DeepSPoC is a neural particle method that replaces direct particle-particle interactions in sequential propagation of chaos (SPoC) with particle‑network interactions, using a neural density representation (KRnet) to approximate the empirical measure. By simulating particles in batches and embedding a neural network into the mean‑field SDE coefficients, DeepSPoC reduces memory usage and computational cost compared to traditional particle methods. The approach is demonstrated on various mean‑field equations, showing improved scalability for high‑dimensional problems.
By Kai Du, Yongle Xie, Tao Zhou, Yuancheng Zhou
arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
By Ram\'on Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely
arXiv:2512.10309v3 Announce Type: replace-cross
Abstract: Chemical reaction networks are widely used to model stochastic dynamics in biophysical processes. Their exact probabilistic description via t...
By Jiayu Weng, Xinyi Zhu, Jing Liu, Linyuan L\"u, Pan Zhang, Ying Tang
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
By Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba, Zachary D. Danziger, Deniz Erdogmus
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...
By Zhichao Han, Yue Zhao, Qianxiao Li
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...
By Noah El Rimawi-Fine, Adam Stecklov, Lucas Nelson, Mathieu Blanchette, Alexander Tong, Stephen Y. Zhang, Lazar Atanackovic
The paper introduces Langevin-Informed Transfer Learning (LITL), a method that recovers target Langevin dynamics from biased source samples using only black-box feedback. LITL learns the leading spectral structure of the target infinitesimal generator and the projected drift via Dirichlet representation learning, enabling kinetic reconstruction and slow-manifold gradient estimation. The authors provide finite-sample guarantees for eigenvalue, eigenfunction, and drift estimation, and demonstrate LITL’s ability to recover physical transition timescales, build kinetic structure from static generative samples, reconstruct spherical symmetries, and steer latent representations in trained neural networks.
By Vladimir R. Kostic, Karim Lounici, H\'el\`ene Halconruy, Timoth\'ee Devergne, Michele Parrinello, Massimiliano Pontil
arXiv:2608. 08040v1 Announce Type: cross Abstract: We introduce conditional cylindrical neural networks for approximating functionals of conditional laws in McKean-Vlasov equations with common noise.
By Nacira Agram, Reda Hmioui, Jan Rems
arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.
By Xin-Yang Liu, Xiantao Fan, Jian-Xun Wang
The paper introduces a physics-constrained neural network surrogate that learns the microstructural evolution of binary mixtures governed by the Cahn‑Hilliard equation. By imposing conservation of the order parameter as a hard constraint on the network output, the model accurately predicts long‑time phase‑separation dynamics for both critical and off‑critical mixtures, maintaining mixture composition and matching the Lifshitz‑Slyozov domain‑growth law. A variant that enforces conservation only through a penalty term drifts from the initial composition and loses predictive accuracy over long rollouts, underscoring the necessity of the hard constraint for stability.
By Vijay Yadav, Pallvi Pandey, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
By Chengyun Wang, Liwei Chen, Nils Thuerey
Lagrangian Neural Networks (LNNs) can learn irreducible three‑body interactions from trajectory data by parameterizing only the potential while prescribing kinetic energy. Using the Axilrod‑Teller triple‑dipole interaction as a test case, the authors show that a signal‑aware sampling strategy allows the LNN to recover the correct radial scaling, angular dependence, and sign reversal from accelerations alone. Symbolic regression on the trained potential reproduces the exact Axilrod‑Teller expression, demonstrating that LNNs can uncover closed‑form many‑body laws without prior functional assumptions.
By Sena Kalabalik, Sukru Caglar, Abdullah Umut Hamzaogullari, Arkadas Ozakin