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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics↗
DOE OSTI2025

Block-Structured Operator Inference for Coupled Multiphysics Model Reduction

This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

42 ENGINEERING↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
DOE OSTI2026

NN-OpInf

SAND2026-18878O The NN-OpInf tool is a PyTorch-based approach to operator inference that uses composable, structure-preserving neural networks to represent nonlinear operators. Operator inference is a machine learning method for inferring low-dimensional systems from data and polynomial models for system dynamics. However, many systems do not conform to polynomial structures, which NN-OpInf addresses by parameterizing operators with neural networks. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
NASA NTRS1988

OFMspert - Inference of operator intentions in supervisory control using a blackboard architecture

The authors proposes an architecture for an expert system that can function as an operator's associate in the supervisory control of a complex dynamic system. Called OFMspert (operator function model (OFM) expert system), the architecture uses the operator function modeling methodology as the basis for the design. The authors put emphasis on the understanding capabilities, i.e., the intent referencing property, of an operator's associate. The authors define the generic structure of OFMspert, particularly those features that support intent inferencing. They also describe the implementation and validation of OFMspert in GT-MSOCC (Georgia Tech-Multisatellite Operations Control Center), a laboratory domain designed to support research in human-computer interaction and decision aiding in complex, dynamic systems.

Jones, Patricia S.↗
DOE OSTI2025

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗
DOE OSTI2025

norma-opinf

SAND2025-10454O norma-opinf is a set of tools to perform operator inference. It is specifically tailored for the norma codebase. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Tezaur, Irina [Sandia National Lab. (SNL-CA), Live↗
NASA NTRS1988

Intent inferencing by an intelligent operator's associate - A validation study

In the supervisory control of a complex, dynamic system, one potential form of aiding for the human operator is a computer-based operator's associate. The design philosophy of the operator's associate is that of 'amplifying' rather than automating human skills. In particular, the associate possesses understanding and control properties. Understanding allows it to infer operator intentions and thus form the basis for context-dependent advice and reminders; control properties allow the human operator to dynamically delegate individual tasks or subfunctions to the associate. This paper focuses on the design, implementation, and validation of the intent inferencing function. Two validation studies are described which empirically demonstrate the viability of the proposed approach to intent inferencing.

Jones, Patricia M.↗
DOE OSTI2026

Toward real-time optimization through model reduction and model discrepancy sensitivities

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs—those that do not require access to the full-order model at evaluation time—is popular because they facilitate the computation of optimization solutions within the wall-clock time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, a limited number of full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. In conclusion, the HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data.

PDE-constrained optimization↗
DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗
DOE OSTI2026

Divertor detachment and heat exhaust mitigation control in KSTAR with tungsten divertor

KSTAR has recently undergone an upgrade to use a new tungsten divertor to run experiments in ITER-relevant scenarios. Even with a high melting point of tungsten, it is important to control the heat flux impinging on tungsten divertor targets to minimize sputtering and contamination of the core plasma. Heat flux on the divertor is often controlled by increasing the degree of detachment of scrape-off layer plasma from the target plates. In this work, we have demonstrated successful divertor detachment and heat exhaust dissipation control experiments using two different methods. The first method uses attachment fraction as a control variable which is estimated using ion saturation current measurements from embedded Langmuir probes in the divertor. The second method uses a novel machine-learning-based surrogate model of 2D UEDGE simulation database, DivControlNN. We demonstrated running inference operation of DivControlNN in realtime to estimate heat flux at the divertor and use it as the control variable in a feedback loop with impurity gas flow. We present interesting insights from these experiments including a systematic approach to tuning controllers and discuss future improvements in the control infrastructure and control variables for future burning plasma experiments.

KSTAR tungsten divertor operations↗
NASA NTRS1981

X-ray imaging - Supernova remnants

Consideration is given to imaging observations of supernova remnants (SNRs) obtained during the first year of the Einstein Observatory's operation. Inferences are drawn regarding models for stellar explosions, remnant evolution, neutron star formation and the interstellar medium. Because the X-ray emission traces the expanding shock boundary and dominates the radiative energy losses of an SNR over much of its lifetime, it can provide data on the possible collapsed remnants of the explosion, such as neutron stars and/or black holes. X-ray emission also allows a supernova shock to be used as a probe of interstellar medium structure. The imaging instrument aboard the Einstein satellite has been used to observe over 30 known Galactic remnants, and a similar number of objects in other galaxies, in the 0.15-4.5 keV band.

Helfand, D. J.↗
NASA NTRS2014

Human-Robot Interaction Directed Research Project

Human-robot interaction (HRI) is a discipline investigating the factors affecting the interactions between humans and robots. It is important to evaluate how the design of interfaces and command modalities affect the human's ability to perform tasks accurately, efficiently, and effectively when working with a robot. By understanding the effects of interface design on human performance, workload, and situation awareness, interfaces can be developed to appropriately support the human in performing tasks with minimal errors and with appropriate interaction time and effort. Thus, the results of research on human-robot interfaces have direct implications for the design of robotic systems. This DRP concentrates on three areas associated with interfaces and command modalities in HRI which are applicable to NASA robot systems: 1) Video Overlays, 2) Camera Views, and 3) Command Modalities. The first study focused on video overlays that investigated how Augmented Reality (AR) symbology can be added to the human-robot interface to improve teleoperation performance. Three types of AR symbology were explored in this study, command guidance (CG), situation guidance (SG), and both (SCG). CG symbology gives operators explicit instructions on what commands to input, whereas SG symbology gives operators implicit cues so that operators can infer the input commands. The combination of CG and SG provided operators with explicit and implicit cues allowing the operator to choose which symbology to utilize. The objective of the study was to understand how AR symbology affects the human operator's ability to align a robot arm to a target using a flight stick and the ability to allocate attention between the symbology and external views of the world. The study evaluated the effects type of symbology (CG and SG) has on operator tasks performance and attention allocation during teleoperation of a robot arm. The second study expanded on the first study by evaluating the effects of the type of navigational guidance (CG and SG) on operator task performance and attention allocation during teleoperation of a robot arm through uplinked commands. Although this study complements the first study on navigational guidance with hand controllers, it is a separate investigation due to the distinction in intended operators (i.e., crewmembers versus ground-operators). A third study looked at superimposed and integrated overlays for teleoperation of a mobile robot using a hand controller. When AR is superimposed on the external world, it appears to be fixed onto the display and internal to the operators' workstation. Unlike superimposed overlays, integrated overlays often appear as three-dimensional objects and move as if part of the external world. Studies conducted in the aviation domain show that integrated overlays can improve situation awareness and reduce the amount of deviation from the optimal path. The purpose of the study was to investigate whether these results apply to HRI tasks, such as navigation with a mobile robot. HRP GAPS This HRI research contributes to closure of HRP gaps by providing information on how display and control characteristics - those related to guidance, feedback, and command modalities - affect operator performance. The overarching goals are to improve interface usability, reduce operator error, and develop candidate guidelines to design effective human-robot interfaces.

Sandor, Aniko↗