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.
arXiv:2505. 07068v2 Announce Type: replace-cross Abstract: In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data.
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.
arXiv:2601. 22328v2 Announce Type: replace Abstract: Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories.
arXiv:2605. 30432v2 Announce Type: replace-cross Abstract: Social systems consist of networks of individuals who influence one another through social interactions.
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.
arXiv:2607. 09801v1 Announce Type: new Abstract: Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements.
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.
arXiv:2510.16656v2 Announce Type: replace Abstract: Modeling dynamical systems and unraveling their underlying structural dependencies is central to many domains in the natural sciences. Various phys...
arXiv:2609.37392v1 Announce Type: new Abstract: Modeling the temporal evolution of macroscopic properties of complex systems is an important scientific task. To predict this evolution without full mi...
arXiv:2606. 04100v1 Announce Type: new Abstract: Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data.
arXiv:2601. 21135v2 Announce Type: replace Abstract: Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions.
arXiv:2606. 09432v1 Announce Type: new Abstract: Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies.