Data-driven discovery of interacting particle systems using Gaussian processes

• URL: http://arxiv.org/abs/2106.02735v1
• Date: Fri, 4 Jun 2021 22:00:53 GMT
• Title: Data-driven discovery of interacting particle systems using Gaussian processes
• Authors: Jinchao Feng, Yunxiang Ren, Sui Tang
• Abstract summary: 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.
• Score: 3.0938904602244346
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Interacting particle or agent systems that display a rich variety of collection motions are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and collective behaviors. In this paper, 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, which can simultaneously fulfill two inference goals: one is the nonparametric inference of interaction kernel function with the pointwise uncertainty quantification, and the other one is the inference of unknown parameters in the non-collective forces of the system. We formulate learning interaction kernel functions as a statistical inverse problem and provide a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. We provide a finite-sample analysis, showing that our posterior mean estimator converges at an optimal rate equal to the one in the classical 1-dimensional Kernel Ridge regression. Numerical results on systems that exhibit different collective behaviors demonstrate efficient learning of our approach from scarce noisy trajectory data.

Related papers

• Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems [70.84976977950075]
  Real-world multi-agent systems are often dynamic and continuous, where the agents co-evolve and undergo changes in their trajectories and interactions over time. We propose a novel model that captures the continuous interaction among agents using a Graph Neural Network (GNN) as the ODE function. The key innovation of our model is to learn time-dependent representations of treatments and incorporate them into the ODE function, enabling precise predictions of potential outcomes.
  arXiv  Detail & Related papers  (2024-02-29T23:07:07Z)
• Inferring Relational Potentials in Interacting Systems [56.498417950856904]
  We propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. It allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting.
  arXiv  Detail & Related papers  (2023-10-23T00:44:17Z)
• Collective Relational Inference for learning heterogeneous interactions [8.215734914005845]
  We propose a novel probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. Overall the proposed model is data-efficient and generalizable to large systems when trained on smaller ones.
  arXiv  Detail & Related papers  (2023-04-30T19:45:04Z)
• Interactive System-wise Anomaly Detection [66.3766756452743]
  Anomaly detection plays a fundamental role in various applications. It is challenging for existing methods to handle the scenarios where the instances are systems whose characteristics are not readily observed as data. We develop an end-to-end approach which includes an encoder-decoder module that learns system embeddings.
  arXiv  Detail & Related papers  (2023-04-21T02:20:24Z)
• Random Feature Models for Learning Interacting Dynamical Systems [2.563639452716634]
  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.
  arXiv  Detail & Related papers  (2022-12-11T20:09:36Z)
• 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)
• Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs [13.436770170612295]
  We study for the first time uncertainty-aware modeling of continuous-time dynamics of interacting objects. Our model infers both independent dynamics and their interactions with reliable uncertainty estimates.
  arXiv  Detail & Related papers  (2022-05-24T08:36:25Z)
• Learning Neural Causal Models with Active Interventions [83.44636110899742]
  We introduce an active intervention-targeting mechanism which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting. We demonstrate superior performance on multiple benchmarks from simulated to real-world data.
  arXiv  Detail & Related papers  (2021-09-06T13:10:37Z)
• Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems [17.623937769189364]
  We develop a complete learning theory which establishes strong consistency and optimal nonparametric min-max rates of convergence for the estimators. The numerical algorithm presented to build the estimators is parallelizable, performs well on high-dimensional problems, and is demonstrated on complex dynamical systems.
  arXiv  Detail & Related papers  (2020-10-08T02:07:53Z)
• Bayesian Sparse Factor Analysis with Kernelized Observations [67.60224656603823]
  Multi-view problems can be faced with latent variable models. High-dimensionality and non-linear issues are traditionally handled by kernel methods. We propose merging both approaches into single model.
  arXiv  Detail & Related papers  (2020-06-01T14:25:38Z)
• End-to-End Models for the Analysis of System 1 and System 2 Interactions based on Eye-Tracking Data [99.00520068425759]
  We propose a computational method, within a modified visual version of the well-known Stroop test, for the identification of different tasks and potential conflicts events. A statistical analysis shows that the selected variables can characterize the variation of attentive load within different scenarios. We show that Machine Learning techniques allow to distinguish between different tasks with a good classification accuracy.
  arXiv  Detail & Related papers  (2020-02-03T17:46:13Z)

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.