Let's say I have a system that I'd like to describe as x_dot = x+u and given information about when and for how long u was applied; I wish to predict the evolution of x_t+k given x_t and u_t. Ideally, I want the model to be able to generalize for any value of u. For example, a cartpole with initial conditions x and theta, and an input force F.
Can the neural ODE framework deal with x_dot being f(x, u)? How do I go about including this input parameterization in the neural ODE framework? My first thought was to just augment the input state with the time dependent value of u when passing it to the neural network, under the hope that the NN will resolve the relationship between the x_t and u_t when predicting x_t+1, but I haven't had much success with that yet.
Let's say I have a system that I'd like to describe as
x_dot = x+uand given information about when and for how longuwas applied; I wish to predict the evolution ofx_t+kgivenx_tandu_t. Ideally, I want the model to be able to generalize for any value ofu. For example, a cartpole with initial conditions x and theta, and an input force F.Can the neural ODE framework deal with
x_dotbeingf(x, u)? How do I go about including this input parameterization in the neural ODE framework? My first thought was to just augment the input state with the time dependent value ofuwhen passing it to the neural network, under the hope that the NN will resolve the relationship between thex_tandu_twhen predictingx_t+1, but I haven't had much success with that yet.