mlsanityData to 7 Oct 2026

Nonparametric inference of interaction laws in systems of agents from trajectory data

arXiv 1812.06003 ↗First posted 14 Dec 2018cs.LG stat.MLcited by 43

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Abstract (arXiv)

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or assumption about their analytical form, from data consisting trajectories of interacting agents. We demonstrate the effectiveness of our learning approach both by providing theoretical guarantees, and by testing the approach on a variety of prototypical systems in various disciplines. These systems include homogeneous and heterogeneous agents systems, ranging from particle systems in fundamental physics to agent-based systems modeling opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Dec 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 6; 2023: 8; 2024: 4; 2025: 6; 2026: 8.

43 papers.

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  1. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  2. 2021The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimationcited by 14
  3. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  4. 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy datacited by 13
  5. 2021Identifiability of interaction kernels in mean-field equations of interacting particlescited by 11
  6. 2022Nonparametric learning of kernels in nonlocal operatorscited by 10
  7. 2022Random Feature Models for Learning Interacting Dynamical Systemscited by 10
  8. 2021Learning Interaction Kernels for Agent Systems on Riemannian Manifoldscited by 7
  9. 2024Universal Approximation of Mean-Field Models via Transformerscited by 7
  10. 2022Learning Interaction Variables and Kernels from Observations of Agent-Based Systemscited by 6
  11. 2023Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-netscited by 6
  12. 2024Self-test loss functions for learning weak-form operators and gradient flowscited by 4
31 more
  1. 2021Learning particle swarming models from data with Gaussian processescited by 3
  2. 2023Reproducing kernel Hilbert spaces in the mean field limitcited by 3
  3. 2021Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Datacited by 2
  4. 2021Learning Swarm Interaction Dynamics from Density Evolutioncited by 2
  5. 2023Learning Continuous Network Emerging Dynamics from Scarce Observations via Data-Adaptive Stochastic Processescited by 2
  6. 2023Learning Collective Behaviors from Observationcited by 2
  7. 2023Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structurescited by 2
  8. 2024Interacting Particle Systems on Networks: joint inference of the network and the interaction kernelcited by 2
  9. 2026Learning interacting particle systems from unlabeled datacited by 2
  10. 2021Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemeridescited by 1
  11. 2022A Data-Adaptive Prior for Bayesian Learning of Kernels in Operatorscited by 1
  12. 2023On kernel-based statistical learning in the mean field limitcited by 1
  13. 2025Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systemscited by 1
  14. 2025Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structurescited by 1
  15. 2026Learning Multi-type heterogeneous interacting particle systemscited by 1
  16. 2026MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Datacited by 1
  17. 2026Nonlocal Mean Field Schr"odinger Bridge with Learned Interactionscited by 1
  18. 2021ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systemscited by 0
  19. 2022Unsupervised learning of observation functions in state-space models by nonparametric moment methodscited by 0
  20. 2022Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectorycited by 0
  21. 2023Benchmarking optimality of time series classification methods in distinguishing diffusionscited by 0
  22. 2023Data-Scarce Identification of Game Dynamics via Sum-of-Squares Optimizationcited by 0
  23. 2024Neural Persistence Dynamicscited by 0
  24. 2025A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Modelcited by 0
  25. 2025Minimax Rates for Learning Pairwise Interactions in Attention-Style Modelscited by 0
  26. 2025Data-driven Learning of Interaction Laws in Multispecies Particle Systems with Gaussian Processes: Convergence Theory and Applicationscited by 0
  27. 2025On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functionscited by 0
  28. 2026Discovery of interaction and diffusion kernels in particle-to-mean-field multi-agent systemscited by 0
  29. 2026Recursive Maximum Likelihood Estimation for Interacting Particle Systems using Virtual Particlescited by 0
  30. 2026Multi-Agent System Identification with Nonlinear Sheaf Diffusioncited by 0
  31. 2026Learning Interaction Kernels from Collective Steady Statescited by 0