We study the ability of neural networks to steer or control trajectories of dynamical systems on graphs . In particular, we introduce a neural-network control (NNC) framework, which represents dynamical systems by neural ordinary different equations (neural ODEs) , and find that NNC can learn control signals that drive networked dynamical systems into desired target states. To identify the influence of different target states on the NNC performance, we study two types of control: (i) microscopic control and (ii) macroscopic control. Microscopic control minimizes the L2 norm between the current and target state and macroscopic control minimizes the corresponding Wasserstein distance. We find that the proposed NNC framework produces low-energy control  signals that are highly correlated with those of optimal control. Our results are robust for a wide range of graph structures and (non-)linear dynamical systems .
We study the ability of neural networks to steer or control trajectories of dynamical systems on graphs , which we represent with neural ordinary differential equations (neural ODEs) . To do so, we introduce a neural-ODE control (NODEC) framework and find that it can learn control signals that drive graph dynamical systems into desired target states. While we use loss functions that do not constrain the control energy, our results show that NODEC produces control signals that are highly correlated with optimal (or minimum energy) control signals. Finally, we empirically showcase the high performance and versatility of NODEC for various (non-)linear dynamics and loss functions on different graphs .
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. In particular, we introduce a neural-network control (NNC) framework, which represents dynamical systems by neural ordinary different
, which we represent with neural ordinary differential
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,
. To do so, we introduce a neural-ODE control (NODEC) framework
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NNC
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networked
graph
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To identify the influence of different target states on the NNC performance, we study two types of control: (i) microscopic control and (ii) macroscopic control. Microscopic control minimizes the L2 norm between the current and target state and macroscopic control minimizes the corresponding Wasserstein distance. We find that the proposed NNC framework produces low-energy
While we use loss functions that do not constrain the
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energy, our results show that NODEC produces control
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those of optimal control. Our results are robust for a wide range of graph structures and
optimal (or minimum energy) control signals. Finally, we empirically showcase the high performance and versatility of NODEC for various
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dynamical systems
dynamics and loss functions on different graphs