Code for the paper: "Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs".
Contains tests with simulation and real data. The experimental data from the robotic exoskeleton is property of Wandercraft.

To start working:

• create a directory for this repo, further named dir
• create dir/Figures/Logs
• clone the repo in dir/src
• unzip the Data.zip file in dir/src to create dir/src/Data
• create a python3 virtual environment for this repo in dir/venv, source it
• install all requirements (pip install -r src/requirements.txt)
• install interpolation repo: git clone https://github.com/aliutkus/torchinterp1d into dir, cd torchinterp1d, pip install -e .
• if any problems occur during the installation of required packages, see src/requirements.txt for possible fixes
• cd ../src: you can now run the scripts.

To reproduce the results of the paper:

• Benchmark of recognition models: run python benchmark_recognition_models/earthquake_difftraj_fullNODE.py 1 KKL_u0T_back for the earthquake model with joint optimization of the dynamical parameters (Fig. 2, left). Similarly for the FitzHugh-Nagumo model (Fig. 2, middle), run python benchmark_recognition_models/FitzHugh_Nagumo_ODE_difftraj_fullNODE.py 1 KKL_u0T_back, and for the Van der Pol model (Fig. 2, right), run python benchmark_recognition_models/vanderpol_difftraj_fullNODE.py 1 KKLu_back. Options for the recognition model (second argument of the python command, the first being the process number) are: KKL_u0T_back for backward KKL (KKL_u0T for forward), KKLu_back for backward KKLu (KKLu for forward), y0T_u0T for direct, y0_u0 for direct with t_c = 0, y0T_u0T_RNN_outNN_back for backward RNN+ (y0T_u0T_RNN_outNN for forward). Modify the other parameters (mostly init_state_obs_T and true_meas_noise_var) to reproduce the ablation studies.
• Harmonic oscillator: run python harmonic_oscillator_testcase/HO_back_physical_coords_NN_difftraj.py 1 KKL_u0T_back for no structure (Fig. 5 a), HO_back_physical_coords_NN_hamiltonian.py for Hamiltonian (Fig. 5 (b)), HO_back_physical_coords_NN_hamiltonian_x1dotx2.py for a particular Hamiltonian (Fig. 5 (c)), HO_back_physical_coords_NN_paramid_linobs.py for a parametric model (Fig. 5 (d)), and HO_back_physical_coords_NN_only_recog. py for the extended state-space model (Fig. 5 (e)). The main options for the recognition method (second argument) are again: KKL_u0T_back, y0T_u0T_RNN_outNN_back, y0T_u0T, y0_u0.
• Robotic exoskeleton: run python wandercraft_id/wandercraft_id_difftraj.py 1 KKL_u0T_back for no structure (Fig. 7 (b)), wandercraft_id_difftraj_x1dotx2.py for x1dot = x2, x3dot = x4 (Fig. 7 (b)) , wandercraft_id_difftraj_x1dotx2_residuals.py for the residuals of the linear prior on top of this constraint (Fig. 7 (c)). The options for the recognition method (second argument) are: KKL_u0T_back, y0T_u0T_RNN_outNN_back, y0T_u0T, y0_u0, KKLu_back.

The code runs in a few minutes on a regular laptop for the first two cases, but will need about a day for the robotics dataset.