numerical simulation of a physical system. Separation between specification and implementation enables engineers to operate at a high level of abstraction, without the need to implement low level algorithms, including derivative computation. It is an open source project created by the [Large-Scale Design Optimization (LSDO) Lab](https://lsdo.eng.ucsd.edu/) in the Department of Mechanical and Aerospace Engineering at the University of California San Diego. To learn more, visit the [CSDL Website](https://csdl-alpha.readthedocs.io/en/latest/).\n", "\n", "## Using CSDL in OpenMDAO\n", "\n", "CSDL models can be used directly in OpenMDAO models using the [csdl_om_connect](https://github.com/lsdolab/csdl_om_connect) package, also created by the LSDO Lab. This document explains how to do that by way of an example. In this example, we optimize the thickness (height) distribution of a cantilever beam.\n", "\n", "The example is based on two existing scripts. The first is a [pure OpenMDAO implementation](https://openmdao.org/newdocs/versions/latest/examples/beam_optimization_example.html) of the beam optimization problem. The second is the same problem solved using [only CSDL](https://modopt.readthedocs.io/en/latest/src/_temp/examples/ex_15_3cantilever_beam_csdl.html).\n", "\n", "The example below is a hybrid where CSDL is used to define the component, but OpenMDAO defines the problem, the driver, and does the optimization.\n", "\n", "The first step is to install the `csdl_om_connect` package, which will also install the `CSDL` package. The use of CSDL and csdl_om_connect is optional for OpenMDAO so if not already installed, the user needs to install it by \n", "issuing the following command at your operating system command prompt:\n", "```\n", "pip install git+https://github.com/lsdolab/csdl_om_connect.git@main\n", "```" ] }, { "cell_type": "code", "execution_count": 2, "id": "29ce4896", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:44:38.446746Z", "iopub.status.busy": "2026-10-02T14:44:38.446466Z", "iopub.status.idle": "2026-10-02T14:44:56.445361Z", "shell.execute_reply": "2026-10-02T14:44:56.444649Z" }, "papermill": { "duration": 18.002252, "end_time": "2026-10-02T14:44:56.446356+00:00", "exception": false, "start_time": "2026-10-02T14:44:38.444104+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output", "active-ipynb" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Collecting git+https://github.com/lsdolab/csdl_om_connect.git@main\r\n", " Cloning 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packages: csdl_om_connect, csdl_alpha\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Building wheel for csdl_om_connect (pyproject.toml) ... \u001b[?25l-" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b \bdone\r\n", "\u001b[?25h Created wheel for csdl_om_connect: filename=csdl_om_connect-0.1.0-py3-none-any.whl size=21874 sha256=690b5c99a1071cb31465e907993adadca18dc1528892794b80fb4a438c1e43f0\r\n", " Stored in directory: /tmp/pip-ephem-wheel-cache-qn4cgdus/wheels/a9/b3/0d/780ee49cffd0334215845a8bb3433b1560c65d12b1adca2b55\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Building wheel for csdl_alpha (pyproject.toml) ... \u001b[?25l-" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b \bdone\r\n", "\u001b[?25h Created wheel for csdl_alpha: filename=csdl_alpha-0.1.0-py3-none-any.whl size=292224 sha256=3a16c9f8ef934344eb9b41494437641098b1974b45ae9a207c12055ce6041f6e\r\n", " Stored in directory: /tmp/pip-ephem-wheel-cache-qn4cgdus/wheels/2b/08/23/c0319bf7785b0e5ed29104507dbac7d304dcedf096f9ede981\r\n", "Successfully built csdl_om_connect csdl_alpha\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Installing collected packages: mpmath, sympy, rustworkx, pydot, iniconfig, pytest, csdl_alpha, csdl_om_connect\r\n", "\u001b[?25l" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r\n", "\u001b[?25h\r\n", "Successfully installed csdl_alpha-0.1.0 csdl_om_connect-0.1.0 iniconfig-2.3.0 mpmath-1.3.0 pydot-4.0.1 pytest-9.1.1 rustworkx-0.18.1 sympy-1.14.0\r\n" ] } ], "source": [ "!pip install git+https://github.com/lsdolab/csdl_om_connect.git@main" ] }, { "cell_type": "markdown", "id": "fcea7a18", "metadata": { "papermill": { "duration": 0.14243, "end_time": "2026-10-02T14:44:56.591477+00:00", "exception": false, "start_time": "2026-10-02T14:44:56.449047+00:00", "status": "completed" }, "tags": [] }, "source": [ "Using an CSDL Component in OpenMDAO is very simple. You only need to instantiate a `CSDLExplicitComponent` class passing it a CSDL Jax Simulator object and also lists of the input and output variables.\n", "\n", "The key to using a CSDL Component in OpenMDAO is to make sure the input and output variable names match both when creating the `CSDLExplicitComponent` object and also when setting the design variables, constraints, and objectives on the OpenMDAO driver. \n", "\n", "Here is the full script of the hybrid example." ] }, { "cell_type": "code", "execution_count": 3, "id": "e7cd53fc", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:44:56.598034Z", "iopub.status.busy": "2026-10-02T14:44:56.597793Z", "iopub.status.idle": "2026-10-02T14:45:02.542907Z", "shell.execute_reply": "2026-10-02T14:45:02.542343Z" }, "papermill": { "duration": 5.949705, "end_time": "2026-10-02T14:45:02.543752+00:00", "exception": false, "start_time": "2026-10-02T14:44:56.594047+00:00", "status": "completed" }, "tags": [ "remove-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952299.382950] [runnervm8df0l:8745 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x563273ef87d0 failed to create UD QP TX wr:256 sge:6 inl:64 resp:0 RX wr:4096 sge:1 resp:0 failed: Operation not supported\n", "[1790952299.383214] [runnervm8df0l:8745 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n", "compiling 'run' function ... (682 nodes)\n", "GPU not found: 'Unknown backend: 'gpu' requested, but no platforms that are instances of gpu are present. Platforms present are: cpu', falling back to CPU\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:08745] pml_ucx.c:313 Error: Failed to create UCP worker\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "compiling 'compute_totals' function ... (1950 nodes)\n", "GPU not found: 'Unknown backend: 'gpu' requested, but no platforms that are instances of gpu are present. Platforms present are: cpu', falling back to CPU\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully (Exit mode 0)\n", " Current function value: 23762.153677633076\n", " Iterations: 140\n", " Function evaluations: 392\n", " Gradient evaluations: 140\n", "Optimization Complete\n", "-----------------------------------\n" ] }, { "data": { "text/plain": [ "Problem: problem\n", "Driver: ScipyOptimizeDriver\n", " success : True\n", " iterations : 393\n", " runtime : 3.1414E+00 s\n", " model_evals : 393\n", " model_time : 1.0362E+00 s\n", " deriv_evals : 140\n", " deriv_time : 1.7432E+00 s\n", " exit_status : SUCCESS" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import openmdao.api as om\n", "import csdl_alpha as csdl\n", "import numpy as np\n", "from csdl_om_connect import CSDLExplicitComponent\n", "\n", "############\n", "# CSDL Model\n", "############\n", "E0, L0, b0, vol0, F0 = 1.0, 1.0, 0.1, 0.01, -1.0\n", "n_el = 50\n", "rec = csdl.Recorder()\n", "rec.start()\n", "\n", "### add design variables ###\n", "x = csdl.Variable(name=\"x\", shape=(n_el,), value=1.0)\n", "\n", "### add objective ###\n", "E, L, b, vol = E0, L0, b0, vol0\n", "L_el = L / n_el\n", "n_nodes = n_el + 1\n", "\n", "# Moment of inertia\n", "I = b * x**3 / 12\n", "\n", "# Force vector\n", "F = np.zeros((n_nodes * 2,))\n", "F[-2] = F0\n", "\n", "# Stiffness matrix\n", "c_el = (\n", " E\n", " / L_el**3\n", " * np.array(\n", " [\n", " [12, 6 * L_el, -12, 6 * L_el],\n", " [6 * L_el, 4 * L_el**2, -6 * L_el, 2 * L_el**2],\n", " [-12, -6 * L_el, 12, -6 * L_el],\n", " [6 * L_el, 2 * L_el**2, -6 * L_el, 4 * L_el**2],\n", " ]\n", " )\n", ")\n", "\n", "K = csdl.Variable(name=\"K\", value=np.zeros((n_nodes * 2, n_nodes * 2)))\n", "for i in range(n_el):\n", " K = K.set(\n", " csdl.slice[2 * i : 2 * i + 4, 2 * i : 2 * i + 4],\n", " K[2 * i : 2 * i + 4, 2 * i : 2 * i + 4] + c_el * I[i],\n", " )\n", "u = csdl.solve_linear(K[2:, 2:], F[2:])\n", "c = csdl.vdot(F[2:], u)\n", "c.add_name(\"compliance\")\n", "\n", "### add constraints ###\n", "v = L_el * b * csdl.sum(x)\n", "v.add_name(\"volume\")\n", "\n", "rec.stop()\n", "\n", "cantilever_beam_sim = csdl.experimental.JaxSimulator(\n", " recorder=rec,\n", " additional_inputs=[x,],\n", " additional_outputs=[c, v],\n", ")\n", "\n", "################\n", "# OpenMDAO Model\n", "################\n", "\n", "# Generate a CSDLExplicitComponent object from a CSDL Jax Simulator\n", "# Define input and output names\n", "# Both are defined as a list of strings of CSDL variable names.\n", "# The names must be valid names of the CSDL variables\n", "# exposed as `additional_inputs` and `additional_outputs` in the JaxSimulator.\n", "in_names = [\"x\",]\n", "out_names = [\"compliance\", \"volume\"]\n", "cantilever_beam_comp = CSDLExplicitComponent(\n", " cantilever_beam_sim, in_names=in_names, out_names=out_names\n", ")\n", "\n", "# Define OpenMDAO Problem\n", "prob = om.Problem()\n", "prob.model.add_subsystem(\"cantilever_beam\", cantilever_beam_comp, promotes=[\"*\"])\n", "\n", "# Set the design variables, objective, and constraints\n", "# Since all the inputs and outputs were promoted, use promoted names\n", "prob.model.add_design_var(\"x\", lower=1e-2)\n", "prob.model.add_objective(\"compliance\")\n", "prob.model.add_constraint(\"volume\", equals=(vol0,))\n", "\n", "prob.setup()\n", "\n", "# setup and run the optimization\n", "prob.driver = om.ScipyOptimizeDriver(optimizer=\"SLSQP\", tol=1e-9, maxiter=200)\n", "prob.run_driver()" ] }, { "cell_type": "code", "execution_count": 4, "id": "63439722", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:45:02.550232Z", "iopub.status.busy": "2026-10-02T14:45:02.549979Z", "iopub.status.idle": "2026-10-02T14:45:02.553863Z", "shell.execute_reply": "2026-10-02T14:45:02.553283Z" }, "papermill": { "duration": 0.007478, "end_time": "2026-10-02T14:45:02.554378+00:00", "exception": false, "start_time": "2026-10-02T14:45:02.546900+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [], "source": [ "# Validate results\n", "opt_x = np.array([\n", " 0.14915759, 0.14764312, 0.14611338, 0.14456706, 0.14300427,\n", " 0.14142408, 0.13982619, 0.13820971, 0.13657403, 0.13491878,\n", " 0.13324254, 0.13154527, 0.12982591, 0.12808316, 0.12631659,\n", " 0.12452485, 0.122707, 0.12086176, 0.118988, 0.1170842,\n", " 0.11514902, 0.11318073, 0.11117753, 0.10913763, 0.10705892,\n", " 0.10493904, 0.10277539, 0.10056523, 0.09830546, 0.09599243,\n", " 0.09362241, 0.09119077, 0.08869255, 0.08612204, 0.08347229,\n", " 0.0807358, 0.07790325, 0.07496383, 0.07190449, 0.0687093,\n", " 0.06535832, 0.06182634, 0.05808047, 0.05407656, 0.04975294,\n", " 0.04501853, 0.03972914, 0.03363155, 0.02620191, 0.01610863,\n", "])\n", "opt_compliance = np.array([23762.15367702])\n", "assert np.allclose(prob.get_val(\"x\"), opt_x, atol=1e-6)\n", "assert np.allclose(prob.get_val(\"compliance\"), opt_compliance, atol=1e-6)\n" ] } ], "metadata": { "celltoolbar": "Tags", "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": "3.13.14" }, "orphan": true, "papermill": { "default_parameters": {}, "duration": 25.971549, "end_time": "2026-10-02T14:45:03.574281+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/experimental/csdl_components.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/experimental/csdl_components.ipynb", "parameters": {}, "start_time": "2026-10-02T14:44:37.602732+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }