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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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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Data Release Report for the Source Physics Experiment Phase II: Dry Alluvium Geology Experiments (DAG-1 through DAG-4), Nevada National Security Site

The Dry Alluvium Geology (DAG) project was Phase II of the Source Physics Experiment and consisted of a series of four chemical explosive tests conducted in the same source hole on the Nevada National Security Site. This hole is located at 37.1146°N and -116.0693°W, with a surface elevation of 1,285.2 meters (m) (4,216.5 feet [ft]) above sea level. The first test (DAG-1) was conducted on July 20, 2018, at 16:51:52.67838 Coordinated Universal Time (UTC). The explosive source for DAG-1 was nitromethane initiated by a small plastic-bonded explosive (PBX) charge, detonated at the depth of 385.0 m (1,263.2 ft) below ground surface. DAG-1 had a trinitrotoluene (TNT) equivalent yield of 0.908 metric tons (2,002 pounds [lbs]). DAG-2 was conducted on December 19, 2018, at 18:45:56.92115 UTC. This test was the largest in the series, with a TNT equivalent yield of 50.997 metric tons (112,429 lbs). The explosive source for DAG-2 was nitromethane initiated by a small PBX charge, detonated at the depth of 299.8 m (983.6 ft) below ground surface. DAG-3 was conducted on April 27, 2019, at 15:49:01.84183 UTC. The explosive source for this test was nitromethane initiated by a small PBX charge, detonated at the depth of 149.9 m (492.0 ft) below ground surface. DAG-3 had a TNT equivalent yield of 0.908 metric tons (2,002 lbs). The final DAG test (DAG-4) was conducted on June 22, 2019, at 21:06:19.87632 UTC. The explosive source for DAG-4 was nitromethane initiated by a small PBX charge, detonated at the depth of 51.6 m (169.3 ft) below ground surface. DAG-4 had a TNT equivalent yield of 10.357 metric tons (22,833 lbs). The four tests were recorded by an extensive set of instrumentation that included sensors both at near-field (less than 200 m) and far-field (200 m or greater) distances. The near-field instruments consisted of three-component (3C) accelerometers installed at various depths ranging from 51.6 to 385 m (169.3 to 1,263.1 ft) below ground surface in boreholes positioned around the source hole, and arrays of single-component and 3C accelerometers on the surface. The far-field network comprised a variety of seismic and acoustic sensors, including short-period geophones, broadband seismometers, and 3C accelerometers at distances of 200 m to 400 kilometers. In addition, the DAG-2, DAG-3, and DAG-4 explosions were recorded by a temporary array of 496 geophones arranged in a densely spaced grid pattern known as “Large N.” This report coincides with the release of these data for analysts and organizations that are not participants in this program. This report describes the four DAG tests and the various types of near-field, far-field, and other data that are available. Assembled data sets are accessible through: Incorporated Research Institutions for Seismology, Data Management Center 1408 NE 45th Street, Suite 201, Seattle, Washington 98105 USA. www.iris.washington.edu

58 GEOSCIENCES↗
DOE OSTI2022

Transfer learning driven design optimization for inertial confinement fusion

Transfer learning is a promising approach to create predictive models that incorporate simulation and experimental data into a common framework. In this technique, a neural network is first trained on a large database of simulations and then partially retrained on sparse sets of experimental data to adjust predictions to be more consistent with reality. Previously, this technique has been used to create predictive models of Omega [Humbird et al., IEEE Trans. Plasma Sci. 48, 61–70 (2019)] and NIF [Humbird et al., Phys. Plasmas 28, 042709 (2021); Kustowski et al., Mach. Learn. 3, 015035 (2022)] inertial confinement fusion (ICF) experiments that are more accurate than simulations alone. Here, in this work, we conduct a transfer learning driven hypothetical ICF campaign in which the goal is to maximize experimental neutron yield via Bayesian optimization. The transfer learning model achieves yields within 5% of the maximum achievable yield in a modest-sized design space in fewer than 20 experiments. Furthermore, we demonstrate that this method is more efficient at optimizing designs than traditional model calibration techniques commonly employed in ICF design. Such an approach to ICF design could enable robust optimization of experimental performance under uncertainty.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Neural network approaches for parameterized optimal control

Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage to enable rapid decision-making and be able to react to changes in the parameter in the online stage. To tackle the curse of dimensionality arising when the state and/or parameter are high-dimensional, we represent the policy using neural networks. We compare two training paradigms: First, our model-based approach leverages the dynamics and definition of the objective function to learn the value function of the parameterized optimal control problem and obtain the policy using a feedback form. Second, we use actor-critic reinforcement learning to approximate the policy in a data-driven way. Using an example involving a two-dimensional convection-diffusion equation, which features high-dimensional state and parameter spaces, we investigate the accuracy and efficiency of both training paradigms. While both paradigms lead to a reasonable approximation of the policy, the model-based approach is more accurate and considerably reduces the number of PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Crystal structures of inhibitor complexes of M‐PMV protease with visible flap loops

Abstract Mason‐Pfizer monkey virus protease (PR) was crystallized in complex with two pepstatin‐based inhibitors in P 1 space group. In both crystal structures, the extended flap loops that lock the inhibitor/substrate over the active site, are visible in the electron density either completely or with only small gaps, providing the first observation of the conformation of the flap loops in dimeric complex form of this retropepsin. The H‐bond network in the active site (with D26N mutation) differs from that reported for the P 2 1 crystal structures and is similar to a rarely occurring system in HIV‐1 PR.

Wosicki, Stanislaw↗
DOE OSTI2021

A two-equation soot-in-flamelet modeling approach applied under Spray A conditions

Soot production (including formation and oxidation) is studied in the transient, high-pressure and turbulent n-dodecane Spray A flames from the Engine Combustion Network (ECN) using computational fluid dynamics (CFD) simulations. A two-equation soot-in-flamelet modeling approach is applied within the framework of the Unsteady Flamelet Progress Variable (UFPV) model and results are validated against experimental data. Equations for soot mass fraction and soot number density derived in the mixture fraction space are solved in the context of detailed flamelet calculations. Source terms for the different steps in the soot chemistry are tabulated and incorporated in the flamelet manifold. For the reference condition, the modeling approach based on the tabulated flamelet manifold reduces the computational cost of a CFD calculation by approximately 40 times compared to a non-tabulated well-mixed (WM) modeling approach. The soot-in-flamelet approach is then extended to study the effect of ambient oxygen concentration, ambient mixture composition and ambient temperature on soot production. Results show that the modeling approach is able to capture the experimental trends for the soot volume fraction (SVF) with good quantitative agreement, especially in the soot ramp-up region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Evaluating the state-of-the-art in remote volcanic eruption characterization Part II: Ulawun volcano, Papua New Guinea

Retrospective eruption characterization is valuable for advancing our understanding of volcanic systems and evaluating our observational capabilities, especially with remote technologies (defined here as a space-borne system or non-local, ground-based instrumentation which include regional and remote infrasound sensors). In June 2019, the open-system Ulawun volcano, Papua New Guinea, produced a VEI 4 eruption. We combined data from satellites (including Sentinel-2, TROPOMI, MODIS, Himawari-8), the International Monitoring System infrasound network, and GLD360 globally detected lightning with information from the local authorities and social media to characterize the pre-, syn- and post-eruptive behaviour. The Rabaul Volcano Observatory recorded ~24 h of seismicity and detected SO 2 emissions ~16 h before the visually-documented start of the Plinian phase on 26 June at 04:20 UTC. Infrasound and SO2 detections suggest the eruption started during the night on 24 June 2019 at 10:39 UTC ~38 h before ash detections with a gas-dominated jetting phase. Local reports and infrasound detections show that the second phase of the eruption started on 25 June 19:28 UTC with ~6 h of jetting. The first detected lightning occurred on 26 June 00:14 UTC, and ash emissions were first detected by Himawari-8 at 01:00 UTC. Post-eruptive satellite imagery indicates new flow deposits to the south and north of the edifice and ash fall to the west and southwest. In particular, regional infrasound data provided novel insight into eruption onset and syn-eruptive changes in intensity. We conclude that, while remote observations are sufficient for detection and tracking of syn-eruptive changes, key challenges in data latency, acquisition, and synthesis must be addressed to improve future near-real-time characterization of eruptions at minimally-monitored or unmonitored volcanoes.

58 GEOSCIENCES↗
DOE OSTI2020

Interfacial Electromechanics Predicts Phase Behavior of 2D Hybrid Halide Perovskites

Quasi-two-dimensional (2D) mixed-cation hybrid halide perovskites (A' 2 A N–1 M N X 3N+1 ; A' = large organic molecule with cationic group, A = [Cs + , CH 3 NH 3 + , HC(NH 2 ) 2 + ], M = [Pb, Sn, Ge], X = [I – , Br – , Cl – ]) have rapidly emerged as candidates to improve the structural stability and device lifetime of 3D perovskite semiconductor devices under operating conditions. The addition of the large A' cation to the traditional AMX 3 structure introduces several synthetic degrees of freedom and breaks M–X bonds, giving rise to peculiar critical phase behavior in the phase space of these complex materials. In this work, we propose a thermodynamic model parametrized by first-principles calculations to generate the phase diagram of 2D and quasi-2D perovskites (q-2DPKs) based on the mechanics and electrostatics of the interface between the A' cations and the metal halide octahedral network. Focusing on the most commonly studied methylammonium lead iodide system where A' is n-butylammonium (BA; CH 3 (CH 2 ) 3 NH 3 + ), we find that the apparent difficulty in synthesizing phase-pure samples with a stoichiometric index N > 5 can be attributed to the energetic competition between repulsion of opposing interfacial dipole layers and mechanical relaxation induced by interfacial stress. Our model shows quantitative agreement with experimental observations of the maximum phase-pure stoichiometric index (N crit ) and explains the nonmonotonic evolution of the lattice parameters with increasing stoichiometric index (N). This model is generalizable to the entire family of q-2DPKs and can guide the design of photovoltaic and optical materials that combine the structural stability of the q-2DPKs while retaining the charge carrier properties of their 3D counterparts.

14 SOLAR ENERGY↗
DOE OSTI2025

SA-GAT-SR: self-adaptable graph attention networks with symbolic regression for high-fidelity material property prediction

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput prediction of material properties, offering a compelling enhancement and alternative to traditional first-principles calculations. While the community has predominantly focused on developing increasingly complex and universal models to enhance predictive accuracy, such approaches often lack physical interpretability and insights into materials behavior. Here, we introduce a novel computational paradigm—Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR)—that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression. Our framework employs a self-adaptable encoding algorithm that automatically identifies and adjust attention weights so as to screen critical features from an expansive 180-dimensional feature space while maintaining O(n) computational scaling. The integrated SR module subsequently distills these features into compact analytical expressions that explicitly reveal quantum-mechanically meaningful relationships, achieving 23 × acceleration compared to conventional SR implementations that heavily rely on first-principle calculations-derived features as input. This work suggests a new framework in computational materials science, bridging the gap between predictive accuracy and physical interpretability, offering valuable physical insights into material behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Predictive machine learning approaches for the microstructural behavior of multiphase zirconium alloys

Abstract Zirconium alloys are widely used in harsh environments characterized by high temperatures, corrosivity, and radiation exposure. These alloys, which have a hexagonal closed packed (h.c.p.) structure thermo-mechanically degrade, when exposed to severe operating environments due to hydride formation. These hydrides have a different crystalline structure, than the matrix, which results in a multiphase alloy. To accurately model these materials at the relevant physical scale, it is necessary to fully characterize them based on a microstructural fingerprint, which is defined here as a combination of features that include hydride geometry, parent and hydride texture and crystalline structure of these multiphase alloys. Hence, this investigation will develop a reduced order modeling approach, where this microstructural fingerprint is used to predict critical fracture stress levels that are physically consistent with microstructural deformation and fracture modes. Machine Learning (ML) methodologies based on Gaussian Process Regression, random forests, and multilayer perceptrons (MLP) were used to predict material fracture critical stress states. MLPs, or neural networks, had the highest accuracy on held-out test sets across three predetermined strain levels of interest. Hydride orientation, grain orientation or texture, and hydride volume fraction had the greatest effect on critical fracture stress levels and had partial dependencies that were highly significant, and in comparison hydride length and hydride spacing have less effects on fracture stresses. Furthermore, these models were also used accurately predicted material response to nominal applied strains as a function of the microstructural fingerprint.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Advancing density functional tight-binding method for large organic molecules through equivariant neural networks

Semi-empirical quantum-mechanical (QM) methods have become valuable tools for studying complex (bio)molecular systems due to their balance between computational efficiency and accuracy. A key aspect of these methods is their parameterization, which not only governs the reliability of the results but also provides an opportunity to enhance their overall performance. In our previous work [J. Phys. Chem. Lett., 2021, 11, 16], we advanced the third-order semi-empirical density functional tight-binding (DFTB3) method for computing multiple properties of small molecules by developing the machine learning (ML) potential NN rep to bridge the gap between DFTB3 electronic components and those of the hybrid DFT-PBE0 functional. To overcome the limitations of NN rep , we introduce the EquiDTB framework, which leverages physics-inspired equivariant neural networks (NN) to parameterize scalable and transferable many-body Δ TB potentials, replacing the standard pairwise DFTB repulsive potential. This advancement extends the applicability of our ML-corrected DFTB approach to larger molecules and non-covalent systems (including only C, N, O, and H atoms), going beyond the chemical space represented in the training QM datasets. The enhanced performance of EquiDTB over the standard TB methods is demonstrated by the accurate computation of the atomic forces of S66x8 molecular dimers, as well as their interaction energies. Moreover, EquiDTB can be effectively employed to explore the potential energy surfaces of large and flexible drug-like molecules—for example, to determine the minimum energy path between isomers, analyze structural transitions during dynamical simulations, compute vibrational modes, and investigate energetic rankings. The performance for single molecules slightly decreases when the DFTB electronic energy is reduced to first-order but remains superior to standard TB methods. Our work thus demonstrates that an optimal integration of an equivariant NN with QM datasets can advance the DFTB method while maintaining high efficiency, paving the way for reliable (bio)molecular simulations.

Medrano Sandonas, Leonardo [Technische Universität↗
DOE OSTI2022

Primordial non-Gaussianity from the completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey II: measurements in Fourier space with optimal weights

ABSTRACT We present measurements of the local primordial non-Gaussianity parameter $f_{\mathrm{NL}}^\mathrm{local} $from the clustering of 343 708 quasars with redshifts 0.8 < z < 2.2 distributed over 4808 deg2 from the final data release (DR16) of the extended Baryon Acoustic Oscillation Spectroscopic Survey (eBOSS), the largest volume spectroscopic survey up to date. Our analysis is performed in Fourier space, using the power spectrum monopole at very large scales to constrain the scale-dependent halo bias. We demonstrate the robustness of our analysis pipeline with EZ-mock catalogues that simulate the eBOSS DR16 target selection. We carefully assess the impact of systematics on our measurement, exploiting a novel neural network scheme for cleaning the DR16 sample as well as test multiple contamination removal methods. We estimate the bias due to the overcorrection of the systematic removal to be sub-dominant compared to the statistical uncertainty. We find fNL = −12 ± 21 (68 per cent confidence) for the main clustering sample including quasars with redshifts between 0.8 and 2.2, after applying redshift weighting techniques, designed for non-Gaussianity measurement from large scales structure, to optimize our analysis, which improve our results by 37 per cent.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Transversity PDFs of the proton from lattice QCD with physical quark masses

We present a lattice QCD calculation of the transversity isovector- and isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we determine the isovector and isoscalar tensor charges for the proton. In both calculations, the disconnected contributions to the isoscalar matrix elements have been ignored. The calculations are performed using a single ensemble of N f = 2 + 1 highly improved staggered quarks simulated with physical-mass quarks and a lattice spacing of a = 0.076 fm . The Wilson-clover action, with physical quark masses and smeared gauge links obtained from one iteration of hypercubic smearing, is used in the valence sector. Using the NLO operator product expansion, we extract the lowest four to six Mellin moments and the PDFs via a neural network from the matrix elements in the pseudo-PDF approach. In addition, we calculate the PDFs in the quasi-PDF approach with hybrid-scheme renormalization and the recently developed leading-renormalon resummation technique, at NLO with the resummation of leading small- x logarithms. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Assessing the Impact of Lightning NOx Emissions in CMAQ Using Lightning Flash Data from WWLLN over the Contiguous United States

Comparison of lightning flash data from the National Lightning Detection Network (NLDN) and from the World Wide Lightning Location Network (WWLLN) over the contiguous United States (CONUS) for the 2016–2018 period reveals temporally and spatially varying flash rates that would influence lightning NO x (LNO x ) production due to known detection efficiency differences especially during summer months over land (versus over ocean). However, the lightning flash density differences between the two networks show persistent seasonal patterns over geographical regions (e.g., land versus ocean). Since the NLDN data are considered to have higher accuracy (lightning detection with >95% efficiency), we developed scaling factors for the WWLLN flash data based on the ratios of WWLLN to NLDN flash data over time (months of year) and space. In this study, sensitivity simulations using the Community Multiscale Air Quality (CMAQ) model are performed utilizing the original data sets (both NLDN and WWLLN) and the scaled WWLLN flash data for LNO x production over the CONUS. The model performance of using the different lightning flash datasets for ambient O 3 and NO x mixing ratios that are directly impacted by LNO x emissions and the wet and dry deposition of oxidized nitrogen species that are indirectly impacted by LNO x emissions is assessed based on comparisons with ground-based observations, vertical profile measurements, and satellite products. During summer months, the original WWLLN data produced less LNO x emissions (due to its lower lightning detection efficiency) compared to the NLDN data, which resulted in less improvement in model performance than the simulation using NLDN data as compared to the simulation without any LNO x emissions. However, the scaled WWLLN data produced LNO x estimates and model performance comparable with the NLDN data, suggesting that scaled WWLLN may be used as a substitute for the NLDN data to provide LNO x estimates in air quality models when the NLDN data are not available (e.g., due to prohibitive cost or lack of spatial coverage).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Vacancy diffusion barrier spectrum and diffusion correlation in multicomponent alloys

Vacancy diffusion serves a crucial role in many important kinetic behaviors and properties of multicomponent alloys. Essential questions, however, persist regarding how chemical complexity affects diffusion and what unique characteristics, if any, set these alloys apart from traditional metals. Using neural network kinetics model, we study vacancy diffusion in NbMoTa alloy across a broad temperature range (2600 to 800 K). Unlike pure metals, the two key diffusion parameters—diffusion correlation factor f and activation energy ΔG m —are not constant in alloys, but instead substantially decrease with decreasing temperature. This temperature dependence arises from a reduced number of active vacancy jump pathways at lower temperatures, leading to more correlated diffusion. Upon examining vacancy diffusion throughout the entire compositional space of the Nb-Mo-Ta system, we discover that the slowest vacancy diffusion surprisingly occurs in the non-equimolar region, rather than the equimolar concentration where the configurational entropy is highest. The diffusion barrier spectrum, characterizing the diffusion energy landscape, is an intrinsic material characteristic, which controls both f and ΔG m and, thereby, the diffusivity. Lastly, we find that the vacancy diffusion rate drops noticeably in the presence of local chemical order in the NbMoTa system, particularly for MoTa alloys with long-range B2 order.

Defects↗
DOE OSTI2021

Short-term nodal load forecasting based on machine learning techniques

This paper introduces an advanced Short-term Nodal Load Forecasting (STNLF) method that forecasts nodal load profiles for the next day in power systems, based on the combined use of three machine learning techniques. Least Absolute Shrinkage and Selection Operator (LASSO) is employed to reduce the number of features for a single nodal load forecasting. Principal Component Analysis (PCA) is used to capture the features of historical loads in low-dimensional space compared to the original high-dimensional load space where features are barely possible to depict. Additionally, Bayesian Ridge Regression (BRR) is utilized to decide the parameters of the prediction model from a statistics perspective. Tests based on modified PJM load data demonstrate the effectiveness of the proposed STNLF method compared to the state-of-the-art General Regression Neural Network (GRNN) method. Moreover, the reliability of the day-ahead Unit Commitment (UC) solution is shown to have been improved, based on the forecasted load data using the proposed STNLF method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simultaneous energy and mass calibration of large-radius jets with the ATLAS detector using a deep neural network

The energy and mass measurements of jets are crucial tasks for the Large Hadron Collider experiments. This paper presents a new calibration method to simultaneously calibrate these quantities for large-radius jets measured with the ATLAS detector using a deep neural network (DNN). To address the specificities of the calibration problem, special loss functions and training procedures are employed, and a complex network architecture, which includes feature annotation and residual connection layers, is used. The DNN-based calibration is compared to the standard numerical approach in an extensive series of tests. The DNN approach is found to perform significantly better in almost all of the tests and over most of the relevant kinematic phase space. In particular, it consistently improves the energy and mass resolutions, with a 30% better energy resolution obtained for transverse momenta $p$ T > $500$ GeV.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗