Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics

• URL: http://arxiv.org/abs/2606.02145v1
• Date: Mon, 01 Jun 2026 12:10:48 GMT
• Title: Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics
• Abstract summary: We propose a hybrid Neural Ordinary Differential Equation framework for data-efficient modeling of free-radical polymerization.<n>The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions.<n>In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model.
• Score: 42.58292307702424
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accurate prediction of polymerization dynamics is essential for process design, control, and optimization. Yet, purely mechanistic models require labor-intensive parameterization of partially characterized kinetics, while purely data-driven models demand large, diverse datasets that are costly to obtain, particularly in early-design stages. We propose a hybrid Neural Ordinary Differential Equation (NODE) framework for data-efficient modeling of free-radical polymerization. Using batch polymerization of methyl methacrylate (MMA) as a case study, the mechanistic mass balances are retained explicitly, and only the partially-characterized effective radical concentration governing monomer consumption is learned from data through a neural network surrogate, while established reactions such as initiator decomposition, propagation, and termination remain physically modeled. The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions, with models trained on as few as ten measurements under both regular and irregular sampling. The hybrid NODE consistently achieves lower prediction errors and more physically consistent extrapolations than both purely data-driven baselines. In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model, demonstrating that learning only a closure term rather than the full dynamics is sufficient for reliable prediction under limited data availability.

Related papers

• Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation [71.74203645336385]
  Impute-EM alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data.<n>We characterize the update and show that the observed mask-indexed marginals match the targets at the limit.
  arXiv  Detail & Related papers  (2026-09-14T09:39:13Z)
• Regularised Iterative Generalised Least Squares with Optimal Selection of the Hyper-Parameter for Identifying Nonlinear Phenomenological Models [0.0]
  In some fields, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models contain parameters to be estimated from experimental data.<n>We introduce a ridge regression scheme to preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem.<n>An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper- parameter at each iteration.
  arXiv  Detail & Related papers  (2026-08-19T09:50:46Z)
• Hybrid Dynamics Modeling for a Flexible 2-DoF Robotic Arm [2.1528661949045533]
  This paper examines three approaches for modeling the dynamics of a flexible-link 2-DoF robotic arm.<n>Two physics informed models combine rigid-body dynamics (RBD) formulations with a Gaussian Mixture Model (GMM) to capture residual model errors and linkage flexibility.<n>A kinematics-based regression model serves as a purely data-driven baseline.
  arXiv  Detail & Related papers  (2026-06-02T00:12:20Z)
• Joint Model and Data Sparsification via the Marginal Likelihood [53.29070892356214]
  We propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification.<n>This symmetric pruning of model and data offers a natural extension that preserves conjugacy.<n> Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
  arXiv  Detail & Related papers  (2026-05-28T13:26:53Z)
• Latent Neural-ODE for Model-Informed Precision Dosing: Overcoming Structural Assumptions in Pharmacokinetics [3.0991186209192794]
  We introduce a novel data-driven alternative based on Latent Ordinary Differential Equations (Latent ODEs) for tacrolimus AUC prediction.<n>This deep learning approach learns individualized dynamics directly from sparse clinical data.<n>Latent ODE model demonstrated superior robustness, maintaining high accuracy even when underlying biological mechanisms deviated from standard assumptions.
  arXiv  Detail & Related papers  (2026-02-03T07:30:48Z)
• Self-Refining Training for Amortized Density Functional Theory [5.5541132320126945]
  We propose a novel method that reduces the dependency of amortized DFT solvers on large pre-collected datasets by introducing a self-refining training strategy.<n>We derive our method as a minimization of the variational upper bound on the KL-divergence measuring the discrepancy between the generated samples and the target Boltzmann distribution defined by the ground state energy.
  arXiv  Detail & Related papers  (2025-06-02T00:32:32Z)
• Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data [0.0]
  Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations.<n>We introduce a fully data-free, generative framework for CG that directly targets the all-atom Boltzmann distribution.<n>We show that the method captures all relevant modes of the Boltzmann distribution, reconstructs atomic configurations, and automatically learns physically meaningful CG representations.
  arXiv  Detail & Related papers  (2025-04-29T17:05:27Z)
• Generalization capabilities and robustness of hybrid models grounded in physics compared to purely deep learning models [2.8686437689115363]
  This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications.<n>Three autoregressive models were compared: a hybrid model (POD-DL) that combines proper decomposition (POD) with a long-short term memory (LSTM) layer, a convolutional autoencoder combined with a convolutional LSTM layer, and a variational autoencoder (VAE) combined with a ConvLSTM layer.<n>While the VAE and ConvLSTM models accurately predicted laminar flow, the hybrid POD-DL model outperformed the others
  arXiv  Detail & Related papers  (2024-04-27T12:43:02Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.