Publications

@article{learningStochasticInteracting,
title = {Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories},
author = {Fei Lu and Mauro Maggioni and Sui Tang},
url = {https://arxiv.org/abs/2007.15174},
year = {2020},
date = {2020-07-31},
journal = {arXiv},
abstract = {We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min-max rate of 1-dimensional non-parametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order 1/2 in terms of the time gaps between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.},
keywords = {interacting particle systems, inverse problems, Machine learning, statistics, stochastic systems},
pubstate = {forthcoming},
tppubtype = {article}
}

@article{DiscoveryEmergentBehaviors,
title = {Data-driven Discovery of Emergent Behaviors in Collective Dynamics},
author = {Mauro Maggioni and Jason Miller and Ming Zhong},
url = {https://arxiv.org/abs/1912.11123},
doi = {https://doi.org/10.1016/j.physd.2020.132542},
year = {2019},
date = {2019-01-01},
journal = {Physica D: Nonlinear Phenomena},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}

@article{IdentifiabilityInteractionFunctions,
title = {On the identifiability of interaction functions in systems of interacting particles},
author = {Fei Lu and Zhongyang Li and Mauro Maggioni and Sui Tang and Cheng Zhang},
url = {https://arxiv.org/abs/1912.11965},
year = {2019},
date = {2019-01-01},
journal = {submitted},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}

@article{LMT:AgentsHeterogeneous,
title = {Learning interaction kernels in heterogeneous systems of agents from multiple trajectories},
author = {Fei Lu and Mauro Maggioni and Sui Tang},
url = {https://arxiv.org/abs/1910.04832},
year = {2019},
date = {2019-01-01},
journal = {submitted},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}

@article{LMTZ:AgentsNonParametric,
title = {Nonparametric inference of interaction laws in systems of agents from trajectory data},
author = {Fei Lu and Ming Zhong and Sui Tang and Mauro Maggioni},
url = {https://www.pnas.org/content/116/29/14424},
doi = {10.1073/pnas.1822012116},
issn = {0027-8424},
year = {2019},
date = {2019-01-01},
journal = {Proceedings of the National Academy of Sciences},
volume = {116},
number = {29},
pages = {14424--14433},
publisher = {National Academy of Sciences},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}