Publications

@article{YYM:ATLAS2,
title = {Nonlinear model reduction for slow-fast stochastic systems near manifolds},
author = {Felix X.-F. Ye, Sichen Yang, Mauro Maggioni},
url = {https://arxiv.org/abs/2104.02120v1},
year = {2021},
date = {2021-04-05},
abstract = {We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only access to a black box simulator from which short bursts of simulation can be obtained, we estimate the invariant manifold, a process of the effective (stochastic) dynamics on it, and construct an efficient simulator thereof. These estimation steps can be performed on-the-fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.},
keywords = {inverse problems, Machine learning, Manifold Learning, model reduction, random walks, statistics, stochastic systems},
pubstate = {published},
tppubtype = {article}
}

@article{LuMMTang21,
title = {Learning interaction kernels in heterogeneous systems of agents from multiple trajectories},
author = {Fei Lu, Mauro Maggioni, Sui Tang},
url = {https://jmlr.csail.mit.edu/papers/v22/19-861.html},
year = {2021},
date = {2021-01-01},
journal = {Journ. Mach. Learn. res.},
volume = {2},
number = {32},
pages = {1–67},
abstract = {Systems of interacting particles, or agents, have wide applications in many disciplines, including Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct an estimator based on the minimization of a suitably regularized least squares functional, that is guaranteed to converge, in a suitable L^2 space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm to construct such estimator, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-prey and swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and can produce accurate predictions of trajectories in large time intervals, even when they are learned from observations in short time intervals.},
keywords = {Active Learning, interacting particle systems, inverse problems, Machine learning},
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 = {2020},
date = {2020-10-09},
journal = {to appear in Stochastic Processes and their Applications},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
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{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}
}

@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://jmlr.csail.mit.edu/papers/volume22/19-861/19-861.pdf},
journal = {Journ. Mach. Learn. Res.},
volume = {22},
number = {32},
pages = {1–67},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}