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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 1,711 records · Page 95
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DOE OSTI2025

CHARGE-MAP: An integrated framework to study the multicriteria EV charging infrastructure expansion problem

The widespread adoption of electric vehicles (EVs) in recent years has necessitated the development of effective charging infrastructures. However, charging infrastructure expansion is a multifaceted problem that requires careful consideration of the existing infrastructure, spatiotemporal distribution of charging demands, power-grid capacity, and budget constraints. Here, to approach this complex problem, we present CHARGE-MAP, a data-driven simulation-optimization framework, focused on ensuring meaningful charging experience for individual EV owners. CHARGE-MAP integrates three modules: an agent-based simulation module that estimates spatiotemporal distribution of charging demands by modeling EV adopter mobility and charging behavior; an optimization module that determines optimal new charging station/charger locations and capacities, while minimizing expected detour distances and wait-times with a limited number of new stations; and a power module that determines how to connect the stations to the power grid while maintaining its stability. Using the state of Virginia (consisting of 95 counties and 38 independent cities) as a case study, our results show that CHARGE-MAP can meet the demand of ~198,600 predicted EVs with 1,305 new public charging stations and 2,164 new chargers. It reduces average detour distances for charging by 66% and wait-times at stations by 72% compared to the existing infrastructure. Furthermore, transformer capacity requirement analysis reveals that only 1.8% of residential transformers require upgrades, while over 80% of commercial charging locations can be supported with modest transformer infrastructure (25 to 50 kVA). This indicates that targeted investments can facilitate cost-effective EV integration. Consequently, CHARGE-MAP provides policymakers and urban planners with crucial data-driven insights for effective EV charging infrastructure expansion. Sign up for PNAS alerts.

charging infrastructure↗
DOE OSTI2016

Reproducing the observed energy-dependent structure of Earth's electron radiation belts during storm recovery with an event-specific diffusion model

Here, we present dynamic simulations of energy-dependent losses in the radiation belt “slot region” and the formation of the two-belt structure for the quiet days after the 1 March storm. The simulations combine radial diffusion with a realistic scattering model, based data-driven spatially and temporally resolved whistler-mode hiss wave observations from the Van Allen Probes satellites. The simulations reproduce Van Allen Probes observations for all energies and L shells (2–6) including (a) the strong energy dependence to the radiation belt dynamics (b) an energy-dependent outer boundary to the inner zone that extends to higher L shells at lower energies and (c) an “S-shaped” energy-dependent inner boundary to the outer zone that results from the competition between diffusive radial transport and losses. We find that the characteristic energy-dependent structure of the radiation belts and slot region is dynamic and can be formed gradually in ~15 days, although the “S shape” can also be reproduced by assuming equilibrium conditions. The highest-energy electrons (E > 300 keV) of the inner region of the outer belt (L ~ 4–5) also constantly decay, demonstrating that hiss wave scattering affects the outer belt during times of extended plasmasphere. Through these simulations, we explain the full structure in energy and L shell of the belts and the slot formation by hiss scattering during storm recovery. We show the power and complexity of looking dynamically at the effects over all energies and L shells and the need for using data-driven and event-specific conditions.

58 GEOSCIENCES↗
DOE OSTI2018

Genome-wide association studies and expression-based quantitative trait loci analyses reveal roles of HCT2 in caffeoylquinic acid biosynthesis and its regulation by defense-responsive transcription factors in Populus

3-O-caffeoylquinic acid, also known as chlorogenic acid (CGA), functions as an intermediate in lignin biosynthesis in the phenylpropanoid pathway. It is widely distributed among numerous plant species and acts as an antioxidant in both plants and animals. Using GC-MS, we discovered consistent and extreme variation in CGA content across a population of 739 4-yr-old Populus trichocarpa accessions. We performed genome-wide association studies (GWAS) from 917 P. trichocarpa accessions and expression-based quantitative trait loci (eQTL) analyses to identify key regulators. The GWAS and eQTL analyses resolved an overlapped interval encompassing a hydroxycinnamoyl-CoA:shikimate hydroxycinnamoyl transferase 2 (PtHCT2) that was significantly associated with CGA and partially characterized metabolite abundances. PtHCT2 leaf expression was significantly correlated with CGA abundance and it was regulated by cis-eQTLs containing W-box for WRKY binding. Among all nine PtHCT homologs, PtHCT2 is the only one that responds to infection by the fungal pathogen Sphaerulina musiva (a Populus pathogen). Validation using protoplast-based transient expression system suggests that PtHCT2 is regulated by the defense-responsive WRKY. These results are consistent with reports of CGA functioning as an antioxidant in response to biotic stress. This study provides insights into data-driven and omics-based inference of gene function in woody species.

Zhang, Jin↗
DOE OSTI2024

Nanoporous Materials Genome Center Final Technical Report

Nanoporous materials (NPMs), including zeolites/zeotypes, metal-organic frameworks (MOFs), covalent organic frameworks, polymers with intrinsic microporosity, and molecular cages, possess enormous potential in diverse areas relevant to the DOE Office of Science Basic Energy Sciences (BES) mission and objectives. The Nanoporous Materials Genome Center (NMGC) has developed exascale-ready software, computational/theoretical chemistry methods, and data-driven science approaches that enable (i) the de-novo design of functional NPMs for chemical separation and catalysis tasks of increasing complexity, (ii) the discovery of the most promising functional NPMs from databases of synthesized and hypothetical adsorbent structures and the optimization of process conditions for specific applications, and (iii) the microscopic-level understanding of the fundamental interactions underlying the function of NPMs including hierarchical architectures, composite materials, responsive frameworks that may undergo phase transitions or post-synthetic modifications, and materials containing defects, partial disorder, or interfaces. A pivotal part of the NMGC project has been a tight collaboration between leading experimental groups for synthesis and characterization of NPMs and of computational groups that allowed for iterative feedback. The NMGC project has resulted in the publication of more than 290 research and review articles including more than 60 publications in high-impact journals and more than 15 journal covers. NMGC publications have already received more than 20,000 citations (with more than 3,000 citations per year in 2021, 2022, and 2023) and contribute to an h-index of more than 72. The NMGC award has supported collaborative research involving 28 research groups and contributed to the training of more than 40 postdocs, more than 60 graduate students, and more than 20 undergraduate students with broad expertise in data-driven science approaches, computational chemistry methods, and high-performance computing, in addition to the skills to thrive in an integrated experimental and computational research environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Improvement and generalization of ABCD method with Bayesian inference

To find New Physics or to refine our knowledge of the Standard Model at the LHC is an enterprise that involves many factors, such as the capabilities and the performance of the accelerator and detectors, the use and exploitation of the available information, the design of search strategies and observables, as well as the proposal of new models. We focus on the use of the information and pour our effort in re-thinking the usual data-driven ABCD method to improve it and to generalize it using Bayesian Machine Learning techniques and tools. We propose that a dataset consisting of a signal and many backgrounds is well described through a mixture model. Signal, backgrounds and their relative fractions in the sample can be well extracted by exploiting the prior knowledge and the dependence between the different observables at the event-by-event level with Bayesian tools. We show how, in contrast to the ABCD method, one can take advantage of understanding some properties of the different backgrounds and of having more than two independent observables to measure in each event. In addition, instead of regions defined through hard cuts, the Bayesian framework uses the information of continuous distribution to obtain soft-assignments of the events which are statistically more robust. To compare both methods we use a toy problem inspired by pp\to hh\to b\bar b b \bar b p p → h h → b b ‾ b b ‾ , selecting a reduced and simplified number of processes and analysing the flavor of the four jets and the invariant mass of the jet-pairs, modeled with simplified distributions. Taking advantage of all this information, and starting from a combination of biased and agnostic priors, leads us to a very good posterior once we use the Bayesian framework to exploit the data and the mutual information of the observables at the event-by-event level. We show how, in this simplified model, the Bayesian framework outperforms the ABCD method sensitivity in obtaining the signal fraction in scenarios with 1% and 0.5% true signal fractions in the dataset. We also show that the method is robust against the absence of signal. We discuss potential prospects for taking this Bayesian data-driven paradigm into more realistic scenarios.

Alvarez, Ezequiel↗
DOE OSTI2025

Multi-physics Topology OPtimization and Additive Manufacturing for High-temperature Heat Exchangers

This research significantly advances the understanding of high-temperature heat exchanger design through an integrated approach that combines topology optimization (TO), triply periodic minimal surface (TPMS) structures, additive manufacturing (AM) and thermohydraulic testing. Each of these components contributes uniquely to a unified, high-performance design, fabrication and testing workflow. Topology optimization serves as the foundation of the design methodology by providing a systematic way to determine the most effective material layout for separating hot and cold fluids while maximizing thermal performance. The researchers introduced a novel three-material optimization framework using two density fields to represent hot fluid, cold fluid, and solid domains. This approach enables automated discovery of optimal shapes and flow paths that cannot be intuitively designed, especially under constraints imposed by manufacturing technologies. Furthermore, constraints such as minimal wall thickness and overhang angles were embedded into the optimization process, ensuring that resulting designs are not only thermally efficient but also manufacturable using modern additive techniques. In parallel, the study delves into the use of Gyroid-based TPMS geometries for constructing the core of the heat exchanger. TPMS structures are known for their high surface area, excellent fluid mixing capabilities, and minimal pressure drop characteristics. The researchers applied a data-driven modeling framework using Heteroscedastic Sparse Gaussian Process Regression (HSGPR) combined with genetic algorithms. This allowed for the rapid evaluation and optimization of key geometric parameters such as frequency, iso-value, and phase shift. The result was a set of Gyroid structures tailored for high heat transfer and low flow resistance, demonstrating clear improvements over conventional straight-channel designs. After the designing process, additive manufacturing played a critical role by turning these highly complex, optimized geometries into physical components. Utilizing Laser Powder Bed Fusion (LPBF) with Haynes 282, the study demonstrated the feasibility of fabricating these heat exchangers at high precision. Post-processing methods, including dilation-erosion operations, were applied to ensure local features adhered to self-supporting constraints. The fabricated structures were then subjected to thermohydraulic testing under conditions representative of supercritical CO 2 Brayton cycles, validating the predicted performance and confirming the viability of the full design-to-fabrication pipeline. Finally, thermohydraulic testing across the above studies served as a crucial experimental validation of advanced heat exchanger. Under consistent high-temperature and high-pressure conditions using supercritical CO 2 , the testing demonstrated that both TO and Gyroid-based TPMS designs significantly outperformed conventional straight-channel HXs. The TO design achieved a 115% increase in UA and NTU and a 27.6% boost in gravimetric power density, while the data-driven optimized Gyroid design delivered a 166% increase in UA and NTU and improved effectiveness from 68.7% to 86.1%. These results validate the simulation models, confirm the manufacturability of complex geometries under AM constraints, and provide key insights into design-performance trade-offs, thereby advancing the development of high-efficiency, compact heat exchangers for extreme environments.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.

Modelling↗
DOE OSTI2018

High-throughput cancer hypothesis testing with an integrated PhysiCell-EMEWS workflow

BackgroundCancer is a complex, multiscale dynamical system, with interactions between tumor cells and non-cancerous host systems. Therapies act on this combined cancer-host system, sometimes with unexpected results. Systematic investigation of mechanistic computational models can augment traditional laboratory and clinical studies, helping identify the factors driving a treatment's success or failure. However, given the uncertainties regarding the underlying biology, these multiscale computational models can take many potential forms, in addition to encompassing high-dimensional parameter spaces. Therefore, the exploration of these models is computationally challenging. We propose that integrating two existing technologiesone to aid the construction of multiscale agent-based models, the other developed to enhance model exploration and optimizationcan provide a computational means for high-throughput hypothesis testing, and eventually, optimization.ResultsIn this paper, we introduce a high throughput computing (HTC) framework that integrates a mechanistic 3-D multicellular simulator (PhysiCell) with an extreme-scale model exploration platform (EMEWS) to investigate high-dimensional parameter spaces. We show early results in applying PhysiCell-EMEWS to 3-D cancer immunotherapy and show insights on therapeutic failure. We describe a generalized PhysiCell-EMEWS workflow for high-throughput cancer hypothesis testing, where hundreds or thousands of mechanistic simulations are compared against data-driven error metrics to perform hypothesis optimization.ConclusionsWhile key notational and computational challenges remain, mechanistic agent-based models and high-throughput model exploration environments can be combined to systematically and rapidly explore key problems in cancer. These high-throughput computational experiments can improve our understanding of the underlying biology, drive future experiments, and ultimately inform clinical practice.

Agent-based model↗
DOE OSTI2022

Computational Tools and Workflows for Quantitative Risk Assessment and Decision Support for Geologic Carbon Storage Sites: Progress and Insights from the U.S. DOE’s National Risk Assessment Partnership

The 2005 Intergovernmental Panel on Climate Change (IPCC) Special Report on CCS raised the profile of CO2 capture and storage (CCS) as an important technology for reducing greenhouse gas (GHG) emissions. CCS is now recognized as a key component of most climate change mitigation scenarios. Since publication of that report the international research, development, and deployment (RD&D) community has advanced key technical aspects, clarified regulatory requirements, explored value chain and infrastructure solutions, and developed incentive paradigms to enable and promote large-scale deployment of CCS. These efforts have included research to better characterize geologic storage resources, to improve injection performance and storage efficiency, to assess and manage subsurface environmental risks, and to advance monitoring technologies to assure system conformance. These efforts have helped to build confidence in the viability of geologic carbon storage (GCS), but stakeholder concerns about long-term risks and liability associated with GCS remain a hurdle to broad acceptance and large-scale deployment of CCS. Since 2010, the U.S. DOE’s National Risk Assessment Partnership (NRAP) – a research collaboration between five contributing national laboratories – has worked to establish and demonstrate methods and tools to quantify and manage the subsurface environmental risks associated with GCS, amidst uncertainty. This work supports the Office of Fossil Energy and Carbon Management Carbon Transport and Storage Program’s goal of advancing safe and secure commercial-scale GCS deployment. To address the technical challenge of simulating the physical response of the GCS site to large-scale CO2 injection, NRAP has adopted an approach that relies on coupling computationally efficient reduced-order and/or data-driven proxy models of important system components (i.e., storage reservoir, sealing caprock, leakage pathways, intermediate formations, overlying groundwater aquifers, and the atmosphere) in integrated assessment framework. That integrated model of the physical system is complemented with fit-for purpose functionality to support site characterization and risk-related decisions. The recently released NRAP Phase II toolset includes the Open-Source Integrated Assessment Model (NRAP-Open-IAM) for evaluation of trends in leakage risk and potential impact, tools to support monitoring design optimization (Designs for Risk Evaluation and Management – DREAM v3.0 and Passive Seismic Monitoring Tool - PSMT), and tools for state of stress evaluation (State-of-Stress Analysis Tool - SOSAT) and forecasting induced seismicity risk. The NRAP team has also released a pair of reports describing conceptual workflows to incorporate physics-based, quantitative risk assessment into many of the design, planning, operation, and closure decisions for GCS projects. An online catalogue highlights published studies where these tools and methods are demonstrated. In this presentation, the utility of these products to assess risks and address key stakeholder questions will be highlighted through examples, and related insights about the safety and security of geologic carbon storage in qualified storage sites will be discussed. The prospect of rapid, large-scale deployment of GCS technology to aggressively reduce anthropogenic CO2 emissions requires careful consideration of interference between multiple commercial-scale storage projects within a basin. Going forward, NRAP is expanding and adapting site-scale risk quantification tools and methods to enable assessment of risks and inform management decisions for basin-scale deployment. Increasingly, this work will leverage next-generation approaches for surrogate modelling, fast prediction, and advanced visualization enabled by machine learning and artificial intelligence to promote virtual learning, scenario evaluation, and augment risk-based decision making.

quantitative risk assessment, geologic carbon stor↗
DOE OSTI2023

What drives the variance of galaxy spectra?

We present a study aimed at understanding the physical phenomena underlying the formation and evolution of galaxies following a data-driven analysis of spectroscopic data based on the variance in a carefully selected sample. We apply principal component analysis (PCA) independently to three subsets of continuum-subtracted optical spectra, segregated into their nebular emission activity as quiescent, star-forming, and active galactic nuclei (AGNs). We emphasize that the variance of the input data in this work only relates to the absorption lines in the photospheres of the stellar populations. The sample is taken from the Sloan Digital Sky Survey (SDSS) in the stellar velocity dispersion range 100–150 km s −1 , to minimize the ‘blurring’ effect of the stellar motion. We restrict the analysis to the first three principal components (PCs) and find that PCA segregates the three types with the highest variance mapping SSP-equivalent age, along with an inextricable degeneracy with metallicity, even when all three PCs are included. Spectral fitting shows that stellar age dominates PC1, whereas PC2 and PC3 have a mixed dependence of age and metallicity. The trends support – independently of any model fitting – the hypothesis of an evolutionary sequence from star formation to AGN to quiescence. As a further test of the consistency of the analysis, we apply the same methodology in different spectral windows, finding similar trends, but the variance is maximal in the blue wavelength range, roughly around the 4000 Å break.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Transverse momentum dependent feed-down fractions for bottomonium production

We extract transverse-momentum-dependent feed-down fractions for bottomonium production using a data-driven approach. We use data published by the ATLAS, CMS, and LHCb Collaborations for √𝑠 =7 TeV proton-proton collisions. Based on this collected data, we produce fits to the differential cross sections for the production of both 𝑆- and 𝑃-wave bottomonium states. Combining these fits with branching ratios for excited state decays from the Particle Data Group, we compute the feed-down fractions for both the ϒ⁡(1⁢𝑆) and ϒ⁡(2⁢𝑆) as a function of transverse momentum. Our results indicate a strong dependence on transverse momentum, which is consistent with prior extractions of the feed-down fractions. When evaluated at the average momentum of the states, we find that approximately 75% of ϒ⁡(1⁢𝑆) and ϒ⁡(2⁢𝑆) states are produced directly. Our results for the transverse-momentum-dependent feed-down fractions are provided in tabulated form so that they can be used by other research groups.

Astronomy & Astrophysics↗
DOE OSTI2024

Personalized, disease-stage specific, rapid identification of immunosuppression in sepsis

Introduction Data overlapping of different biological conditions prevents personalized medical decision-making. For example, when the neutrophil percentages of surviving septic patients overlap with those of non-survivors, no individualized assessment is possible. To ameliorate this problem, an immunological method was explored in the context of sepsis. Methods Blood leukocyte counts and relative percentages as well as the serum concentration of several proteins were investigated with 4072 longitudinal samples collected from 331 hospitalized patients classified as septic (n=286), non-septic (n=43), or not assigned (n=2). Two methodological approaches were evaluated: (i) a reductionist alternative, which analyzed variables in isolation; and (ii) a non-reductionist version, which examined interactions among six (leukocyte-, bacterial-, temporal-, personalized-, population-, and outcome-related) dimensions. Results The reductionist approach did not distinguish outcomes: the leukocyte and serum protein data of survivors and non-survivors overlapped. In contrast, the non-reductionist alternative differentiated several data groups, of which at least one was only composed of survivors (a finding observable since hospitalization day 1). Hence, the non-reductionist approach promoted personalized medical practices: every patient classified within a subset associated with 100% survival subset was likely to survive. The non-reductionist method also revealed five inflammatory or disease-related stages (provisionally named ‘early inflammation, early immunocompetence, intermediary immuno-suppression, late immuno-suppression, or other’). Mortality data validated these labels: both ‘suppression’ subsets revealed 100% mortality, the ‘immunocompetence’ group exhibited 100% survival, while the remaining sets reported two-digit mortality percentages. While the ‘intermediary’ suppression expressed an impaired monocyte-related function, the ‘late’ suppression displayed renal-related dysfunctions, as indicated by high concentrations of urea and creatinine. Discussion The data-driven differentiation of five data groups may foster early and non-overlapping biomedical decision-making, both upon admission and throughout their hospitalization. This approach could evaluate therapies, at personalized level, earlier. To ascertain repeatability and investigate the dynamics of the ‘other’ group, additional studies are recommended.

Immunology↗
DOE OSTI2023

A General Spatiotemporal Imputation Framework for Missing Sensor Data

Many applications from precision agriculture, environmental monitoring and transportation networks rely on data collected across space and time over a large geographic area. Missing data poses a significant challenge for any data-driven inference and control tasks. Data imputation or the estimation of missing data can help fill these gaps by utilizing inherent spatial relationships and temporal patterns. A variety of spatiotemporal imputation models have been developed to address missing data in spatiotemporal datasets. However, these classical methods rely on the assumption that the underlying data follows a smooth trend and fail to provide accurate estimates when there is a large number of missing points in the data. Even though there are machine learning driven tensor completion approaches such as convolutional neural network based tensor completion (CoSTCo) that capture the non-linear relationships in the dataset, the transductive nature makes the algorithm less scalable. Thus, existing approaches for estimating the missing information do not effectively capture all dimensions of the spatiotemporal data structure, resulting in erroneous predictions and poor performance. The main contributions of this paper are: (1) We propose a novel inductive framework (G-LSTM) for missing data imputation that integrates a graph neural network with LSTMs to effectively capture both spatial and temporal dependencies. (2) Experimental results on a traffic dataset demonstrate that the proposed GNN integrated with an LSTM framework achieves improved imputation and maintains steady performance even when there are extreme missing conditions in comparison with the state-of-the-art imputation framework (i.e, CoSTCo). (3) The simulation results on a traffic network show up to 69% reduction in mean absolute error and 61% reduction in root mean square error when compared to CoSTCo.

Tharzeen, Aabila↗
DOE OSTI2018

Unsupervised Parsing of Gaze Data with a Beta-process Vector Auto-regressive Hidden Markov Model

The first stage of analyzing eye-tracking data is commonly to code the data into sequences of fixations and saccades. This process is usually automated using simple, predetermined rules for classifying ranges of the time series into events, such as “if the dispersion of gaze samples is lower than the threshold, then code as a fixation; otherwise code as a saccade.” More recent approaches incorporate additional eye-movement categories in automated parsing algorithms, particularly glissades, by using time-varying, data-driven thresholds. We describe an alternative approach using the beta-process auto-regressive hidden Markov model (BP-AR-HMM). The BP-AR-HMM offers two main advantages over existing frameworks. First, it provides a statistical model for eye movement classification rather than a single estimate. Second, the BP-AR-HMM uses a latent process to model the number and nature of the types of eye-movements and hence is not constrained to predetermined categories. We applied the BP-AR-HMM both to high-sampling rate gaze data from Andersson, Larsson, Holmqvist, Stridh, and Nyström (2016) and to low-sampling rate data from the DIEM project (Mital, Smith, Hill, & Henderson, 2011). Driven by the data properties, the BP-AR-HMM identified clusters of samples resembling saccades, fixations and smooth pursuit, and a category that approximately corresponds to glissades (as well as blinks, errors, etc.). The BP-AR-HMM serves as an effective algorithm for data-driven event parsing alone or as an initial step in exploring the characteristics of gaze data sets.

eye tracking, fixation, fixation, saccade, smooth ↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗