Simulation of the behavior of a vehicle in a fluid by Hamiltonian neural network
A method for simulating the behavior of a system ( 20 ) composed of a subsystem ( 10 ), such as an aerial vehicle, in a physical environment ( 21 ) made of an incompressible fluid, comprising training a multilayer neural network (HNN) by means of a training set associating coordinates (x, y) in said physical environment ( 21 ) and respective values of a gradient of the current function (ψ) at said coordinates (x,y), and a loss function configured to minimize an error between a gradient (S ψ ) of the output of said neural network and said gradient of the current function; using said neural network to predict a value of a current function (ψ) and a velocity field (u) by providing it with input coordinates.
1 . A method for simulating the behavior of a system ( 20 ) composed of a subsystem ( 10 ), in a physical environment ( 21 ) composed of an incompressible fluid, comprising:
training a multilayer neural network (HNN) by means of a training set associating coordinates (x, y) in said physical environment ( 21 ) and respective values of a gradient of the current function (ψ) at said coordinates (x,y), and a loss function configured to minimize an error between a gradient (S ψ ) of the output of said neural network and said gradient of the current function; and
using said neural network to predict a value of a current function (ψ) and a velocity field (u) by providing it with input coordinates,
wherein the training of the multilayer neural network comprises a back-propagation of the gradient of the error between the gradient (S ψ ) of the output of said neural network and said gradient of the current function in order to iteratively develop synaptic weights of the multilayer neural network.
2 . The method according to claim 1 , wherein said loss function (L) is expressed by:
ℒ
=
dx
dt
-
d
ψ
dy
2
+
dy
dt
+
d
ψ
dx
2
,
where t represents time.
3 . The method according to claim 1 , wherein said training set is generated by determining a value ψ(x,y,t) of said current function, for coordinates, x,y chosen randomly and a fixed time t in said physical environment ( 21 ).
4 . The method according to claim 3 , wherein said value is determined on the basis of a physical model used in computational fluid dynamics, CFDs.
5 . The method according to claim 4 , wherein the subsystem comprises all or part of an aerial vehicle.
6 . The method according to claim 5 , wherein said aerial vehicle is an airplane.
7 . A non-transitory computer-readable storage medium having a computer program comprising instructions stored thereon which, when executed by a computer, lead said computer to implement the method according to claim 1 .
8 . A device for simulating behavior of a system ( 20 ) composed of a subsystem ( 10 ), in a physical environment ( 21 ) composed of an incompressible fluid, comprising a means for:
training a multilayer neural network (HNN) by means of a training set associating coordinates (x, y) in said physical environment ( 21 ) and respective values of a gradient of a current function (ψ) at said coordinates (x,y), and a loss function configured to minimize an error between a gradient (S ψ ) of an output of said neural network and said gradient of the current function; and
using said neural network to predict values of a current function (ψ) and of a velocity field (u) by providing it with input coordinates,
wherein the training of the multilayer neural network comprises a back-propagation of the gradient of the error between the gradient (S ψ ) of the output of said neural network and said gradient of the current function in order to iteratively develop synaptic weights of the multilayer neural network.
9 . The device according to claim 8 , wherein said loss function (L) is expressed as:
ℒ
=
dx
dt
-
d
ψ
dy
2
+
dy
dt
+
d
ψ
dx
2
,
where t represents time.
10 . The device according to claim 8 , further comprising a means for generating said training set by determining a value ψ(x,y,t) of said current function, for coordinates, x,y chosen randomly and a fixed time t in said physical environment ( 21 ).
11 . The device according to claim 10 , wherein said value is determined on the basis of a physical model used in computational fluid dynamics, CFD.
12 . The device according to claim 11 , wherein said subsystem is all or part of an aerial vehicle.
13 . The device according to claim 12 , wherein said aerial vehicle is an airplane.
14 . The device according to claim 8 , further comprising an interface for retrieving said coordinates and providing said values to a simulation tool.
15 . A server, or set of servers, implementing a device according to claim 8 , the server or set of servers comprising interfaces adapted to make the device accessible in a form of a service available via a computer cloud.