Results for “data reduction methods” — Page 6

DOE OSTI2022

Real-Time Highly Resolved Spatial-Temporal Vehicle Energy Consumption Estimation Using Machine Learning and Probe Data

Real-time highly resolved spatial-temporal vehicle energy consumption is a key missing dimension in transportation data. Most roadway link-level vehicle energy consumption data are estimated using average annual daily traffic measures derived from the Highway Performance Monitoring System; however, this method does not reflect day-to-day energy consumption fluctuations. As transportation planners and operators are becoming more environmentally attentive, they need accurate real-time link-level vehicle energy consumption data to assess energy and emissions; to incentivize energy-efficient routing; and to estimate energy impact caused by congestion, major events, and severe weather. This paper presents a computational workflow to automate the estimation of time-resolved vehicle energy consumption for each link in a road network of interest using vehicle probe speed and count data in conjunction with machine learning methods in real time. The real-time pipeline can deliver energy estimates within a couple seconds on query to its interface. The proposed method was evaluated on the transportation network of the metropolitan area of Chattanooga, Tennessee. The volume estimation results were validated with ground truth traffic volume data collected in the field. To demonstrate the effectiveness of the proposed method, the energy consumption pipeline was applied to real-world data to quantify road transportation-related energy reduction because of mitigation policies to slow the spread of COVID-19 and to measure energy loss resulting from congestion.

Severino, Joseph↗

DOE OSTI2022

Scalable training of graph convolutional neural networks for fast and accurate predictions of HOMO-LUMO gap in molecules

Abstract Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN surrogate for molecular design requires large-scale graph datasets and is usually a time-consuming process. Recent advances in GPUs and distributed computing open a path to reduce the computational cost for GCNN training effectively. However, efficient utilization of high performance computing (HPC) resources for training requires simultaneously optimizing large-scale data management and scalable stochastic batched optimization techniques. In this work, we focus on building GCNN models on HPC systems to predict material properties of millions of molecules. We use HydraGNN, our in-house library for large-scale GCNN training, leveraging distributed data parallelism in PyTorch. We use ADIOS, a high-performance data management framework for efficient storage and reading of large molecular graph data. We perform parallel training on two open-source large-scale graph datasets to build a GCNN predictor for an important quantum property known as the HOMO-LUMO gap. We measure the scalability, accuracy, and convergence of our approach on two DOE supercomputers: the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF) and the Perlmutter system at the National Energy Research Scientific Computing Center (NERSC). We present our experimental results with HydraGNN showing (i) reduction of data loading time up to 4.2 times compared with a conventional method and (ii) linear scaling performance for training up to 1024 GPUs on both Summit and Perlmutter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

FedOSAA: Improving Federated Learning with One-Step Anderson Acceleration

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly those incorporating variance reduction techniques, are the most widely used FL algorithms due to their simple implementation and stable performance. However, these methods tend to be slow and require a large number of communication rounds to reach the global minimizer. We propose FedOSAA, a novel approach that preserves the simplicity of first-order methods while achieving the rapid convergence typically associated with second-order methods. Our approach applies one Anderson acceleration (AA) step following classical local updates based on first-order methods with variance reduction, such as FedSVRG and SCAFFOLD, during local training. This AA step is able to leverage curvature information from the history points and gives a new update that approximates the Newton-GMRES direction, thereby significantly improving the convergence. We establish a local linear convergence rate to the global minimizer of FedOSAA for smooth and strongly convex loss functions. Numerical comparisons show that FedOSAA substantially improves the communication and computation efficiency of the original first-order methods, achieving performance comparable to second-order methods like GIANT.

Feng, Xue [University of California, Davis]↗

DOE OSTI2021

Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy

Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Here, two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.

58 GEOSCIENCES↗

DOE OSTI2023

Unsupervised classification for region of interest in X-ray ptychography

X-ray ptychography offers high-resolution imaging of large areas at a high computational cost due to the large volume of data provided. To address the cost issue, we propose a physics-informed unsupervised classification algorithm that is performed prior to reconstruction and removes data outside the region of interest (RoI) based on the multimodal features present in the diffraction patterns. The preprocessing time for the proposed method is inconsequential in contrast to the resource-intensive reconstruction process, leading to an impressive reduction in the data workload to a mere 20% of the initial dataset. This capability consequently reduces computational time dramatically while preserving reconstruction quality. Through further segmentation of the diffraction patterns, our proposed approach can also detect features that are smaller than beam size and correctly classify them as within the RoI.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗

DOE OSTI2024

Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 5: Utah FORGE Well 16B(78)-32

Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 4: Utah FORGE Well 78B-32

Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 3: Utah FORGE Well 56-32

Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 1: Summary of Utah FORGE Wells 16A(78)-32, 56-32, 78B-32 and 16B(78)-32

Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.

15 GEOTHERMAL ENERGY↗

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 OSTI2020

A neural network for determination of latent dimensionality in Nonnegative Matrix Factorization

Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy datasets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored dataset. Unfortunately, and this quantity is rarely known a priori. The existing methods for determining latent dimensionality, such as Automatic Relevance Determination (ARD), are mostly heuristic and utilize different characteristics to estimate the number of hidden features. However, all of them require human presence to make a final determination of K. Here we utilize a supervised machine learning approach in combination with a recent method for model determination, called NMFk, to determine the number of hidden features automatically. NMFk performs a set of NMF simulations on an ensemble of matrices, obtained by bootstrapping the initial dataset, and estimates which K produces stable groups of latent features that reconstruct the initial dataset well. We then train a Multi-Layter Perceptron (MLP) classifier network to determine the correct number of latent features utilizing the statistics and characteristics of the NMF solution, obtained from NMFk. In order to train the MLP classifier, a training set of 58,660 matrices with predetermined latent features were factorized with NMFk. The MLP classifier in conjunction with NMFk maintains a greater than 95% success rate when applied to a held out test set. Additionally, when applied to two well-known benchmark datasets, the swimmer and MIT face data, NMFk/MLP correctly recovers the established number of hidden features. Finally, we compare the accuracy of our method to the ARD, AIC and Stability-based methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Efficient near-field ptychography reconstruction using the Hessian operator

X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.

Carlsson, Marcus [Lund Univ. (Sweden)] (ORCID:0000↗

DOE OSTI2025

Packages of Distributed Energy Technologies Demonstrating Demand Flexibility at Community Scale

The combination of increased electric load growth across all sectors, deferred electrical infrastructure investment, and other factors resulting in variable electric power supply, has created technical challenges to maintaining a resilient and reliable grid. Many federal, regional, and local efforts are in play to modernize the electric grid, including advancing building technologies and distributed energy resources (DERs) that are utilizing smarter controls to become responsive to both occupant and grid needs. This report reviews ten pilot projects demonstrating how groups of buildings combined with behind-the-meter (BTM) DERs such as electric vehicle (EV) charging, battery storage, flexible HVAC and domestic hot water systems, and photovoltaic systems can reliably and cost effectively provide grid services. Each of the ten pilot projects aim to deliver both energy efficiency and demand flexibility (DF) while supporting load growth. The ten demonstration teams are piloting flexible DER packages across diverse communities of residential and commercial buildings to address a variety of regional grid needs. The outcomes of these pilot projects will be used to inform future scaling through utility program development. This paper characterizes the ten teams, showcasing the decision-making process used by each group to develop their packages (Section 2), the grid services they plan to deliver (Section 3), the types of DER packages selected for deployment within building sectors (Section 4) and trends between building sector, DER types, and grid services In order to achieve community scale benefits, the pilot projects must utilize aggregated control mechanisms for coordinating buildings and DERs together. Several types of coordinated control architectures have evolved amongst the teams, influenced by use type, existing market conditions, and integration type. Three coordinated controls architectures have been characterized, highlighting their use cases, benefits, challenges, and tradeoffs in their design. These insights can aid utilities, control vendors, and developers in scaling community-level energy systems (Paul, 2024). Ultimately, the technology packages selected by the ten teams will be coordinated to provide power system services, also known as grid services. Insights from these demonstrations will be useful for grid operators, regulators, aggregators and other stakeholders as they look to deploy demand flexible resources as grid services in the future. The grid services that each team is targeting for demonstration are described in Section 3 and Section 4. Methods for evaluating the grid services have been described in the paper Metrics for Evaluating Grid Service Provision from Communities of Grid-interactive and Efficient Buildings and other DER (MacDonald, 2023). To identify technology packages for demonstration, Section 2 shows that project teams used a range of analysis approaches, including building energy modeling, AMI data analysis, cost-benefit frameworks, and utility pilot data. Some teams emphasized technical modeling to quantify grid impacts and demand reduction potential, while others prioritized economic evaluations, stakeholder input, or exploratory pilots to inform deployment decisions. This diversity reflects the need to tailor selection methods to project goals, available data, and organizational context. Section 5 discusses trends between the DER technologies deployed and the grid service provisions from each team. Residential buildings (multifamily and single family) lean towards technologies that enhance energy efficiency (e.g. weatherization upgrades, smart thermostats) and onsite power generation integration (e.g. solar PV). Commercial building demonstrations prioritize technologies that ensure operational reliability (e.g. battery storage) and centralized energy management systems and optimization solutions. Teams that are deploying controllable storage-based technologies are more likely to provide grid services that require a near real-time response. Teams incorporating load shifting technologies like smart thermostats with HEMs are likely to include energy markets participation and customer bill management offerings. Campus demonstrations are adopting diverse sets of DERs to emphasize renewable generation, paired with centralized control. This section also describes technologies that were considered during project planning but ultimately excluded from final deployment. These demonstrations reveal that effective DER package design should be tailored to building type, customer segment, and construction vintage. Multifamily buildings benefit from centralized HVAC upgrades and supervisory controls, while single-family homes are well-suited for individualized technologies like solar, storage, and smart home energy monitors. Commercial and campus settings prioritize EMIS integration and load optimization. New construction enables cost-effective integration of DER-ready infrastructure, whereas retrofits require deployments aligned with owner and tenant value streams. For utility program planners, early coordination with developers and building owners, paired with segmented and modular program offerings, can improve adoption, scalability, and grid impact.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Confidentiality-preserving machine learning algorithms for soft-failure detection in optical communication networks

Automated fault management is at the forefront of next-generation optical communication networks. The increase in complexity of modern networks has triggered the need for programmable and software-driven architectures to support the operation of agile and self-managed systems. In these scenarios, the European Telecommunications Standards Institute zero-touch network and service management approach is imperative. The need for machine learning algorithms to process the large volume of telemetry data brings safety concerns as distributed cloud-computing solutions become the preferred approach for deploying reliable communication network automation. This paper’s contribution is twofold. First, we propose a simple yet effective method to guarantee the confidentiality of the telemetry data based on feature scrambling. The method allows the operation of third-party computational services without direct access to the full content of the collected data. Additionally, the effectiveness of four unsupervised machine learning algorithms for soft-failure detection is evaluated when applied to the scrambled telemetry data. The methods are based on factor analysis, principal component analysis, nonlinear principal component analysis, and singular value decomposition. Most dimensionality reduction algorithms have the common property that they can maintain similar levels of fault classification performance while hiding the data structure from unauthorized access. Evaluations of the proposed algorithms demonstrate this capability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Applying Waveform Correlation to Reduce Seismic Analyst Workload Due to Repeating Mining Blasts

Agencies that monitor for underground nuclear tests are interested in techniques that automatically characterize mining blasts to reduce the human analyst effort required to produce high–quality event bulletins. Waveform correlation is effective in finding similar waveforms from repeating seismic events, including mining blasts. We report the results of an experiment to detect and identify mining blasts for two regions, Wyoming (U.S.A.) and Scandinavia, using waveform templates recorded by multiple International Monitoring System stations of the Preparatory Commission for the Comprehensive Nuclear–Test–Ban Treaty Organization (CTBTO PrepCom) for up to 10 yr prior to the time of interest. We discuss approaches for template selection, threshold setting, and event detection that are specialized for characterizing mining blasts using a sparse, global network. We apply the approaches to one week of data for each of the two regions to evaluate the potential for establishing a set of standards for waveform correlation processing of mining blasts that can be generally applied to operational monitoring systems with a sparse network. Here, we compare candidate events detected with our processing methods to the Reviewed Event Bulletin of the International Data Centre to assess potential reduction in analyst workload.

58 GEOSCIENCES↗

DOE OSTI2021

FAIR data infrastructure and tools for AI-assisted streamflow prediction

Focal Area(s) Areas: We discuss how the integration of AI into Earth Science models can impact streamflow predictions at both the science and data levels. Doing so, we address cross-cutting needs related to the goal of making data FAIR (Findable, Accessible, Interoperable, and Re-usable [1]) for seamless use with Artificial Intelligence/Machine Learning (AI/ML) in Earth System Science at DOE. A novel idea is that AI/ML itself can help with the FAIR data goal and address issues in targeted areas e.g. missing data, data quality and reduction. In addition, the interpretability of results obtained with new AI methods is poised to impact broader scientific challenges in hydrology..

54 ENVIRONMENTAL SCIENCES↗

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↗