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 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.
arXiv:2606. 06094v1 Announce Type: cross Abstract: Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning.
By Shah Pallav Dhanendrakumar, Saikat Pal, Sitikantha Roy
The article reviews modern machine learning techniques for estimating the committor and related kinetic statistics from molecular dynamics simulations. It emphasizes self‑supervised methods that solve the underlying dynamical equations instead of relying on labeled data, and unifies various approaches—generator‑based PDEs, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks—under a common operator framework. The review also discusses practical guidance for handling non‑Markovian effects, sampling strategies, and outlines future research directions such as connections to reinforcement learning and generative modeling.
By Jonathan Weare, Aaron R. Dinner
The paper introduces a data‑driven framework for modeling the hyperelastic and viscoelastic behavior of digital materials made by multi‑material 3D printing. It extends a classical constitutive formulation by Bergström and Boyce, preserving multiplicative kinematics and invariant‑based strain‑energy functions while learning equilibrium and nonequilibrium parameters from multi‑rate uniaxial compression data across different compositions. The approach can either predict closed‑form model parameters as functions of composition or construct polyconvex strain‑energy functions using neural ordinary differential equations, ensuring thermodynamic consistency and capturing rate‑dependent stiffness and hysteresis.
By Josu\'e Garc\'ia-\'Avila (Department of Mechanical Engineering, Columbia University, New York City, USA), Beijun Shen (Department of Mechanical Engineering, Columbia University, New York City, USA), Manuel K. Rausch (Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, USA, Department of Biomedical Engineering, University of Texas at Austin, Austin, USA, Department of Mechanical Engineering, University of Texas at Austin, Austin, USA), Mary C. Boyce (Department of Mechanical Engineering, Columbia University, New York City, USA), Adri\'an Buganza-Tepole (Department of Mechanical Engineering, Columbia University, New York City, USA)
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:2607. 07425v1 Announce Type: cross Abstract: Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data.
By Rebecca M. Crossley, Yuan Yin, Sarah L. Waters, Ruth E. Baker
arXiv:2606. 10682v1 Announce Type: new Abstract: While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference.
By Fateme Mohammad Mohammadi, Hector Budman, Joshua L. Pulsipher
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:2607. 05280v1 Announce Type: new Abstract: Many real-world systems evolve continuously, yet most machine learning models interpret time series as discrete sequences.
By Benjamin Walker
arXiv:2605. 26833v2 Announce Type: replace-cross Abstract: Polymers underpin applications across energy, healthcare, and materials science, yet their vast chemical space makes systematic discovery challenging.
By Yasharth Yadav, Tze Kwang Gerald Er, Atsushi Goto, Kelin Xia
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
By Zhen Zhang, Alessandro Alla, George Em Karniadakis