Search NASA⌕ Search

SEARCH · Search NASA

Results for “model selection”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Decomposing a renewable energy design and dispatch model

We address a mixed-integer linear programming model which selects a cost-minimizing set of available technologies with which to design a renewable energy system and prescribe their associated dispatch decisions. Realistically sized instances of such models pose computational challenges. To this end, we develop a Lagrangian heuristic based on a decomposition methodology which partitions the model into blocks and optimizes these more manageable, smaller subproblems. It also provides a lower bound to assess solution quality. In conclusion, we apply this methodology to the National Renewable Energy Laboratory's Renewable Energy Integration and Optimization (REopt TM ) model to generate near-optimal solutions to realistic instances containing, on average, approximately 300,000 variables and at least as many constraints, with a mean 30% optimality gap improvement using a five-minute solution time limit, compared to directly solving the original monolith.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Glass Property-Composition Models Update for use in Direct Feed High-Level Waste Flowsheet Development

A set of preliminary glass property models and constraints were developed and augmented by models from literature for use in design of direct-feed high-level waste (DFHLW) glasses for flowsheet evaluation, testing, and design of the Tank Waste Treatment and Immobilization Plant (WTP) high-level waste (HLW) Facility. These models and constraints are meant to be used as a place-holder while glass property-composition data gaps are filled and final plant operating models are developed. This report describes the motivation and intended use of the models, the compilation of data, model fitting and selection, methods to apply the models and constraints in glass design and offers example calculations demonstrating their intended use.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Glass Property-Composition Models Update for use in Direct Feed High-Level Waste Flowsheet Development: EWG2.6

A set of preliminary glass property models and constraints were developed and augmented by models from literature for use in design of direct-feed high-level waste (DFHLW) glasses for flowsheet evaluation, testing, and design of the Waste Treatment and Immobilization Plant (WTP) high-level waste (HLW) Facility. These models and constraints are meant to be used as a place-holder while glass property-composition data gaps are filled and final plant operating models are developed. This report describes the motivation and intended use of the models, the compilation of data, model fitting and selection, methods to apply the models and constraints in glass design and offers example calculations demonstrating their intended use.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Harnessing large language models’ zero-shot and few-shot learning capabilities for regulatory research

Abstract Large language models (LLMs) are sophisticated AI-driven models trained on vast sources of natural language data. They are adept at generating responses that closely mimic human conversational patterns. One of the most notable examples is OpenAI's ChatGPT, which has been extensively used across diverse sectors. Despite their flexibility, a significant challenge arises as most users must transmit their data to the servers of companies operating these models. Utilizing ChatGPT or similar models online may inadvertently expose sensitive information to the risk of data breaches. Therefore, implementing LLMs that are open source and smaller in scale within a secure local network becomes a crucial step for organizations where ensuring data privacy and protection has the highest priority, such as regulatory agencies. As a feasibility evaluation, we implemented a series of open-source LLMs within a regulatory agency’s local network and assessed their performance on specific tasks involving extracting relevant clinical pharmacology information from regulatory drug labels. Our research shows that some models work well in the context of few- or zero-shot learning, achieving performance comparable, or even better than, neural network models that needed thousands of training samples. One of the models was selected to address a real-world issue of finding intrinsic factors that affect drugs' clinical exposure without any training or fine-tuning. In a dataset of over 700 000 sentences, the model showed a 78.5% accuracy rate. Our work pointed to the possibility of implementing open-source LLMs within a secure local network and using these models to perform various natural language processing tasks when large numbers of training examples are unavailable.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Characterizing How Meteorological Forcing Selection and Parameter Uncertainty Influence Community Land Model Version 5 Hydrological Applications in the United States

Despite the increasing use of large-scale Land Surface Models (LSMs) in predicting hydrological responses in extreme conditions, there's a critical gap in understanding the uncertainties in these predictions. This study addresses this gap through a detailed diagnostic evaluation of the uncertainties arising from meteorological forcing selection and model parametrization in hydrological simulations of the Community Land Model version 5 (CLM5). CLM5 is configured at a spatial scale of about 12-km to simulate runoff processes for 464 headwater watersheds, selected from the Catchment Attributes for Large-Sample Studies (CAMELS) dataset to be representative of physiographic and climatic gradients across the conterminous United States. For each watershed, CLM5 is driven by five commonly used gridded forcing datasets in combination with a large ensemble (> 1200) of key CLM5 hydrologic parameters. Our results suggest that uncertainty in CLM5 runoff simulations resulting from both forcing and parametric sources is markedly higher in arid regions, e.g., Great Plains and Midwest regions. Uncertainty in low flow is dominated by parametric uncertainty, while the selection of meteorological forcing contributes more dominantly to high flow and seasonal flows during fall and spring. Our analysis also demonstrates that the selection of forcing datasets and the metrics used to calibrate CLM5 significantly impact the model’s predictive accuracy in extreme event severity for both floods and droughts. Overall, the results from this study highlight the need to understand and account for forcing and parametric uncertainties in CLM5 simulations, particularly for hazard and risk assessments addressing hydrologic extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Supplementary table, figures and DNA sequences of sorghum gene models SbiRTx430.01G455400 and SbiRTx.02G006600 that feature primers, gRNAs and indels created

In-context promoter bashing via genome editing is a route to identify and characterize critical regulatory regions that govern expression of genes of interest. The outcomes of in-context promoter bashing can be used to inform editing strategies to modulate the expression of selected gene models in a desired fashion. Here we employed in-context promoter bashing to characterize the proximal upstream regulatory regions of sorghum genes encoding phosphoenolpyruvate carboxykinase (Sb.PEPCK.BS, SbiTx430.01G455400) and alanine aminotransferase (SbiTx430.02G006600, SbAlaAT.BS), two proteins involved in the PCK C4 pathway. Characterized germinal edits within the targeted regions upstream of these two genes ranged in size from 138 bp up to 1790 bp. A 138 bp within the Sb.PEPCK.BS upstream region and a 1643 bp element within the Sb.AlaAT.BS upstream region were determined to be important for maintenance of transcription levels. No change in development or various physiological parameters was observed in characterized lineages carrying promoter edits. However, significant changes in seed reserves and a reduction in 100 seed weight were consistently observed, under both greenhouse and field environments, in plants carrying an edit in the promoter of Sb.PEPCK.BS gene were significantly reduced in transcript accumulation for this gene.

Quach, Truyen [Center for Plant Science Innovation↗
DOE OSTI2025

In–context promoter bashing of the Sorghum bicolor gene models functionally annotated as bundle sheath cell preferred expressing phosphoenolpyruvate carboxykinase and alanine aminotransferase

In-context promoter bashing via genome editing is a route to identify and characterize critical regulatory regions that govern expression of genes of interest. The outcomes of in-context promoter bashing can be used to inform editing strategies to modulate the expression of selected gene models in a desired fashion. Here, we employed in-context promoter bashing to characterize the proximal upstream regulatory regions of sorghum genes encoding phosphoenolpyruvate carboxykinase bundle sheath (SbPEPCK.BS, SbiTx430.01G455400) and alanine aminotransferase bundle sheath (SbAlaAT.BS, SbiTx430.02G006600), two proteins involved in the PCK C 4 pathway. Characterized germinal edits within the targeted regions upstream of these two genes ranged in size from 138 up to 1790 bp. A 138 bp within the SbPEPCK.BS upstream region and a 1643 bp element within the SbAlaAT.BS upstream region were determined to be important for maintenance of transcription levels. No change in development or various physiological parameters was observed in characterized lineages carrying promoter edits. However, significant changes in seed reserves and a reduction in 100-seed weight were consistently observed, under both greenhouse and field environments, in plants carrying an edit in the promoter of SbPEPCK.BS gene, which were significantly reduced in transcript accumulation for this gene.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Design strategies for ion-sieving charge mosaic membranes toward sustainable lithium extraction

Membrane-based technologies are essential for realizing sustainable ion-sieving processes such as lithium extraction. Much effort was devoted to designing new membrane materials, whereas the effect of charge distribution has been largely overlooked. Here, we filled this knowledge gap by providing a quantitative transport model for selective ion diffusion through a charge mosaic membrane (CMM). Composed of alternating regions of Li-selective ceramic and anion-selective polymeric materials, CMMs offered the unique advantage of promoting the transport of both Li + and anions while blocking other cations. As a result, the membrane achieved a high Li/Mg selectivity of 62 and a high permeation rate of 59 mmol·m −2 ·h −1 at a low feeding concentration of 30 mM, without any external driving force. Systematical experiments revealed the influence of brine Mg/Li ratio and membrane ceramic/polymer ratio on the overall extraction rate, which was consistent with the prediction of our transport model. In conclusion, the model developed in this work not only presented the design strategies of CMMs for Li extraction but also provided guidance for the development of other ion-sieving processes in general.

25 ENERGY STORAGE↗
DOE OSTI2024

Toward Spatial Control of Reaction Selectivity on Photocatalysts Using Area-Selective Atomic Layer Deposition on the Model Dual Site Electrocatalyst Platform

Photocatalytic water splitting is a promising route to low-cost, green H 2 . However, this approach is currently limited in its solar-to-hydrogen conversion efficiency. One major source of efficiency loss is attributed to the high rates of undesired side and back reactions, which are exacerbated by the proximity of neighboring oxidation and reduction sites. Nanoscopic oxide coatings have previously been used to selectively block undesired reactants from reaching active sites; however, a coating encapsulating the entire photocatalyst particle limits activity as it cannot facilitate both half-reactions. In this work, area selective atomic layer deposition (AS-ALD) was used to selectively deposit semipermeable TiO 2 films onto model metallic cocatalysts for enhancing reaction selectivity while maintaining a high overall activity. Pt and Au were used as exemplary reduction and oxidation cocatalyst sites, respectively, where Au was deactivated toward ALD growth through self-assembled thiol monolayers while TiO 2 was coated onto Pt sites. Electroanalytical measurements of monometallic thin film electrodes showed that the TiO 2 -encapsulated Pt effectively suppressed undesired H 2 oxidation and Fe(II)/Fe(III) redox reactions while still permitting the desired hydrogen evolution reaction (HER). A planar model photocatalyst platform containing patterned interdigitated arrays of Au and Pt microelectrodes was further assessed using scanning electrochemical microscopy (SECM), demonstrating the successful use of AS-ALD to enable local reaction selectivity in a dual-reaction-site (photo)electrocatalytic system. Finally, interdigitated microelectrodes having independent potential control were used to show that selectively deposited TiO 2 coatings can suppress the rate of back reactions on neighboring active sites by an order of magnitude compared with uncoated control samples.

08 HYDROGEN↗
DOE OSTI2026

Towards Anomaly Detection at the CMS High-Level Trigger System

Traditional trigger strategies in CMS typically rely on model-dependent selections or rigid kinematic cuts, risking the omission of unexpected exotic signatures. To address this, we propose a novel anomaly detection (AD) algorithm for the High-Level Trigger (HLT), designed to serve as a complementary second layer of filtering to the Level-1 AXOL1TL AD algorithm. We employ a transformer-based foundation model trained on a diverse ensemble of Standard Model processes. By combining a joint contrastive and classification objective, and using particle kinematics as inputs, the model learns to map events to a physics-informed latent space where anomalous events are isolated from dominant backgrounds. Preliminary results show that this strategy enhances the signal-to-background ratio across a range of rare SM and BSM scenarios. Furthermore, this work constitutes foundational R&D for the potential implementation of an analogous AD algorithm in the Level-1 trigger system for Phase-2.

Cruz, Roy [U. Wisconsin, Madison (main)] (ORCID:00↗
DOE OSTI2024

Emulator-Based Bayesian Calibration of the CISNET Colorectal Cancer Models

Purpose To calibrate Cancer Intervention and Surveillance Modeling Network (CISNET)'s SimCRC, MISCAN-Colon, and CRC-SPIN simulation models of the natural history colorectal cancer (CRC) with an emulator-based Bayesian algorithm and internally validate the model-predicted outcomes to calibration targets.Methods We used Latin hypercube sampling to sample up to 50,000 parameter sets for each CISNET-CRC model and generated the corresponding outputs. We trained multilayer perceptron artificial neural networks (ANNs) as emulators using the input and output samples for each CISNET-CRC model. We selected ANN structures with corresponding hyperparameters (i.e., number of hidden layers, nodes, activation functions, epochs, and optimizer) that minimize the predicted mean square error on the validation sample. We implemented the ANN emulators in a probabilistic programming language and calibrated the input parameters with Hamiltonian Monte Carlo-based algorithms to obtain the joint posterior distributions of the CISNET-CRC models' parameters. We internally validated each calibrated emulator by comparing the model-predicted posterior outputs against the calibration targets.Results The optimal ANN for SimCRC had 4 hidden layers and 360 hidden nodes, MISCAN-Colon had 4 hidden layers and 114 hidden nodes, and CRC-SPIN had 1 hidden layer and 140 hidden nodes. The total time for training and calibrating the emulators was 7.3, 4.0, and 0.66 h for SimCRC, MISCAN-Colon, and CRC-SPIN, respectively. The mean of the model-predicted outputs fell within the 95% confidence intervals of the calibration targets in 98 of 110 for SimCRC, 65 of 93 for MISCAN, and 31 of 41 targets for CRC-SPIN.Conclusions Using ANN emulators is a practical solution to reduce the computational burden and complexity for Bayesian calibration of individual-level simulation models used for policy analysis, such as the CISNET CRC models. In this work, we present a step-by-step guide to constructing emulators for calibrating 3 realistic CRC individual-level models using a Bayesian approach.

artificial neural networks↗
DOE OSTI2026

Towards Spatial Control of Reaction Selectivity on Photocatalysts using Area Selective Atomic Layer Deposition on Model Dual Site Electrocatalyst Platform

Photocatalytic water splitting is a promising route to low-cost H2; however, this approach is currently limited by solar-to-hydrogen (STH) conversion efficiencies in the sub-10% range. Z-scheme water splitting, in which H2 and O2 evolving particles are operated in separate compartments and electronically coupled by a soluble redox mediator, offers improvements in STH efficiency but introduces high rates of undesired side and back reactions. Nanoscopic oxide coatings (e.g., CrOx, and SiOx) have previously been used to selectively block undesired reactants from reaching active sites; however, a coating encapsulating the entire photocatalyst particle limits activity as the particle can no longer facilitate both half reactions. In contrast to photodeposition, which may produce non-uniform overlayers due to the difficulty of controlling local electrochemical reactivity on the surface, area-selective atomic layer deposition (AS-ALD) can be used to deposit conformal ultrathin oxide coatings while preserving access to non-growth areas of a substrate surface. To develop this technique for Z-scheme photocatalysts, we performed AS-ALD of TiO2 on a dual site planar electrocatalyst based on interdigitated arrays of Pt and Au. Self-assembled monolayers of 1-octadecanethiol (ODT) were used to block growth on the Au array, resulting in a patterned surface in which only the Pt sites were encapsulated with TiO2. These electrocatalysts demonstrated localized reaction selectivity for hydrogen evolution reaction (HER) over the TiO2/Pt sites, while the uncoated Au sites retained activity towards Fe(II)/Fe(III) redox (FeRR). Under independent potential control, these microelectrodes showed that selectively deposited TiO2 coatings can suppress the rate of back reactions on neighboring active sites by an order of magnitude compared to uncoated control samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Guiding Principles for Geochemical/Thermodynamic Model Development and Validation in Nuclear Waste Disposal: A Close Examination of Recent Thermodynamic Models for H + —Nd 3+ —NO 3 - (—Oxalate) Systems

Development of a defensible source-term model (STM), usually a thermodynamical model for radionuclide solubility calculations, is critical to a performance assessment (PA) of a geologic repository for nuclear waste disposal. Such a model is generally subjected to rigorous regulatory scrutiny. In this article, we highlight key guiding principles for STM model development and validation in nuclear waste management. We illustrate these principles by closely examining three recently developed thermodynamic models with the Pitzer formulism for aqueous H + —Nd 3+ —NO 3 - (—oxalate) systems in a reverse alphabetical order of the authors: the XW model developed by Xiong and Wang, the OWC model developed by Oakes et al., and the GLC model developed by Guignot et al., among which the XW model deals with trace activity coefficients for Nd(III), while the OWC and GLC models are for concentrated Nd(NO 3 ) 3 electrolyte solutions. The principles highlighted include the following: (1) Principle 1. Validation against independent experimental data: A model should be validated against experimental data or field observations that have not been used in the original model parameterization. We tested the XW model against multiple independent experimental data sets including electromotive force (EMF), solubility, water vapor, and water activity measurements. The results show that the XW model is accurate and valid for its intended use for predicting trace activity coefficients and therefore Nd solubility in repository environments. (2) Principle 2. Testing for relevant and sensitive variables: Solution pH is such a variable for an STM and easily acquirable. All three models are checked for their ability to predict pH conditions in Nd(NO 3 ) 3 electrolyte solutions. The OWC model fails to provide a reasonable estimate for solution pH conditions, thus casting serious doubt on its validity for a source-term calculation. In contrast, both the XW and GLC models predict close-to-neutral pH values, in agreement with experimental measurements. (3) Principle 3. Honoring physical constraints: Upon close examination, it is found that the Nd(III)-NO 3 association schema in the OWC model suffers from two shortcomings. Firstly, its second stepwise stability constant for Nd(NO 3 ) 2+ (log K 2 ) is much higher than the first stepwise stability constant for NdNO 3 2+ (log K 1 ), thus violating the general rule of (log K 2 –log K 1 ) < 0, or $\frac{K1}{K2}$>1. Secondly, the OWC model predicts abnormally high activity coefficients for Nd(NO 3 ) 2 + (up to ~900) as the concentration increases. (4) Principle 4. Minimizing degrees of freedom for model fitting: The OWC model with nine fitted parameters is compared with the GLC model with five fitted parameters, as both models apply to the concentrated region for Nd(NO 3 ) 3 electrolyte solutions. The latter appears superior to the former because the latter can fit osmotic coefficient data equally well with fewer model parameters. The work presented here thus illustrates the salient points of geochemical model development, selection, and validation in nuclear waste management.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Local Chain Dynamics in Sequence-Controlled Polymers as a Tunable Handle for Rare Earth Sequestration

Chain dynamics govern the intricate behaviors of proteins, underpinning functions such as catalysis, recognition, and stimulus response, and are an increasingly appreciated aspect of structure–function relationships. Analogously, manipulating chain dynamics and structure in abiotic polymers via sequence control is an exciting, yet underexplored, strategy for improving material functions. In this work, we report a systematic study relating the sequence of polymeric sequestrants to their structure and dynamics, as well as to their binding affinity and selectivity for model substrates, rare earth elements (REEs). A series of sequence-controlled polymers with metal chelating, solubilizing, and structure forming monomers was synthesized via multiblock polymerization, yielding compositionally identical polymers with spectroscopically resolved domains and distinct morphologies. Using a combination of small-angle X-ray scattering and 19 F NMR relaxometry measurements, we connected differences in polymer structure and dynamics to polymer sequence variables such as the patchiness (density) of the structure forming monomer and the location of the chelating monomer. Furthermore, we found that, relative to calcium, all polymers in the series collapse more and have slower dynamics when binding REEs (lanthanum and lutetium) , though the extent of these effects were sequence-dependent and localized to specific domains within the polymer. Notably, sequence-controlled polymers that exhibited the largest conformational and dynamic changes upon binding REEs also bound REEs with the greatest affinity and modest selectivity. Collectively, these results correlate monomer patterning with dynamics, morphology, and REE binding performance en route to the development of efficient and selective macromolecular chelators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Search for Long-Lived Particles with Muon Detector Shower Signature in the CMS Run-3 data

Many beyond standard model theories predict the existence of long-lived particles (LLPs). These LLPs can have sizable lifetimes and decay several meters from their production vertex. In this poster/talk, we present the analysis strategy for searching for LLPs using the Compact Muon Solenoid (CMS) Experiment. The proton-proton collision data used in this analysis were collected from 2022 to 2024 at a center-of-mass energy of 13.6 TeV, corresponding to an integrated luminosity of 170 fb^-1. The LLP decays are reconstructed as a high-multiplicity cluster of detector hits in the cathode strip chambers (CSC) of the muon system endcap. This signature is referred to as the Muon Detector Showers (MDS). This search requires events to contain at least one MDS cluster. The analysis focuses on LLP hadronic decays and LLP masses up to a few tens of GeV. We present the signal properties in MonteCarlo simulation, event selection, background modeling, and evaluation of the expected sensitivity. The results are interpreted under the Twin Higgs model benchmark.

Agyemang-Duah, Andrews [Grambling State U.]↗
DOE OSTI2026

Correlating binding energies of adsorbed CO and H on model surfaces with CO/H 2 selectivity from co-electrolysis of CO 2 and H 2 O over copper–palladium bimetallic catalysts

Binding energies of adsorbed CO and H are key descriptors governing the activity and selectivity of the co-electrolysis of CO 2 and H 2 O to produce syngas with desired CO/H 2 ratios. Palladium hydride (PdH), which forms in situ at negative overpotentials, has been identified as the active Pd phase for CO 2 reduction to syngas. Herein, binding energies of CO and H are determined using temperature programmed desorption (TPD) of CO and H 2 from Pd(111), PdH/Pd(111), and Cu/PdH/Pd(111) under ultra-high vacuum (UHV) conditions. TPD results reveal that desorption of H 2 from subsurface PdH occurs at 460 K, while desorption from surface PdH is more facile at 320 K. CO desorption temperatures shift 20 K lower on PdH/Pd(111) compared to on Pd(111). The presence of 0.7 ML Cu further increases the desorption temperature of H 2 by 30 K while simultaneously reducing CO desorption temperatures by 70 K. Density functional theory (DFT) calculations show that CO adsorption onto Pd sites is hindered on the 0.7 ML Cu/PdH/Pd(111) surface while the kinetic barrier for H 2 desorption is increased. The trends in the binding energies of CO and H on model surfaces are consistent with electrochemical measurements of CuPd powder catalysts in a membrane electrode assembly (MEA), where H 2 evolution is reduced while CO production is enhanced compared to unmodified Pd catalysts. Overall, the results from model surface studies (TPD and DFT) provide a prediction and explanation for the activity and CO/H 2 ratios observed in electrochemical experiments. This study also demonstrates that CuPd is a promising catalyst with reduced Pd-loading to produce CO-rich syngas.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Generic and Multifunctional Electromagnetic Transient Model for Grid-Following Inverters

This paper presents a generic and multifunctional electromagnetic transient (EMT) dynamic model of grid-following (GFL) inverter-based resources (IBRs) using the PSCAD software platform. The features of the model include flexibility in selecting various types and combinations of DC sources covering photovoltaic modules, battery modules, and ideal DC-source modules as well as flexibility in selecting either switching or averaged models of the inverter. This model also covers exhaustive lists of controller algorithm, including open-loop/closed-loop PQ dispatch control, DC voltage and AC terminal voltage control, and conventional current control designed in the dq-domain, the ..alpha....beta.. -domain, and the positive-/negative-sequence domain. Moreover, this model is equipped with flexibility in selecting various types of current-limiting schemes, including saturation-based and latching-based current limiters, and anti-windup protection. Also, the EMT model is agnostic to the MVA rating and is suitable for interfacing transmission systems by complying with IEEE Std. 2800. The generality in the power circuits and the multifunctional options in the operation and control of the developed EMT model make it suitable for both academia and industry to study various power system aspects, including, but not limited to, the fault behavior of GFL IBRs, the impacts on the protection system, and the transient stability of a system interfaced with large numbers of GFL IBRs.

integrated circuit modeling↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗