The paper presents a differentiable hybrid modelling framework that combines a JAX finite volume population balance solver with neural network components to learn constitutive laws and initial conditions directly from experimental data. This approach addresses biases from hand‑picked models and the limitations of black‑box surrogates, enabling more accurate transport predictions. The framework’s differentiability also facilitates optimisation of experimental settings for desired process outcomes.
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. 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
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. 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
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: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: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. 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: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:2502. 02205v4 Announce Type: replace Abstract: The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention.
By Peiyan Hu, Xiaowei Qian, Wenhao Deng, Rui Wang, Haodong Feng, Ruiqi Feng, Tao Zhang, Long Wei, Yue Wang, Zhi-Ming Ma, Tailin Wu
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou