The paper presents a differentiable hybrid modelling framework that combines a JAX finite volume population balance solver with learnable neural network components. This approach learns constitutive laws and initial conditions directly from experimental data, improving the fidelity of transport models in chemical engineering. The framework’s differentiability also enables optimisation of experimental settings for desired process outcomes.
By Arthur Jessop, Mohammed Alsubeihi, Ben Moseley, Ashwin Kumar Rajagopalan
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:2606. 02145v1 Announce Type: new Abstract: Accurate prediction of polymerization dynamics is essential for process design, control, and optimization.
By Marah Almanasreh, Alexander Mitsos, Eike Cramer
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
By Fanghui Song, Zhongjian Wang, Jiebao Sun
arXiv:2606. 26128v1 Announce Type: new Abstract: The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs).
By Vijay Yadav, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
By Qiyao Zhou, Xujia Zhu, Pierre Joli, Yu Cong, Sibo Cheng
arXiv:2606. 05202v1 Announce Type: cross Abstract: In reactor physics, neutronics can be treated with different fidelity levels, according to the needs of the user.
By Stefano Riva, Carolina Introini, J. Nathan Kutz, Antonio Cammi
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask
arXiv:2603. 11249v4 Announce Type: replace Abstract: Accurate prediction of phase equilibria remains a central challenge in chemical engineering.
By Karim K. Ben Hicham, Moreno Ascani, Jan G. Rittig, Alexander Mitsos
arXiv:2603. 18907v2 Announce Type: replace Abstract: We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution, parametrically with respect to the location of the initial mass.
By Riccardo Saporiti, Fabio Nobile
The paper introduces a new federated learning protocol for partial differential equations called solution-space PDE-Dirichlet, which transforms continuous supervised responses into reusable solution bins and measures client separation via optimal transport. It establishes an exact inverse relationship between population allocation heterogeneity and Dirichlet concentration, and shows how response heterogeneity can cause gradient disagreement, local-update dispersion, and parameter divergence. Experiments on seven PDE tasks, three neural-operator families, and five random seeds demonstrate that lower concentration consistently increases solution distance and optimization heterogeneity, with the most pronounced error increase observed in low-viscosity Burgers equations.
By Ping Luo, Jiahuan Wang, Ziqing Wen, Tao Sun, Dongsheng Li