ChemNODE: A neural ordinary differential equations framework for efficient chemical kinetic solvers

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and solve the desired ODE with the off-the-shelf (fixed) solver to obtain reconstructed images. We extend this model and incorporate the knowledge of off-the-shelf ODE solvers into the network design (learned solvers). We investigate several models based on three ODE solvers and compare models with fixed solvers and learned solvers. Our models achieve better reconstruction results and are more parameter efficient than other popular methods such as UNet and cascaded CNN. We introduce a new way of tackling the MRI reconstruction problem by modeling the continuous optimization dynamics using neural ODEs.

RoseNNa: A performant, portable library for neural network inference with application to computational fluid dynamics

Inferring ecological interactions is hard because we often lack suitable parametric representations to portray them. Neural ordinary differential equations (NODEs) provide a way of estimating interactions non‐parametrically from time‐series data. NODEs, however, are slow to fit, and inferred interactions usually are not compared with the ground truth. We provide a fast NODE fitting method, Bayesian neural gradient matching (BNGM), which relies on interpolating time series with neural networks and fitting NODEs to the interpolated dynamics with Bayesian regularisation. We test the accuracy of the approach by inferring ecological interactions in time series generated by an ODE model with known interactions. We compare these results against three existing approaches for estimating ecological interactions, standard NODEs, ODE models and convergent cross‐mapping (CCM). We also infer interactions in experimentally replicated time series of a microcosm featuring an algae, flagellate and rotifer population, in the hare and lynx system, and the Maizuru Bay community featuring 11 species. Our BNGM approach allows us to reduce the fitting time of NODE systems to only a few seconds and provides accurate estimates of ecological interactions in the artificial system, as true ecological interactions are recovered with minimal error. Our benchmark analysis reveals that our approach is both faster and more accurate than standard NODEs and parametric ODEs, while CCM was found to be faster but less accurate. The analysis of the replicated time series reveals that only the strongest interactions are consistent across replicates, while the analysis of the Maizuru community shows the strong negative impact of the chameleon goby on most species of the community, and a potential indirect negative effect of temperature by favouring goby population growth. Overall, NODEs alleviate the need for a mechanistic understanding of interactions, and BNGM alleviates the heavy computational cost. This is a crucial step availing quick NODE fitting to larger systems, cross‐validation and uncertainty quantification, as well as more objective estimation of interactions, and complex context dependence, than parametric models.

<div class="section abstract"><div class="htmlview paragraph">In this work, the multi-disciplinary problem arising from fluid sloshing within a partially filled tanker truck undergoing lateral acceleration is investigated through the use of multiphysics coupling between a computational fluid dynamics (CFD) solver and a multi-body dynamics (MBD) solver. This application represents a challenging test case for simulation technology within the design of commercial vehicles and is intended to demonstrate a novel approach in the field of computer aided engineering.</div><div class="htmlview paragraph">Computer aided engineering is playing a more predominant role in the design process for commercial and passenger vehicles. Better understanding of the real time loading and responses on a vehicle during intended or unintended use can result in improved design and reduced cost over traditional designs that relied heavily on assumed loads. Liquid sloshing within the cargo tank of a commercial tanker truck results in increased loading on the vehicle's suspension when undergoing acceleration maneuvers. The change in loading can have a significant effect on the design of the vehicles suspension components and braking components. The ability to investigate the fully coupled behavior of the mechanical and fluid systems is a key technology to enable improved designs for these types of applications.</div><div class="htmlview paragraph">The following paper presents a multiphysics analysis of a simplified tanker truck undergoing a lane change maneuver. Bi-directionally coupled CFD and MBD solvers are used to compute the response of the vehicle during a lane change maneuver. The distribution of the liquid within the cargo tank is computed by the CFD solver, <i>AcuSolve</i> using an Arbitrary Lagrange-Eulerian (ALE) mesh motion approach. The forces resulting from the sloshing are then passed to the MBD solver, <i>MotionSolve</i> and the response of the tanker truck is computed. This exchange of forces and displacements occurs at run time and is enabled through a socket connection between the two solvers.</div></div>

Chapter 30 - Parallel Computing for Fluid/Structure Coupled Simulation

Adapting legacy applications for use in a modern heterogeneous environment is a serious challenge for an industrial software vendor (ISV). The adaptation of the NUMECA FINE/Turbo computational fluid dynamics (CFD) solver for accelerated CPU/GPU execution is presented. An incremental instrumentation with OpenACC directives has been used to obtain a global solver acceleration greater than 2X on the OLCF Titan supercomputer. The implementation principals and procedures presented in this paper constitute one successful path towards obtaining meaningful heterogeneous performance with a legacy application. The presented approach minimizes risk and developer-hour cost, making it particularly attractive for ISVs.

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint-based design optimization requires coupling an adjoint-enabled computational fluid dynamics (CFD) solver with an adjoint-enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Machine learning (ML) surrogate models offer a promising route to accelerate material property prediction, bypassing costly atomistic simulations. Here, we introduce IsothermODE, a neural ordinary differential equation (NODE) framework for reconstructing full uptake and heat of adsorption $$\left(\Delta {H}_{{\rm{ads}}}\right)$$ isotherms for CO2 adsorption in metal-organic frameworks (MOFs) using only sparse pressure data. Unlike traditional ML models, IsothermODE leverages the intrinsic structure of differential equations to produce smooth, physically-consistent predictions that generalize across wide pressure ranges. We demonstrate high-fidelity interpolation and extrapolation, even with only five pressure points. To address the stochasticity inherent in Grand Canonical Monte Carlo (GCMC) simulations, we integrate uncertainty quantification, yielding tight bounds on predicted enthalpy curves. We further interpret the learned latent dynamics in terms of adsorption thermodynamics and textural properties, offering insight into structure-property relationships. Finally, we demonstrate IsothermODE’s long-range interpolation and extrapolation capabilities with sparse isotherm data (5 pressure points) and large incomplete intervals featuring missing data between 4–40 (case 1) and 25–50 (case 2) bars. IsothermODE provides a fast, robust alternative to simulation-heavy workflows, enabling scalable screening and design of next-generation carbon capture materials.

Measurement noise is an integral part of collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We discuss a methodology to learn differential equation(s) using noisy and irregularly sampled measurements. In our methodology, the main innovation can be seen in the integration of deep neural networks with the neural ordinary differential equations (ODEs) approach. Precisely, we aim at learning a neural network that provides (approximately) an implicit representation of the data and an additional neural network that models the vector fields of the dependent variables. We combine these two networks by constraints using neural ODEs. The proposed framework to learn a model describing the vector field is highly effective under noisy measurements. The approach can handle scenarios where dependent variables are unavailable at the same temporal grid. Moreover, a particular structure, e.g. second order with respect to time, can easily be incorporated. We demonstrate the effectiveness of the proposed method for learning models using data obtained from various differential equations and present a comparison with the neural ODE method that does not make any special treatment to noise. Additionally, we discuss an ensemble approach to improve the performance of the proposed approach further.

Dynamic process modeling is essential for simulating time‐evolving biochemical systems, particularly those with multistate interactions and combinatorial complexity. Traditional Ordinary Differential Equation (ODE) models offer mechanistic clarity but struggle with scalability and context‐sensitive encoding. Rule‐Based Modeling (RBM) frameworks address these limitations through modular rule abstraction, yet require manual specification and lack adaptive learning. This study introduces algorithmic innovations within the Neural Ordinary Differential Equation (Neural ODE) paradigm to bridge the gap between mechanistic interpretability and scalable expressivity. Neural ODEs can be considered as a revolutionary approach in the field of modeling dynamic biochemical interactions. They have made it possible to create models of such interactions that are flexible enough to adapt to different scenarios and do so without requiring any manual intervention in terms of rule encoding or predefined reaction schemes. This is achieved by employing differential solvers within the framework of neural networks, thus enabling a learning process that is in accordance with the behavior of the system. Using the DARPP‐32 signaling network—a benchmark system characterized by multivalent phosphorylation and dynamic perturbations—the proposed Neural ODE framework demonstrates the ability to replicate key dynamic behaviors observed in ODE and RBM models. Comparative simulations under baseline and perturbed conditions reveal that Neural ODEs maintain trajectory fidelity while offering enhanced modularity and computational efficiency. Feature importance analysis and latent space visualizations further validate the model's interpretability and robustness. Unlike ODEs and RBMs, Neural ODEs adapt to structural mutations and binding schemes through latent trajectory learning, enabling flexible simulation of biochemical variability without manual rule encoding. This work establishes Neural ODEs as a viable and scalable alternative for modeling complex biochemical systems, combining the strengths of data‐driven learning with the interpretability of differential equations.

Data is one of the most important limiting factors of deep machine learning (ML) model in drilling applications. Though a big size of historical data can be available, high-quality cleaned and labeled data is usually limited. In this case study, we show that with limited labeled data, physics-based data augmentation combined with unsupervised learning significantly improves both stability and accuracy in bit wear ML model. It provides a pathway to overcome labeled data shortage and field data quality limitations. Labeled bit wear data is usually limited because only the final bit dull state can be labeled using dull photos for the entire drilling distance. To overcome this difficulty, an encoder-decoder unsupervised ML framework based on Bi-directional LSTM architecture is first applied to the data of entire drilling distance to extract and maximize data learnings. Then, a physics-based wear estimator is implemented in the learned latent space to augment labeled wear dataset, guided by true wear labels and offset-well data. Weighting factor in loss function is applied to optimize augmented and true datasets in final supervised learning step. The proposed real-time bit wear model is built on a combination of physics-based data augmentation and unsupervised data learning method. The model is applied on multiple field bit runs. Results show that by implementing the unsupervised data learnings only, the prediction accuracy is improved by 30% compared to the baseline ML model. By combining physics-based augmentation, the accuracy is further improved by 10%. More importantly, adding physics-based data augmentation significantly reduces prediction variance and unphysical wear outputs, therefore improving prediction stability by more than 30%. It should be noted that the prediction stability of AI/ML model is crucial in real-time application and decision making. The results show physics-based data augmentation not only increases the size of label dataset and prevents model overfitting, but also applies physics-based guidance to the ML model effectively. It is learned weighting factor plays a crucial role in balancing loss contributions from true wear labels and physics-based labels. While low weighting factor of physics-based labels diminishes the augmented data, high weighting factor disrespects the true wear labels leading to a high prediction bias. Overall, the bit wear model study shows physic-based data augmentation combined with unsupervised data learning can effectively improve model accuracy, stability, and overcome labeled data shortage difficulty. The proposed paper shows a case study for the bit wear ML model using a combination of physics-based data augmentation and unsupervised data learning. While labeled data is one of the major challenges of ML models in many drilling applications, this study provides a pathway to improve both accuracy and stability of deep ML models with limited labeled data.

Empty Fruit Bunch (EFB) and Palm Mesocarp Fiber (PMF) are abundant by-products of palm-oil milling whose energetic valorisation is limited by high moisture and corrosive ash constituents (K, Cl). Using a computational model developed in Python and solved with the Livermore Solver for Ordinary Differential Equations with Automatic method switching algorithm, this study presents a moisture-free, mass- and energy-balanced kinetic framework that predicts the time-resolved combustion behavior of both biomasses, thereby strengthening the reproducibility and transparency of the modeling framework. The kinetic model tracks the consumption of elemental species and formation of combustion products, calibrated with data from the NIST Chemical Kinetics Database. The model accurately reproduces the low-heating-value energy releases reported in the literature – 147.11 MJ for EFB and 158.27 MJ for PMF – while additionally resolving transient species profiles, heat-release rates and combustion-power curves. Simulations reveal that EFB attains its maximum heat release at an Air to Fuel Ratio ≈ 13 % lower than PMF, yet still delivers greater boiler-usable enthalpy after accounting for moisture-free energy balance. Our results demonstrate that rigorous physicochemical characterisation combined with detailed chemical kinetics provides a reliable, transferable toolset for designing next-generation biomass boilers and unlocking the energy potential of agro-industrial residues such as EFB.

Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows6 6 Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). .

Recent results from experiments and modeling by the authors are reviewed for the ignition of acetylene, ethylene, and ethane in oxygen/argon mixtures at temperatures between 1000 and 2300 K and pressures near 1 atm. The ignition measurements were obtained behind reflected shock waves using emission from electronically excited OH and CH radicals to monitor the reaction progress. While many discrepancies exist amongst previous studies for these lower-order hydrocarbons, the accuracy afforded by the present experiments provides conclusive evidence verifying the trends seen in certain studies from the literature. Several modern, detailed chemical kinetics mechanisms were compared to the new results with some models showing quite good agreement with both ignition delay times and species profiles, particularly for stoichiometric mixtures. However, improvement is still required to match the entire range of fuel concentrations, temperatures, and mixture ratios, particularly for fuel-rich mixtures.

Couplings connect the spinning shafts of driving and driven machines in the industry. A coupling guard encloses the coupling to protect personnel from the high-speed rotating coupling. The American Petroleum Institute API publishes standards that restrict the overheating of the coupling guards due to windage caused by the spinning shaft. Based on the most recent version of API 671, the peak temperature for the coupling guard should not exceed 60 °C. This paper proposes a machine learning (ML) model and an empirical formula to predict the maximum guard temperature and power loss. The ML models use a database obtained from simulated computational fluid dynamics (CFD) cases for different coupling guards under various conditions. Also, the paper provides validation for the CFD models with experimental tests for different cases. The proposed ML model uses eight different input parameters to predict temperature and power loss. The model shows an accurate prediction for a varied number of CFD cases. The performance of the generated model has been verified with the experimental results. Also, an empirical formula has been created using the same database from CFD results. The results show that the ML model has better prediction accuracy than the empirical formula for predicting peak temperature and power loss for all cases.