2022
Feng, Jinchao; Maggioni, Mauro; Martin, Patrick; Zhong, Ming
Learning Interaction Variables and Kernels from Observations of Agent-Based Systems Proceeding Forthcoming
Forthcoming.
Abstract | Links | BibTeX | Tags: agent-based models, inverse problems, Machine learning, statistics
@proceedings{nokey,
title = {Learning Interaction Variables and Kernels from Observations of Agent-Based Systems},
author = {Jinchao Feng and Mauro Maggioni and Patrick Martin and Ming Zhong},
url = {https://arxiv.org/abs/2208.02758},
year = {2022},
date = {2022-08-04},
urldate = {2022-08-04},
journal = {arXiV preprint},
abstract = {Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems.},
keywords = {agent-based models, inverse problems, Machine learning, statistics},
pubstate = {forthcoming},
tppubtype = {proceedings}
}
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc…), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems.
2021
Sichen Yang Felix X.-F. Ye, Mauro Maggioni
Nonlinear model reduction for slow-fast stochastic systems near manifolds Journal Article
In: 2021.
Abstract | Links | BibTeX | Tags: inverse problems, Machine learning, Manifold Learning, model reduction, random walks, statistics, stochastic systems
@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}
}
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.
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
@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},
doi = {https://doi.org/10.1016/j.spa.2020.10.005},
year = {2021},
date = {2021-02-01},
journal = {Stochastic Processes and their Applications},
volume = {132},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
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}
}
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.
2020
Sui Tang Jason Miller, Ming Zhong
Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems Online Forthcoming
Forthcoming.
Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning
@online{LearningInteractionkernels2ndorder,
title = {Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems},
author = {Jason Miller, Sui Tang, Ming Zhong, Mauro Maggioni},
url = {https://arxiv.org/abs/2010.03729},
year = {2020},
date = {2020-10-08},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning},
pubstate = {forthcoming},
tppubtype = {online}
}
2019
Maggioni, Mauro; Miller, Jason; Zhong, Ming
Data-driven Discovery of Emergent Behaviors in Collective Dynamics Journal Article
In: Physica D: Nonlinear Phenomena, 2019.
Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics
@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}
}
Lu, Fei; Zhong, Ming; Tang, Sui; Maggioni, Mauro
Nonparametric inference of interaction laws in systems of agents from trajectory data Journal Article
In: Proceedings of the National Academy of Sciences, vol. 116, no. 29, pp. 14424–14433, 2019, ISSN: 0027-8424.
Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics
@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}
}
0000
Lu, Fei; Maggioni, Mauro; Tang, Sui
Learning interaction kernels in heterogeneous systems of agents from multiple trajectories Journal Article
In: Journ. Mach. Learn. Res., vol. 22, no. 32, pp. 1–67, 0000.
Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics
@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}
}
- Lectures at Summer School at Peking University, July 2017.
- PCMI Lectures, Summer 2016: Lecture 1, Lecture 2, Problems/discussion points
- Google Scholar
- Papers on the ArXiv
- Papers on MathsciNet
- Tutorials on diffusion geometry and multiscale analysis on graphs at the MRA Internet Program at IPAM: Part I and Part II.
- Diffusion Geometries, Diffusion Wavelets and Harmonic Analysis of large data sets, IPAM, Multiscale Geometric Analysis Program, Fall 2004.
- Diffusion Geometries, global and multiscale, IPAM, 2005.