Random Feature Models for Learning Interacting Dynamical Systems
- URL: http://arxiv.org/abs/2212.05591v1
- Date: Sun, 11 Dec 2022 20:09:36 GMT
- Title: Random Feature Models for Learning Interacting Dynamical Systems
- Authors: Yuxuan Liu, Scott G. McCalla, Hayden Schaeffer
- Abstract summary: We consider the problem of constructing a data-based approximation of the interacting forces directly from noisy observations of the paths of the agents in time.
The learned interaction kernels are then used to predict the agents behavior over a longer time interval.
In addition, imposing sparsity reduces the kernel evaluation cost which significantly lowers the simulation cost for forecasting the multi-agent systems.
- Score: 2.563639452716634
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Particle dynamics and multi-agent systems provide accurate dynamical models
for studying and forecasting the behavior of complex interacting systems. They
often take the form of a high-dimensional system of differential equations
parameterized by an interaction kernel that models the underlying attractive or
repulsive forces between agents. We consider the problem of constructing a
data-based approximation of the interacting forces directly from noisy
observations of the paths of the agents in time. The learned interaction
kernels are then used to predict the agents behavior over a longer time
interval. The approximation developed in this work uses a randomized feature
algorithm and a sparse randomized feature approach. Sparsity-promoting
regression provides a mechanism for pruning the randomly generated features
which was observed to be beneficial when one has limited data, in particular,
leading to less overfitting than other approaches. In addition, imposing
sparsity reduces the kernel evaluation cost which significantly lowers the
simulation cost for forecasting the multi-agent systems. Our method is applied
to various examples, including first-order systems with homogeneous and
heterogeneous interactions, second order homogeneous systems, and a new sheep
swarming system.
Related papers
- Learning Controlled Stochastic Differential Equations [61.82896036131116]
This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion.
We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity.
Our method is available as an open-source Python library.
arXiv Detail & Related papers (2024-11-04T11:09:58Z) - Data-Driven Model Selections of Second-Order Particle Dynamics via
Integrating Gaussian Processes with Low-Dimensional Interacting Structures [0.9821874476902972]
We focus on the data-driven discovery of a general second-order particle-based model.
We present applications to modeling two real-world fish motion datasets.
arXiv Detail & Related papers (2023-11-01T23:45:15Z) - Learning minimal representations of stochastic processes with
variational autoencoders [52.99137594502433]
We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process.
Our approach enables for the autonomous discovery of unknown parameters describing processes.
arXiv Detail & Related papers (2023-07-21T14:25:06Z) - Cheap and Deterministic Inference for Deep State-Space Models of
Interacting Dynamical Systems [38.23826389188657]
We present a deep state-space model which employs graph neural networks in order to model the underlying interacting dynamical system.
The predictive distribution is multimodal and has the form of a Gaussian mixture model, where the moments of the Gaussian components can be computed via deterministic moment matching rules.
Our moment matching scheme can be exploited for sample-free inference, leading to more efficient and stable training compared to Monte Carlo alternatives.
arXiv Detail & Related papers (2023-05-02T20:30:23Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - A Causality-Based Learning Approach for Discovering the Underlying
Dynamics of Complex Systems from Partial Observations with Stochastic
Parameterization [1.2882319878552302]
This paper develops a new iterative learning algorithm for complex turbulent systems with partial observations.
It alternates between identifying model structures, recovering unobserved variables, and estimating parameters.
Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable parameterizations for many complex nonlinear systems.
arXiv Detail & Related papers (2022-08-19T00:35:03Z) - Learning Interaction Variables and Kernels from Observations of
Agent-Based Systems [14.240266845551488]
We propose a learning technique that, given observations of states and velocities along trajectories of agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself.
This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data.
We demonstrate the learning capability of our method to a variety of first-order interacting systems.
arXiv Detail & Related papers (2022-08-04T16:31:01Z) - Multi-Agent Imitation Learning with Copulas [102.27052968901894]
Multi-agent imitation learning aims to train multiple agents to perform tasks from demonstrations by learning a mapping between observations and actions.
In this paper, we propose to use copula, a powerful statistical tool for capturing dependence among random variables, to explicitly model the correlation and coordination in multi-agent systems.
Our proposed model is able to separately learn marginals that capture the local behavioral patterns of each individual agent, as well as a copula function that solely and fully captures the dependence structure among agents.
arXiv Detail & Related papers (2021-07-10T03:49:41Z) - Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning [89.31889875864599]
We propose an efficient model-based reinforcement learning algorithm for learning in multi-agent systems.
Our main theoretical contributions are the first general regret bounds for model-based reinforcement learning for MFC.
We provide a practical parametrization of the core optimization problem.
arXiv Detail & Related papers (2021-07-08T18:01:02Z) - Data-driven discovery of interacting particle systems using Gaussian
processes [3.0938904602244346]
We study the data-driven discovery of distance-based interaction laws in second-order interacting particle systems.
We propose a learning approach that models the latent interaction kernel functions as Gaussian processes.
Numerical results on systems that exhibit different collective behaviors demonstrate efficient learning of our approach from scarce noisy trajectory data.
arXiv Detail & Related papers (2021-06-04T22:00:53Z) - Consistency of mechanistic causal discovery in continuous-time using
Neural ODEs [85.7910042199734]
We consider causal discovery in continuous-time for the study of dynamical systems.
We propose a causal discovery algorithm based on penalized Neural ODEs.
arXiv Detail & Related papers (2021-05-06T08:48:02Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.