Package: jax-fdm
JAX FDMA differentiable, hardware-accelerated framework for inverse form-finding in structural design.Crafted with care in theForm-Finding LabatPrinceton University❤️🇺🇸JAX FDM enables the solution of inverse form-finding problems for discrete force networks using the force density method (FDM) and gradient-based optimization.
It streamlines the integration of form-finding simulations into deep learning models for machine learning research.Key featuresLegendary form-finding solver.JAX FDM computes static equilibrium states for discrete force networks with theforce density method (FDM), the time-tested form-finding solver backed up by over 50 years of peer-reviewed research 📚.Derivatives, JIT compilation and parallelization.JAX FDM is written inJAX, a library for high-performance numerical computing and machine learning research, and it thus inherits many of JAX's perks: calculate derivatives, parallelize, and just-in-time (JIT) compile entire form-finding simulations written in Python code, and run them on a CPU, a GPU, or a TPU 🤯.Autotune those force densities, loads and supports.A form-found structure should fulfill additional design requirements to become a feasible structure.
Formulate an inverse form-finding scenario like this as an optimization problem with JAX FDM.
Then, let one of its gradient-based optimizers solve the problem by automatically tweaking the network's force densities, applied loads and support positions 🕺🏻.A rich bank of goals, constraints and loss functions.No two structures are alike.
JAX FDM allows you to model a custom inverse form-finding problem with its (growing!) collection of goals, constraints, and loss functions via a simple, object-oriented API.
The available goals and constraints in the framework are granular and applicable to an entire network; to a subset of its nodes, edges, and combinations thereof 💡.Form-finding simulations as another layer in a neural network.As an auto-differentiable library, JAX FDM can be seamlessly added as a layer in a differentiable function approximator like a neural network that can be then trained end-to-end.
Let the neural network learn the underlying physics of static equilibriumdirectlyfrom the form-finding simulation, instead of resorting to laborious techniques like data augmentation 🤖.JAX FDM is a research project under development.
Expect sharp edges and possibly some API breaking changes as we continue to support a broader set of features.InstallationFirst, create a newAnacondaenvironment and then activate it:condacreate-njaxenv
condaactivatejaxenvNext, install COMPAS and COMPAS VIEW2 viaconda:condainstall-cconda-forgecompascompas_view2==0.7.0Finally, install JAX FDM with a one-liner viapip:pipinstalljax-fdmJAX FDM requires Python 3.7+, JAX 0.3.17+, Numpy 1.23.3+, Scipy 1.9.1+, and COMPAS 1.16.0+.
For visualization, it uses COMPAS_VIEW2 0.7.0.Are you a Windows user?JAX is only officially supported on Linux (Ubuntu 16.04 or later) and macOS (10.12 or later) platforms.
This is the case with JAX FDM too.
Consequently, installing JAX FDM on Windows may require a different approach from that given by the instructions listed above.Oneworkingalternative for Windows users is to install JAX and JAX FDM using theWindows build for JAX.
Note that this is a community build that has been reported to workonly on Windows 11.
Another option to install JAX on Windows is to do so via theWindows Subsystem for Linux, with the limitation of having marginal graphical output.
Please refer toJAX's installation instructionsfor other alternatives to install JAX on Windows.DocumentationWork in progress! Expect a release soon.Quick exampleSuppose you are interested in generating a form in static equilibrium for a 10-meter span arch subjected to vertical point loads of 0.3 kN.
The arch has to be a compression-only structure.
You model the arch as ajax_fdmnetwork (download the archjsonfilehere).
Then, you apply a force density of -1 to all of its edges, and compute the required shape with the force density method.fromjax_fdm.datastructuresimportFDNetworkfromjax_fdm.equilibriumimportfdmnetwork=FDNetwork.from_json("data/json/arch.json")network.edges_forcedensities(q=-1.0)network.nodes_supports(keys=[nodefornodeinnetwork.nodes()ifnetwork.is_leaf(node)])network.nodes_loads([0.0,0.0,-0.3])f_network=fdm(network)You now wish to find a new form for this arch that minimizes thetotal Maxwell's load path, while keeping the length of the arch segments between 0.75 and 1 meters.
You solve this constrained form-finding problem with the SLSQP gradient-based optimizer.fromjax_fdm.equilibriumimportconstrained_fdmfromjax_fdm.optimizationimportSLSQPfromjax_fdm.constraintsimportEdgeLengthConstraintfromjax_fdm.goalsimportNetworkLoadPathGoalfromjax_fdm.lossesimportPredictionErrorfromjax_fdm.lossesimportLossloss=Loss(PredictionError(goals=[NetworkLoadPathGoal()]))constraints=[EdgeLengthConstraint(edge,0.75,1.0)foredgeinnetwork.edges()]optimizer=SLSQP()c_network=constrained_fdm(network,optimizer,loss,constraints=constraints)You finally visualize the unconstrained form-found archf_network(gray) and the constrained one,c_network(in teal) with theViewer.fromjax_fdm.visualizationimportViewerviewer=Viewer(width=1600,height=900)viewer.add(c_network)viewer.add(f_network,as_wireframe=True)viewer.show()The constrained form is shallower than the unconstrained one as a result of the optimization process.
The length of the arch segments also varies within the prescribe bounds to minimize the load path: segments are the longest where the arch's internal forces are lower (1.0 meter, at the appex); and conversely, the segments are shorter where the arch's internal forces are higher (0.75 m, at the base).More examplesNotebooksThese notebooks run directly from your browser without having to install anything locally!Arch: Control the height and the horizontal projection of a 2D arch.3D spiral: Calculate the loads required to maintain a compression-only 3D spiral in equilibrium(Angelillo, et al. 2021).Creased masonry vault: Best-fit a target surface(Panozzo, et al. 2013).ScriptsThese python scripts require a local installation of JAX FDM.Pointy dome: Control the tilt and the coarse width of a brick dome.Triple-branching saddle: Design the distribution of thrusts at the supports of a monkey saddle network while constraining the edge lengths.Saddle bridge: Create a crease in the middle of the bridge while constraining to transversal edges of the network to a target plane.CitationIf you found this library to be useful in academic or industry work, please consider 1) starring the project on Github, and 2) citing it:@inproceedings{pastrana_jaxfdm_2023,title={{JAX}~{FDM}: A differentiable solver for inverse form-finding},author={Rafael Pastrana and Deniz Oktay and Ryan P. Adams and Sigrid Adriaenssens},booktitle={ICML 2023 Workshop on Differentiable Almost Everything: Differentiable Relaxations, Algorithms, Operators, and Simulators},year={2023},url={https://openreview.net/forum?id=Uu9OPgh24d}}@software{pastrana_jaxfdm_software_2023,title={{JAX~FDM}: {A}uto-differentiable and hardware-accelerated force density method},author={Rafael Pastrana and Deniz Oktay and Ryan P. Adams and Sigrid Adriaenssens},year={2023},doi={10.5281/zenodo.7258292},url={https://github.com/arpastrana/jax\_fdm}}AcknowledgementsThis work has been supported by theU.S. National Science Foundationunder grantOAC-2118201and theInstitute for Data Driven Dynamical Design.See alsoCOMPAS CEM: Inverse design of 3D trusses with the combinatorial equilibrium modeling (CEM) framework.JAX CEM: The combinatorial equilibrium modeling (CEM) framework in JAX.JAX: Composable transformations of Python+NumPy programs.LicenseMIT