Predicting of the function values There is a function: $f(t,x,y,z)$, where $t$- time, $x,y,z$- some arguments.

The values of $f$ for $t\in [a,b]$ are known (100 samples). What is the most accurate way of predicting the value of $f$ for $t=b+1$, if the values of $x,y,z$ for $t\in [a,b+1]$ are known? 

May I implement deep-learning, and if yes, which method would be more reliable?

ADDITIONAL INFO

I'm propagating the satellite position using an analytical method. During the propagation, the errors accumulate. I endeavor to predict the future position errors. $f$ represents the error value and arguments $x,y,z$ are the affecting parameters, such as distance to the Moon, Sun, solar flux, atmospheric density, etc.
Before trying out deep learning I suggest you to try out Random Forests as the nature of your data seems non-linear to me and RFs are good at fitting non-linear data. If it doesn't work out well try doing a simple feed forward neural network with non-linear activation function as it also fits non linear functions really well. Also, machine learning is more about trying and testing as every dataset is different and you can never know in advance which model will work out well.