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We detail how incorporating physics into neural network design can signi...
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Tomography of timedependent quantum spin networks with machine learning
Interacting spin networks are fundamental to quantum computing. Databas...
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Anticipating synchronization with machine learning
In applications of dynamical systems, situations can arise where it is d...
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Machine Learning assisted Chimera and Solitary states in Networks
Chimera and Solitary states have captivated scientists and engineers due...
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Machine learning prediction of critical transition and system collapse
To predict a critical transition due to parameter drift without relying ...
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Inferring Global Dynamics Using a Learning Machine
Given a segment of time series of a system at a particular set of parame...
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Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems
We propose an effective and lightweighted learning algorithm, Symplecti...
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Adaptable Hamiltonian neural networks
The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which represent a major class of physicsenhanced neural networks. We introduce a class of HNNs capable of adaptable prediction of nonlinear physical systems: by training the neural network based on time series from a small number of bifurcationparameter values of the target Hamiltonian system, the HNN can predict the dynamical states at other parameter values, where the network has not been exposed to any information about the system at these parameter values. The architecture of the HNN differs from the previous ones in that we incorporate an input parameter channel, rendering the HNN parameter–cognizant. We demonstrate, using paradigmatic Hamiltonian systems, that training the HNN using time series from as few as four parameter values bestows the neural machine with the ability to predict the state of the target system in an entire parameter interval. Utilizing the ensemble maximum Lyapunov exponent and the alignment index as indicators, we show that our parametercognizant HNN can successfully predict the route of transition to chaos. Physicsenhanced machine learning is a forefront area of research, and our adaptable HNNs provide an approach to understanding machine learning with broad applications.
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