Recovering the state and dynamics of autonomous system with partial states solution using neural networks
This work addresses modeling challenges in fields like chemistry and physics, but it is incremental as it builds on an existing deep hidden physics model.
The paper tackles the problem of recovering unknown states and dynamics of autonomous systems using neural networks, achieving successful estimation of dynamics from partial state information in 2D linear/nonlinear and Lorenz systems.
In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be found in nature and have applications in modeling chemical concentrations, population dynamics, n-body problems in physics etc. In this work we consider dynamics of states, which explain how the states will evolve are unknown to us. We approximate state and dynamics both using neural networks. We have considered examples of 2D linear/nonlinear and Lorenz systems. We observe that even without knowing all the states information, we can estimate dynamics of certain states whose state information are known.