@article{choudhary_radhakrishnan_lindner_sinha_ditto_2023, title={Neuronal diversity can improve machine learning for physics and beyond}, volume={13}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-023-40766-6}, abstractNote={Abstract}, number={1}, journal={SCIENTIFIC REPORTS}, author={Choudhary, Anshul and Radhakrishnan, Anil and Lindner, John F. and Sinha, Sudeshna and Ditto, William L.}, year={2023}, month={Nov} }
 @article{choudhary_lindner_holliday_miller_sinha_ditto_2021, title={Forecasting Hamiltonian dynamics without canonical coordinates}, volume={103}, ISSN={["1573-269X"]}, DOI={10.1007/s11071-020-06185-2}, abstractNote={Conventional neural networks are universal function approximators, but they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here, we prepend a conventional neural network to a Hamiltonian neural network and show that the combination accurately forecasts Hamiltonian dynamics from generalised noncanonical coordinates. Examples include a predator–prey competition model where the canonical coordinates are nonlinear functions of the predator and prey populations, an elastic pendulum characterised by nontrivial coupling of radial and angular motion, a double pendulum each of whose canonical momenta are intricate nonlinear combinations of angular positions and velocities, and real-world video of a compound pendulum clock.}, number={2}, journal={NONLINEAR DYNAMICS}, author={Choudhary, Anshul and Lindner, John F. and Holliday, Elliott G. and Miller, Scott T. and Sinha, Sudeshna and Ditto, William L.}, year={2021}, month={Jan}, pages={1553–1562} }
 @article{miller_lindner_choudhary_sinha_ditto_2021, title={Negotiating the separatrix with machine learning}, volume={12}, ISSN={["2185-4106"]}, url={https://doi.org/10.1587/nolta.12.134}, DOI={10.1587/nolta.12.134}, abstractNote={: Physics-informed machine learning has recently been shown to efficiently learn complex trajectories of nonlinear dynamical systems, even when order and chaos coexist. However, care must be taken when one or more variables are unbounded, such as in rotations. Here we use the framework of Hamiltonian Neural Networks (HNN) to learn the complex dynamics of nonlinear single and double pendulums, which can both librate and rotate, by mapping the unbounded phase space onto a compact cylinder. We clearly demonstrate that our approach can successfully forecast the motion of these challenging systems, capable of both bounded and unbounded motion. It is also evident that HNN can yield an energy surface that closely matches the surface generated by the true Hamiltonian function. Further we observe that the relative energy error for HNN decreases as a power law with number of training pairs, with HNN clearly outperforming conventional neural networks quantitatively.}, number={2}, journal={IEICE NONLINEAR THEORY AND ITS APPLICATIONS}, author={Miller, Scott T. and Lindner, John F. and Choudhary, Anshul and Sinha, Sudeshna and Ditto, William L.}, year={2021}, pages={134–142} }
 @article{choudhary_saha_krueger_finke_rosa_freund_feudel_2021, title={Weak-winner phase synchronization: A curious case of weak interactions}, volume={3}, ISSN={["2643-1564"]}, DOI={10.1103/PhysRevResearch.3.023144}, abstractNote={We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase synchronization while the strongly coupled oscillator pair does not. This intriguing "weak-winner" synchronization phenomenon can be explained by the interplay between non-isochronicity and natural frequency of the oscillator, as coupling strength is varied. Further, we present sufficient conditions under which the weak-winner phase synchronization can occur for limit cycle as well as chaotic oscillators. Employing model system from ecology as well as a paradigmatic model from physics, we demonstrate that this phenomenon is a generic feature for a large class of coupled oscillator systems. The realization of this peculiar yet quite generic weak-winner dynamics can have far reaching consequences in a wide range of scientific disciplines that deal with the phenomenon of phase synchronization. Our results also highlight the role of non-isochronicity (shear) as a fundamental feature of an oscillator in shaping the emergent dynamics.}, number={2}, journal={PHYSICAL REVIEW RESEARCH}, author={Choudhary, Anshul and Saha, Arindam and Krueger, Samuel and Finke, Christian and Rosa, Epaminondas, Jr. and Freund, Jan A. and Feudel, Ulrike}, year={2021}, month={May} }