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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2021

Airborne hyperspectral imaging of nitrogen deficiency on crop traits and yield of maize by machine learning and radiative transfer modeling

Nitrogen is an essential nutrient that directly affects plant photosynthesis, crop yield, and biomass production for bioenergy crops, but excessive application of nitrogen fertilizers can cause environmental degradation. To achieve sustainable nitrogen fertilizer management for precision agriculture, there is an urgent need for nondestructive and high spatial resolution monitoring of crop nitrogen and its allocation to photosynthetic proteins as that changes over time. Here, we used visible to shortwave infrared (400–2400 nm) airborne hyperspectral imaging with high spatial (0.5 m) and spectral (3–5 nm) resolutions to accurately estimate critical crop traits, i.e., nitrogen, chlorophyll, and photosynthetic capacity (CO 2 -saturated photosynthesis rate, V max,27 ), at leaf and canopy scales, and to assess nitrogen deficiency on crop yield. We conducted three airborne campaigns over a maize (Zea mays L.) field during the growing season of 2019. Physically based soil-canopy Radiative Transfer Modeling (RTM) and data-driven approaches i.e. Partial-Least Squares Regression (PLSR) were used to retrieve crop traits from hyperspectral reflectance, with ground truth of leaf nitrogen, chlorophyll, V max,27 , Leaf Area Index (LAI), and harvested grain yield. To improve computational efficiency of RTMs, Random Forest (RF) was used to mimic RTM simulations to generate machine learning surrogate models RTM-RF. The results show that prior knowledge of soil background and leaf angle distribution can significantly reduce the ill-posed RTM retrieval. RTM-RF achieved a high accuracy to predict leaf chlorophyll content (R 2 = 0.73) and LAI (R 2 = 0.75). Meanwhile, PLSR exhibited better accuracy to predict leaf chlorophyll content (R 2 = 0.79), nitrogen concentration (R 2 = 0.83), nitrogen content (R 2 = 0.77), and V max,27 (R 2 = 0.69) but required measured traits for model training. We also found that canopy structure signals can enhance the use of spectral data to predict nitrogen related photosynthetic traits, as combining RTM-RF LAI and PLSR leaf traits well predicted canopy-level traits (leaf traits × LAI) including canopy chlorophyll (R 2 = 0.80), nitrogen (R 2 = 0.85) and V max,27 (R 2 = 0.82). Compared to leaf traits, we further found that canopy-level photosynthetic traits, particularly canopy V max,27 , have higher correlation with maize grain yield. This study highlights the potential for synergistic use of process-based and data-driven approaches of hyperspectral imaging to quantify crop traits that facilitate precision agricultural management to secure food and bioenergy production.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Mean field model parameterization to recover coverage-dependent kinetics

Lateral interactions between adsorbates introduce coverage dependence into adsorption energies and activation barriers of surface reactions. Lattice-based kinetic Monte Carlo (kMC) simulations can capture these interactions quantitatively but are laborious to parameterize and solve. Mean field models are more tractable, but protocols to construct and parameterize them are unclear. Here we explore the ability of a coverage-aware mean-field model to map to a lattice-kMC model of a generic two-step reaction network, including quasi-equilibrated adsorption and rate-limiting dissociation steps. We derive expressions for mean-field and coverage-dependent adsorption energies and dissociation barriers and parameterize against lattice-kMC predictions. We show that the parameterized mean-field rates correlate with ground truth lattice-kMC results across a wide range of reaction conditions and identify regions where the mean field fails. The mean field model similarly captures kMC-derived rate-order, Arrhenius and Sabatier plots at a greatly reduced computational cost. Further, the results provide guidance for parameterizing mean-field models, benchmarked against explicit lattice-based approaches for incorporating the influence of coverage effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Accelerating discrete dislocation dynamics simulations with graph neural networks

Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the computational cost of DDD simulations remains a bottleneck that limits its range of applicability. Here, we introduce a new DDD-GNN framework in which the expensive time-integration of dislocation motion is entirely substituted by a graph neural network (GNN) model trained on DDD trajectories. As a first application, we demonstrate the feasibility and potential of our method on a simple yet relevant model of a dislocation line gliding through an array of obstacles. We show that the DDD-GNN model is stable and reproduces very well unseen ground-truth DDD simulation responses for a range of straining rates and obstacle densities, without the need to explicitly compute nodal forces or dislocation mobilities during time-integration. Our approach opens new promising avenues to accelerate DDD simulations and to incorporate more complex dislocation motion behaviors.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Evaluation of Subseasonal-to-Seasonal (S2S) precipitation forecast from the North American Multi-Model ensemble phase II (NMME-2) over the contiguous U.S.

The second phase of the North America Multi-Model Ensemble (NMME-2) provides globally available Subseasonal-to-Seasonal (S2S) precipitation forecasts with a daily resolution. The S2S precipitation forecasts are getting increasing attention for their potentials in providing hydrometeorological forcing information for water resources planning at an extended range. However, the forecast skills of many existing S2S forecast products will significantly decrease when the lead time increases, hindering their applicability for watershed-scale hydrologic modeling. Therefore, forecast validation and large-scale evaluation are of great importance for water resources planning and hydrological applications. In this study, we comprehensively evaluate the S2S precipitation forecasts from the NMME-2 dataset over the contiguous United States (CONUS) and during the study period from 1982 to 2011. Three aspects of precipitation forecast capabilities are compared and analyzed: bias, skill scores, and the ability to predict extreme precipitation events. The Parameter-elevation Regressions on Independent Slopes Model (PRISM) is used as ground truth reference. Differs from other regional forecast validation study, we further examined and analyzed the dependences of NMME-2 precipitation forecast skills according to different seasonality, geographical locations, and lead times. Results show that the forecast biases are not sensitive to lead times but are seasonally dependent of all NMME-2 models. Overestimations are found in the Western U.S. in cooler seasons while underestimations are observed in the central regions of the U.S. in warmer seasons. The forecast skill of all individual NMME-2 models generally decreases as increases of lead times. The simple model averaging (SMA) of five NMME-2 models demonstrates a higher forecast skill than any individual NMME-2 models. Spatially, the highest forecast skill scores are observed at coastal areas in the Western U.S. with an one-week lead time. As compared to the historical resampled forecasts, NMME-2 also shows better performance in predicting extreme precipitation events above 99% percentiles and below 1% percentiles with higher probability of detections and lower false alarm ratios. Finally, the obtained results suggest the great potentials of NMME-2 precipitation forecasts in assisting ensemble hydrologic forecasts at the S2S scale over the CONUS.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A deep learning-based workflow for fast prediction of 3D state variables in geological carbon storage: A dimension reduction approach

Deep learning (DL) models are extensively used as surrogate models for high-fidelity simulations of multiphase fluid flow in porous media at large scales, enabling fast forecasts of the spatial–temporal evolution of three-dimensional (3D) state variables in geological carbon storage (GCS). However, training these models in high-dimensional space remains computationally demanding and prone to overfitting because of limited training data. This paper presents a novel workflow to address these challenges by integrating dimension reduction (DR) methods. Here, the proposed workflow employed pre-trained DR models to extract the latent variables of geological models and state variables and utilized the multi-layer perceptron (MLP) for constructing mapping functions between the input and output variables in latent spaces. Subsequently, the pre-trained reconstruction models converted the MLP-predicted latent state variables to their original high-dimensional form. Furthermore, we proposed a novel strategy for the DR and reconstruction of 3D saturation fields to account for the unique data characteristics of sparsity, nonuniformity, and discontinuity. The proposed strategy applied PCA and inverse PCA for 2D average saturation fields and developed a DL-based 3D reconstruction model, leveraging three 2D average saturation fields as input to produce a 3D saturation field as output. The pre-training of DR and reconstruction models and training of MLP models were conducted on 84 Gulf of Mexico (GoM) simulations and evaluated on 12 testing simulations. Each simulation contained 720 monthly time steps, with the first 360 months as the injection period and the rest as the post-injection period. The proposed workflow, incorporating DR and DL models, accurately predicts the normalized 3D pressure fields, achieving mean square error (MSE) of 2.92 × 10 -7 compared to the ground truth obtained from a full-physics simulator. Furthermore, the proposed strategy outperformed PCA and convolutional autoencoder (CAE) models on 3D saturation fields, resulting in minor workflow prediction errors with an MSE of 2.93 × 10 -5 . The results suggest the proposed workflow provides sufficient predictive fidelity across temporal and spatial scales, and enables a speedup of 160 times compared to the full-physics simulator, facilitating improved decision-making and risk assessment for large-scale GCS management in real-time scenarios.

3D reconstruction model↗

DOE OSTI2023

Explainable AI (XAI)-driven vibration sensing scheme for surface quality monitoring in a smart surface grinding process

Local Interpretable and Model-agnostic Explanation (LIME), an explainable artificial intelligence (XAI) approach is adapted to identify the globally important time-frequency bands for predicting average surface roughness (Ra) in a smart grinding process. The smart grinding setup consisted of a Supertech CNC precision surface grinding machine, instrumented with a Dytran piezoelectric accelerometer attached to the tailstock quill along the tangential direction (Y-axis). For every grinding pass, vibration signatures were captured, and the ground truth surface roughness values were recorded using a Mahr Marsurf M300C portable surface roughness profilometer. The roughness values ranged from 0.06 to 0.14 microns over the complete set of experiments. Time-frequency domain spectrogram frames were extracted for each of the vibration signals collected during the grinding process. Convolutional Neural Networks (CNNs) were modeled to predict the surface roughness based on these spectrogram frames and their image augmentations. The best CNN model was able to predict the roughness values with an overall R2-score of 0.95, training R2-score of 0.99, and testing R2-score of 0.81 with only 80 sets of vibration signals corresponding to 4 experiments with 20 trials each. Although the data size is not large enough to guarantee such performance metrics in real-world scenarios, one can extract statistically consistent explanations underlying the relationships these complex deep learning models capture. Further, the LIME methodology was implemented on the developed surface roughness CNN model to identify the important time-frequency bands (i.e., the superpixels of a spectrogram) influencing the predictions. Based on the identified important regions on the spectrogram frames, the corresponding frequency characteristics were determined that influence the surface roughness predictions. The important frequency range based on LIME results was approximately 11.7 to 19.1 kHz. The power of XAI was demonstrated by cutting down the sampling rate from 160 kHz to 30, 20, 10, and 5 kHz based on the important frequency range and considering Nyquist criteria. Separate CNN models were developed for these ranges by only extracting time-frequency contents below their corresponding Nyquist cut-offs. A proper data acquisition strategy is proposed by comparing the model performances to argue the selection of a sufficient sampling rate to capture the grinding process successfully and robustly.

42 ENGINEERING↗

DOE OSTI2023

Reprint of: Explainable AI (XAI)-driven vibration sensing scheme for surface quality monitoring in a smart surface grinding process

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Effect of threshold parameters on infrared segmentation methods for porosity detection in electron beam powder bed fusion

In-situ process monitoring has seen significant interest in additive manufacturing to address qualification and certification goals. This is especially prevalent in metal powder bed fusion processes such as electron beam powder bed fusion (PBF-EB), with layer-wise infrared imaging being commonly used to detect defects. Here, this work compares two different segmentation methods (static thresholding and statistical thresholding) used for detecting porosity from in-situ infrared imaging data for PBF-EB. Samples were manufactured at a variety of focus offset values to induce porosity. Then, the segmented infrared images were compared to ex-situ X-ray computed tomography scans, which served as a ground-truth reference for objective evaluation. Through this analysis framework, the influential parameters, static threshold and N-value (number of standard deviations above the mean pixel value), respectively, for both image segmentation methods were analyzed and compared for their effects on porosity detection. With optimal parameter settings, the two methods had similar porosity detection performance, but the statistical method performed better under a larger variety of parameter settings.

Infrared imaging↗

DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Generating synthetic signaling networks for in silico modeling studies

Predictive models of signaling pathways have proven to be difficult to develop. Reasons include the uncertainty in the number of species, the complexity in species’ interactions, and the sparseness and uncertainty in experimental data. Traditional approaches to developing mechanistic models rely on collecting experimental data and fitting a single model to that data. This approach works for simple systems but has proven unreliable for complex systems such as biological signaling networks. For example, uncertainty and sparseness of the data often result in overfitted models that have little predictive value beyond recapitulating the experimental data itself. Thus, there is a need to develop new approaches to create predictive mechanistic models of complex systems. However, to determine the effectiveness of any new algorithm, a baseline model is needed to test its performance. To meet this need, we developed a method for generating artificial synthetic networks that are reasonably realistic and thus can be treated as ground truth models. These synthetic models can then be used to generate synthetic data for developing and testing algorithms designed to recover the underlying network topology and associated parameters. Here, we describe a simple approach for generating synthetic signaling networks that can be used for this purpose.

42 ENGINEERING↗

DOE OSTI2021

Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization

Here, we present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in L 2 -norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler–Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the experimental stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Uncertainty guided online ensemble for non-stationary data streams in fusion science

Machine Learning (ML) is poised to play a pivotal role in the development and operation of next-generation fusion devices. Fusion data shows non-stationary behavior with distribution drifts, resulted by both experimental evolution and machine wear-and-tear. ML models assume stationary distribution and fail to maintain performance when encountered with such non-stationary data streams. Online learning techniques have been leveraged in other domains, however it has been largely unexplored for fusion applications. In this paper, we investigate online learning for continuous adaptation to drifting data streams in the prediction of Toroidal Field (TF) coils deflection at the DIII-D fusion facility. We further address the short-term performance degradation inherent to standard online learning, which arises because ground truth is unavailable at prediction time. To mitigate this issue, we propose an uncertainty-guided online ensemble framework. The method leverages the Deep Gaussian Process Approximation (DGPA) for calibrated uncertainty estimation and uses these uncertainty measures to guide a meta-algorithm that aggregates predictions from learners trained over different historical horizons. Our results show that online learning reduces prediction error by 80% compared to a static model. The online ensemble and the proposed uncertainty-guided ensemble further reduce error by approximately 6%, and 10% respectively, relative to standard single-model online learning, while also providing calibrated uncertainty estimates to support operational decision-making.

AI↗

DOE OSTI2026

Segmentation method comparison for residual fiber length measurement across tiled microscopy images

Fiber length distribution (FLD), in part, governs mechanical properties in discontinuous fiber composites, yet manual measurement methods limit the high-throughput characterization needed for materials design optimization. This study compares deep learning segmentation approaches for automated FLD measurement in large-field microscopy, evaluating how method choice affects the microstructural descriptors used in structure-property-processing relationships. A critical challenge is that high-resolution microscopy images (10,000×10,000 pixels) must be tiled for deep learning analysis, fragmenting fibers at boundaries. We demonstrate that segmentation method proves crucial for measurement accuracy. For example, instance segmentation with Slicing Aided Hyper Inference (SAHI) preserves individual fiber integrity across tiles while semantic segmentation prioritizes speed. Comparing against manual measurement of extracted carbon fibers, YOLOv11-SAHI matched manual ground truth (238 μm weighted mean) with 40x speedup (4.5 vs 167 minutes per image). U-Net provides rapid quantification although it is at the cost of reduced accuracy due only reliably measuring stand-alone fibers. Our comparative analysis reveals that instance segmentation with SAHI better preserves length measurements while semantic segmentation prioritizes speed, providing empirical guidance for method selection. The characterization provides essential inputs for mechanical property prediction models and inverse design workflows, accelerating composite materials development cycles.

Additive manufacturing↗

DOE OSTI2023

Automated integration gate selection for Gaussian mixture model pulse shape discrimination

Pulse shapes differ between neutron and gamma particles when measured with detector devices employing pulse shape discriminating (PSD) scintillators. Digitized waveforms can be used in detection systems to perform pulse shape discrimination for this application. Prior Gaussian Mixture Model (GMM) methods require access to the pulse full-waveform. Reducing the waveform to a smaller set of combined samples reduces computational cost while affecting PSD performance. In this work, we develop a method for selecting the best performing combination of integration gates, or contiguous summed segments of the digitized pulse for PSD. The method uses a discrimination score based on the GMM PSD approach. Furthermore, the final selection is performed using Bayesian Optimization. PSD detection results are compared with varying numbers of selected gates on time-of-flight (TOF) data. This method can be used to fully automate the selection of gates in an unsupervised (without ground truth labels) setting.

42 ENGINEERING↗

DOE OSTI2023

Demonstration of sub-micron UCN position resolution using room-temperature CMOS sensor

High spatial resolution of ultracold neutron (UCN) measurement is of growing interest to UCN experiments such as UCN spectrometers, UCN polarimeters, quantum physics of UCNs, and quantum gravity. Here we utilize physics informed deep learning to enhance the experimental position resolution and to demonstrate sub-micron spatial resolutions for UCN position measurements obtained using a room-temperature CMOS sensor, extending our previous work that demonstrated a position uncertainty of 1.5 microns. We explore the use of the open-source software Allpix Squared to generate experiment-like synthetic hit images with ground-truth position labels. We use physics-informed deep learning by training a fully connected neural network (FCNN) to learn a mapping from input hit images to output hit position. The automated analysis for sub-micron position resolution in UCN detection combined with the fast data rates of current and next generation UCN sources will enable improved precision for future UCN research and applications.

10B nanometer thin film↗

DOE OSTI2025

Machine learning for reactor power monitoring with limited labeled data

Real-time reactor power monitoring is critical for a variety of nuclear applications, spanning safety, security, operations, and maintenance. While machine learning methods have shown promise in monitoring reactor power levels, there is limited research on their efficacy in label-starved environments. The goal of this work is to assess the feasibility of classifying nuclear reactor power level using multisource data in scenarios with limited labels. Data were collected using low-resolution multisensors at four nuclear reactor facilities: two large research reactors and two TRIGA reactors. Within each pair, one reactor dataset served as the source and the other as the target in a transfer learning paradigm. Twenty-three supervised models were trained on labeled sequences of magnetic field and acceleration data from each of the target sites. Self-learning and transfer learning methods were applied to the top performing models to assess their classification performance with increasing amounts of labeled data. While reactor power level classification was achieved with a Matthews Correlation Coefficient of up to 0.739 ± 0.003 and 0.622 ± 0.009 with only 400 sequences per power state for the large research reactor and TRIGA target sites, respectively, self-learning and transfer learning leveraging source site data did not improve target classification performance. These findings suggest that alternative methods, such as higher sensitivity sensors, digital twins, or the use of physics-informed models, are required to enable high-performance classification in machine learning approaches to reactor monitoring with a dearth of target ground truth.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Deep-learning-based workflow for boundary and small target segmentation in digital rock images using UNet++ and IK-EBM

We report three-dimensional (3D) X-ray micro-computed tomography (μCT) has been widely used in petroleum engineering because it can provide detailed pore structural information for a reservoir rock, which can be imported into a pore-scale numerical model to simulate the transport and distribution of multiple fluids in the pore space. The partial volume blurring (PVB) problem is a major challenge in segmenting raw μCT images of rock samples, which impacts boundaries and small targets near the resolution limit. We developed a deep-learning (DL)-based workflow for accurate and fast partial volume segmentation. The DL model's performance depends primarily on the training data quality and model architecture. This study employed the entropy-based-masking indicator kriging (IK-EBM) to segment 3D Berea sandstone images as training datasets. The comparison between IK-EBM and manual segmentation using a 3D synthetic sphere pack, which had a known ground truth, showed that IK-EBM had higher accuracy on partial volume segmentation. We then trained and tested the UNet++ model, a state-of-the-art supervised encoder-decoder model, for binary (i.e., void and solid) and four-class segmentation. We compared the UNet++ with the commonly used U-Net and wide U-Net models and showed that the UNet++ had the best performance in terms of pixel-wise and physics-based evaluation metrics. Specifically, boundary-scaled accuracy demonstrated that the UNet++ architecture outperformed the regular U-Net architecture in the segmentation of pixels near boundaries and small targets, which were subjected to the PVB effect. Feature map visualization illustrated that the UNet++ bridged the semantic gaps between the feature maps extracted at different depths of the network, thereby enabling faster convergence and more accurate extraction of fine-scale features. The developed workflow significantly enhances the performance of supervised encoder-decoder models in partial volume segmentation, which has extensive applications in fundamental studies of subsurface energy, water, and environmental systems.

02 PETROLEUM↗

DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗