Publications – Mauro Maggioni's personal home page

@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

https://link.springer.com/content/pdf/10.1007/s10208-021-09521-z.pdf},

doi = {doi.org/10.1007/s10208-021-09521-z},

year  = {2021},

date = {2021-04-01},

urldate = {2021-04-01},

journal = {Foundation of Computational Mathematics},

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 spacings 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 al- gorithm 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 = {agent-based models, interacting particle systems, Machine learning, statistics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

Lu, Fei; Li, Zhongyang; Maggioni, Mauro; Tang, Sui; Zhang, Cheng

On the identifiability of interaction functions in systems of interacting particles Journal Article

In: Stochastic Processes and their Applications, vol. 132, 2021.

Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics

Jason Miller Mauro Maggioni, Hongda Qiu

Learning Interaction Kernels for Agent Systems on Riemannian Manifolds Proceedings

ICML, 2021.

Abstract | Links | BibTeX | Tags: agent-based models, interacting particle systems, Machine learning, model reduction, statistics

Mauro Maggioni Fei Lu, Sui Tang

Learning interaction kernels in heterogeneous systems of agents from multiple trajectories Journal Article

In: Journ. Mach. Learn. res., vol. 2, no. 32, pp. 1–67, 2021.

Abstract | Links | BibTeX | Tags: Active Learning, interacting particle systems, inverse problems, Machine learning

@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}

}