I want to combine neural network with physical model in vehicle dynamics modeling, but I don't know if I need to write differential equations of vehicle dynamics in the program, or there are other methods.
It is already well studied area and match your query, e.g., see the links bellow:
Article Longitudinal Vehicle Dynamics: A Comparison of Physical and ...
Article Longitudinal Vehicle Dynamics: A Comparison of Physical and ...
https://www.diva-portal.org/smash/get/diva2:1115795/FULLTEXT02.pdf
https://books.google.com.au/books?hl=en&lr=&id=A0JqDQAAQBAJ&oi=fnd&pg=PR7&dq=overview+on+network+with+physical+model+in+vehicle+dynamics+modeling&ots=HmUQmS03Mc&sig=Afh2rWmj48MoKOllay9946c69I8#v=onepage&q&f=false
You need to formulate the Dynamics of vehicles using a system of differential equations and most Probably that will be nonlinear in nature. Then you need to find the parameter values and initial conditions for each and every state accurately for gaining the most appropriate result or simulation.
You can use a system of nonlinear ordinary differential equations for a system of nonlinear partial differential equations for modelling that dynamics.While working with physical system modelling in matlab I noticed the Vehicle Dynamics modelling with a system of nonlinear ordinary differential equations. I noticed that Optimal Control theory was being used for modelling the Vehicle Dynamics.
After modelling the whole system mathematically you can use a neural network for verifying or justifying the prediction of mathematical models. The outcome you want to get from the mathematical model obviously will be the same as the output of a neural network. All the parameters of the mathematical model can be derived from the data set you already have.
Mathematical models of a system of differential equations had been called grey box models and neural network models and well known as Black Box models. For modelling the whole system mathematically you need a very strong mathematical concept. otherwise you will not achieve the desired result.Programming in matlab will be better and flexible than any other languages in this case.
And your problem description should be more specific if you want to get the exact solution.
dynamics modeling means differential equations solving. For this task you can use neural networks and python. for some material look here https://towardsdatascience.com/how-to-solve-an-ode-with-a-neural-network-917d11918932
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