Thanduriel / StableNN

experiments to build stable neural networks for physical simulations

StableNN

A collection of experiments to build stable neural networks as explicit time-stepping schemes for physical simulations. The two prototypical examples are the gravity pendulum and the 1D heat equation for non-homogeneous media.

Build

The only necessary dependency is

• libtorch installed anywhere,

but optionally you may also want

• SFML to visualize the simulations; either installed such that cmake can find it or to build from source clone it into dependencies/SFML,
• Eigen for performance measures although the related code is commented out and not faster than the manual implementation.

Then just run

$ git clone https://github.com/Thanduriel/StableNN.git
$ cd StableNN
$ mkdir build
$ cd build
$ cmake .. -DCMAKE_PREFIX_PATH="<path to libtorch>/share/cmake/Torch" -DUSE_GRAPHICS=<ON/OFF> -DCMAKE_BUILD_TYPE=Release

Make sure to use a release build with NDEBUG defined for experiments, because otherwise very little data is generated to allow for debugging with reasonable speed.

The programs where tested with libtorch-1.7.0 and both g++-11.1 and msvc-19.29.

Usage

Each simulation has its own executable, pendulum and heateq. All parameters are set in the code and require recompiling. General settings including the mode (training or evaluation) are set in defs.hpp. Parameters of the systems and networks can be found in mainpendulum.cpp + pendulumeval.hpp and mainheateq.cpp + heateqeval.hpp.

Most parameters are saved with the network during training in an .hparam file of the same name. However, to load a network a few compile time parameters may need to be adjusted manually. These are the NetType and UseWrapper. A nn::Integrator also needs to be defined with the correct number of inputs. These are usually created by the problem specific evaluate functions. For pendulum uses the global value NUM_INPUTS, while for heateq values can be set per network using wrapNetwork<>() like this:

auto net1 = nn::load<nn::Convolutional, USE_WRAPPER>(params, "cnn");
auto net2 = nn::load<nn::ExtTCN, USE_WRAPPER>(params, "tcn_4");
auto net2 = nn::load<nn::ExtTCN, USE_WRAPPER>(params, "tcn_8");

// NUM_INPUTS needs to be at least as high as the maximum number of steps expected by the network
evaluate<NUM_INPUTS>(systems, states, timeStep, options, 
				net1, // default case without wrapper is a single step
				wrapNetwork<4>(net2),
				wrapNetwork<8>(net3));

For examples how the various evaluation methods are used take a look at the experiments branch. The plot scripts provided can be used for basic visualization of the generated data but will require manual tweaks regading file names and the number of data series in a file. There are also a number of matlab scripts that contain an implementation of the basic network for the pendulum and computation of its Jacobian. The required data can be imported by first saving the network weights via nn::exportTensor().