The paper introduces a learning method for identifying interaction kernels in particle systems using only single-snapshot observations of collective steady states, rather than trajectory data. By regularizing with empirical distributions from varied, unseen initial conditions, the authors address the ill‑posed inverse problem and demonstrate stable, accurate recovery of interaction laws across several models. The recovered laws enable faithful reproduction of both steady‑state patterns and, in many cases, the preceding dynamics.
By Baoli Hao, Mauro Maggioni, Ming Zhong
The paper presents a variational learning framework that simultaneously infers non‑parametric interaction kernels and environmental or intra‑agent forces in collective dynamics. It extends existing methods to handle both interaction and environmental components, validating the approach on benchmark models such as synchronization, alignment, and attraction‑repulsion systems. A model‑selection procedure is also introduced to identify the best explanatory framework from trajectory data, enabling direct recovery of mechanistic interaction mechanisms.
By Nipuni de Silva, Ming Zhong, James M. Greene
arXiv:2606. 21199v2 Announce Type: replace-cross Abstract: We introduce a semi-parametric framework for nonlinear system identification, which decouples discrepancy functions from physics-based components.
By Swapnil Manna, Timothy J. Rogers, Lawrence Bull
arXiv:2510. 12311v2 Announce Type: replace-cross Abstract: We develop interacting particle algorithms for learning latent variable models with energy-based priors.
By Joanna Marks, Tim Y. J. Wang, O. Deniz Akyildiz
arXiv:2606. 24966v1 Announce Type: new Abstract: Estimating parameters of dynamical systems from sparse, noisy, and irregularly sampled data is often severely ill-conditioned.
By Cristian Brugnara, Lea Multerer, Marco Forgione, Laura Azzimonti
The paper introduces kernel-based methods for learning Hamiltonian systems directly from trajectory data, offering both a 2‑step approach (reconstruct trajectories first, then learn the Hamiltonian) and a 1‑step approach (joint inference). Experiments on mass‑spring dynamics, a nonlinear pendulum, and the Henon‑Heiles system show that the methods achieve accurate, data‑efficient predictions, outperforming 2‑step baselines especially when data are scarce, while preserving the Hamiltonian structure. The authors also provide a priori error estimates and a general numerical framework applicable to arbitrary dynamical systems.
By Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi, Peyman Tavallali, Houman Owhadi
arXiv:2601. 22328v2 Announce Type: replace Abstract: Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories.
By Luca Muscarnera, Silas Ruhrberg Est\'evez, Samuel Holt, Evgeny Saveliev, Mihaela van der Schaar
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
The paper introduces a continuous normalizing flow model for infinite-dimensional Bayesian inference in inverse problems governed by partial differential equations. By defining a neural ordinary differential equation in an infinite-dimensional Hilbert space, a simple reference measure is transformed into a complex prior that captures prior information. The authors establish a theoretical framework for well-posedness, present training methods for two data settings, and provide sampling algorithms, applying the approach to smooth, scattering, and heat conduction inverse problems with supporting numerical experiments.
By Yang Zhao, Junxiong Jia, Tao Zhou
The paper introduces an active diffusion-based inverse problem solver that trains a diffusion model to map between parameter and observable spaces. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method can discover and learn the correct parameter region even when initial training bounds exclude the true parameters. The authors demonstrate the solver on a toy inverse problem with infinite solutions and on parameterizing quantum correlation functions for a Quantum Chromodynamics analysis of nucleon structure.
By Jitao Xu, Nobuo Sato, Yaohang Li
arXiv:2609.37227v1 Announce Type: new
Abstract: Inference-time steering adapts pretrained diffusion and flow-based models to new tasks, e.g., to generate samples from a conditional distribution or sa...
By Adhithyan Kalaivanan, Zheng Zhao, Jens Sj\"olund, Fredrik Lindsten
arXiv:2606. 30467v1 Announce Type: cross Abstract: We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data.
By Richard Schwank, Mathias Drton