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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Remote Development Process and Platform for Power Electronic Systems

Like many areas in research and development, power electronic and distributed energy resource research and development slowed during the COVID pandemic. While the presence of the virus has reduced and workers are returning to shared offices, uncertainty of potential future challenges are still present. This work proposes a development and testing network that provides researchers the ability to operate remotely and coordinate control and debug activities for power electronic systems. This development and testing network has been demonstrated in both controller hardware-in-the-loop (C-HIL) and hardware testing.

Starke, Michael↗
DOE OSTI2025

Modeling Cyber Supply Chain Incidents with Multilayered Graph Motifs

As noted within the literature, supply chain includes people and organizations---manufacturers, integrators, and third-party vendors---that are involved in one or more stages of a product lifecycle. Since supply chains, by definition, include organizations and people, supply chain risk management activities must consider dependencies between an organization's business processes and third-party resources. Just as adversarial tactics can be implemented via techniques implemented via networked computer systems, so can such tactics be expressed via legal business relationships. A cyber incident may have an exponential impact downstream, for example, by leveraging a product's distribution channel (e.g. malicious updates in SolarWinds, buggy updates in CrowdStrike). Similarly, legitimate and legal business relationships also affect the attack surface exposure of systems, enabling long-term persistence and/or unknown impacts to product quality that are hard to detect. This paper catalogs several recent digital supply chain incidents and applies a multilayered network formalism to develop structural indicators (graph motifs) that reflect potentially-adversarial behavior. Finally, we compare and contrast the characteristics of adversarial tactics (e.g. Loss of Availability, Data Collection) that leverage cyber-physical dependencies to those that leverage legal organizational relationships.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High Energy Physics Network Requirements Review: Two-Year Update

The Energy Sciences Network (ESnet) is the high-performance network user facility for the US Department of Energy (DOE) Office of Science (SC) and delivers highly reliable data transport capabilities optimized for the requirements of data-intensive science. In essence, ESnet is the circulatory system that enables the DOE science mission by connecting all its laboratories and facilities in the US and abroad. ESnet is funded and stewarded by the Advanced Scientific Computing Research (ASCR) program and managed and operated by the Scientific Networking Division at Lawrence Berkeley National Laboratory (LBNL). ESnet is widely regarded as a global leader in the research and education networking community. ESnet interconnects DOE national laboratories, user facilities, and major experiments so that scientists can use remote instruments and computing resources as well as share data with collaborators, transfer large datasets, and access distributed data repositories. ESnet is specifically built to provide a range of network services tailored to meet the unique requirements of the DOE’s data-intensive science. In July 2023, the Energy Sciences Network (ESnet) and the High Energy Physics program (HEP) of the DOE SC organized an interim ESnet requirements review of HEP-supported activities, to follow up on the work started during the 2020 HEP Network Requirements Review. Preparation for these events included checking back with the key stakeholders: program and facility management, research groups, and technology providers. Each stakeholder group was asked to prepare updates to their previously submitted case study documents, so that ESnet could update the understanding of any changes to the current, near-term, and long-term status, expectations, and processes that will support the science activities of the program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Covalent Triazine Framework-Derived Membranes: Engineered Sol–Gel Construction and Gas Separation Application

Covalent triazine frameworks (CTFs) represent one of the most extensively studied organic networks characterized by graphitic π-conjugated structures linked by aza-fused rings, possessing unique features such as compositions of light elements (e.g., C, H, and N), porous architectures abundant heteroatom involvement, and extensively conjugated structures. In addition, the textural and chemical structures of CTFs could be engineered via synthesis control to accommodate diverse applications. CTF materials with notable characteristics, including plentiful (ultra-)micropores, high surface areas, and the presence of CO 2 -philic functional groups involving nitrogen (N), oxygen (O), and fluorine (F), hold great promise as potential candidates for anthropogenic CO 2 capture and sequestration (CCS) applications. However, the conventional high-temperature involved ionothermal procedures and the solution-based coupling pathway only afforded CTF materials in powder form, which is difficult to be processed toward membrane formation. Successful fabrication of CTF-derived membranes will rely on the development of alternative polymerization approaches as well as structural engineering to afford membrane architectures with controllable porosity distribution and active interaction sites with CO 2 benefiting the CO 2 separation procedure. In this Account, a demonstration of the latest progress in the development of CTF-derived membranes was provided. The CTF membranes were mainly synthesized via a superacid (e.g., CF 3 SO 3 H)-promoted sol–gel approach involving the polymerization of aromatic nitrile monomers. The formation of the triazine unit through the trimerization of cyano groups served as the cross-linkers, resulting in the creation of π-conjugated networks alongside the arenes present in the starting materials. The aromatic nitrile monomers with rigid and sterically hindered structures were required to afford CTF membranes with nanoporous architectures. The acidity of the superacid and reactivity of the aromatic monomers played critical roles in the polymerization efficiency. The monomer diversity and synthesis tunability endowed the introduction of CO 2 -philic functionalities (e.g., pyrazole and fluorine) within the CTF skeletons, and integration of ionic moieties was achieved by adopting FSO 3 H with stronger acidity as the catalyst and aromatic nitrile monomers with pyrazine structures. To ensure the successful construction of fluorinated CTF membranes, it is important to avoid any fluorines on the ortho-position of the cyano groups on the benzene ring. Through control over the monomers and reaction conditions, flexible, transparent, and insoluble CTF membranes could be fabricated. The sol–gel method could be further expanded to membrane fabrication through acetyl-to-benzene transformation through synthesis control. The mild oxidation-exfoliation-filtration method was also demonstrated to fabricate substrate-supported CTF membranes. The as-afforded membranes are well characterized to determine the structural features and provide information to study the structure-performance relationship. Here, the application of CTF membranes in CO 2 separation was summarized, focusing on the approaches being developed to enhance CO 2 uptake and separation performance. In addition to utilizing the pristine CTF membranes for gas separation, functionalized carbon molecular sieve membranes could be obtained from the pyrolysis of thermally stable CTF membrane precursors toward efficient CO 2 separation, benefiting from the abundant ultramicropores being created during the pyrolysis/decomposition procedure and involvement of CO 2 -philic functionalities such as fluorine and nitrogen-containing moieties. Based on these achievements, unsolved issues in CTF membrane-related fabrication and applications, including the potential solution approaches, have been proposed to advance the application of CTF membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Exponential Escape Rate of Filamentary Incubation in Mott Spiking Neurons

Mott materials such as vanadium oxides, when subject to a strong applied voltage, present an inhomogeneous insulator-to-metal transition with formation of metallic filaments within the insulating bulk. This property is enabling the development of compact and power-efficient neuromorphic devices known as Mott neurons. However, the nature of the transition has not been fully understood yet, as it may be attributed to different effects, including Joule self-heating and hot-carrier injection. Moreover, the experimental determination of the threshold voltage needed to induce the transition has proven to be challenging, as the transition becomes increasingly unpredictable when the threshold is approached. The physical understanding of these issues would not only deepen our understanding of Mott insulators, but would also be an important step toward the realization of neuromorphic devices based on such materials. In this work we use numerical simulations based on the Mott resistor network model to study the nature of the filament incubation and formation process. Here, we show that both electronic and thermal effects, in the form of current density focusing and Joule self-heating, respectively, contribute to the filamentary incubation and growth. Remarkably, we find that the percolation of the metallic filaments near the threshold is intrinsically stochastic, qualitatively similar to the familiar Arrhenius activated behavior and to the stochastic firing of biological neurons. More precisely, we characterize the filament percolation as a Poisson point process, which has the same probability distribution as mathematical models of neuronal firing with an exponential escape rate. Finally, we support the numerical simulation results by performing experiments in VO 2 that are in agreement with the exponential escape rate behavior. Thus, we establish a functionality of Mott insulators that opens a path toward implementing neuromorphic hardware with quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Low-latency NuMI Trigger for the CHIPS-5 Neutrino Detector

The CHIPS R&D project aims to develop affordable water Cherenkov detectors for large-scale underwater installations. In 2019, a 5kt prototype detector CHIPS-5 was deployed in northern Minnesota to study neutrinos generated by the nearby NuMI beam. This contribution presents a dedicated low-latency time distribution system for CHIPS-5 that delivers timing signals from the Fermilab accelerator to the detector with sub-nanosecond precision. Exploiting existing NOvA infrastructure, the time distribution system achieves this only with open-source software and conventional network elements. In a time-of-flight study, the presented system has reliably offered a time budget of $610 \pm 330\text{ ms}$ for on-site triggering. This permits advanced analysis in real-time as well as a novel hardware-assisted active triggering mode, which reduces DAQ computing load and network bandwidth outside triggered time windows.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Evaluating Energy Savings Measures for Building Retrofits in an Interactive Workshop Environment

As part of the Better Buildings Summit 2025, a workshop was developed to simulate the decision process for implementing a set of energy savings measures on an existing building. As part of the workshop a "game" was created around energy savings strategies, and workshop participants selected renovation cards that provided data around the impacts of that renovation choice. Participants then were able to calculate overall savings and payback from the selected retrofit opportunities. This publication has been produced to package the resources used in the activity in an organized document so that the materials can be distributed and reused more broadly. It provides a comprehensive framework for replicating the workshop, including step-by-step instructions, retrofit "game cards" with data points, and facilitation guidance. By using these materials, readers can conduct their own version of this interactive workshop with stakeholders in their networks, such as building owners, energy managers, or policy makers. The goal is to empower users to simulate the decision-making processes for energy projects, foster collaboration, and drive meaningful discussions around cost-effective retrofit opportunities and goal-oriented outcomes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Real-time confinement regime detection in fusion plasmas with convolutional neural networks and high-bandwidth edge fluctuation measurements

Abstract A real-time detection of the plasma confinement regime can enable new advanced plasma control capabilities for both the access to and sustainment of enhanced confinement regimes in fusion devices. For example, a real-time indication of the confinement regime can facilitate transition to the high-performing wide-pedestal (WP) quiescent H-mode, or avoid unwanted transitions to lower confinement regimes that may induce plasma termination. To demonstrate real-time confinement regime detection, we use the 2D beam emission spectroscopy (BES) diagnostic system to capture localized density fluctuations of long wavelength turbulent modes in the edge region at a 1 MHz sampling rate. BES data from 330 discharges in either L-mode, H-mode, quiescent H (QH)-mode, or WP QH-mode were collected from the DIII-D tokamak and curated to develop a high-quality database to train a deep-learning classification model for real-time confinement detection. We utilize the 6×8 spatial configuration with a time window of 1024 µ s and recast the input to obtain spectral-like features via fast Fourier transform preprocessing. We employ a shallow 3D convolutional neural network for the multivariate time-series classification task and utilize a softmax in the final dense layer to retrieve a probability distribution over the different confinement regimes. Our model classifies the global confinement state on 44 unseen test discharges with an average F 1 score of 0.94, using only ∼1 ms snippets of BES data at a time. This activity demonstrates the feasibility for real-time data analysis of fluctuation diagnostics in future devices such as ITER, where the need for reliable and advanced plasma control is urgent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2022

Sensing Electrical Networks Securely & Economically (SENSE)

The growing adoption of distributed energy resources (DERs) like battery energy storage systems and roof top solar/PV and the rapid penetration of electric vehicles (EVs), the electric grid is undergoing a major transformation with elevated stress on legacy grid assets. Despite a lot of expenditure to address these challenges, both in dollars and manpower, utilities have not been able to receive the value that was promised. The gains have been most visible at the transmission and substation level, especially where the main objective was improving operational and economic efficiency for the utility. Improving visibility and control at a few select points enhances the existing and established paradigm of centralized command and control. With changing load patterns, load types and the overall transition to an “active grid”, the centralized control and coordination paradigm gets challenged. To address the challenges, a new architecture and mechanism is needed, one that supports decentralized control and decision making, extracting value streams at the grid edge, particularly as the changes are fueled by transitions occurring in the distribution system. To address this, a communications and data processing platform, “GAMMA” was developed and demonstrated through the project. At the heart of the platform, are distributed, intelligent edge nodes with sensing and compute capabilities, that can record and analyze information locally. They are embedded in sensors and actuators specific to different distribution system applications. Phase 1 of the project focused on developing novel sensor technology that can be used for monitoring utility pole top distribution transformers. The sensors were designed with the objective of being low-cost, communicating with the GAMMA cloud using novel “delay-tolerant” networking using Bluetooth and a secure mobile application. They were non-intrusive in nature so that they can be installed quickly in the field, resulting in overall low cost of deployment and operations. Following the successful completion of Phase 1, the team manufactured 100 units for a field demonstration in Phase 2. The field demonstration was carried out on two real feeder systems with the local utility partner. In total, 100 sensors were installed and operated over a period of 6 months in the state of Georgia. The platform is operational end to end, with the cloud infrastructure deployed on a distributed, serverless environment that can serve multiple data streams, an analytics engine and a portal to securely view the data from multiple assets. The data collected through the GAMMA Mobile Phone app showcased the viability of the novel delay tolerant networking architecture, and the data processing algorithms developed through the course of the project, were successful in extracting important information about the overall network, improving the utility’s visibility and situational awareness in the distribution feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Efficient and mechanically-robust organic solar cells based on vertical stratification modulation through sequential blade-coating

Mechanically durable organic solar cells (OSCs) with high efficiency are deemed as the ideal candidate for the power source of the next generation wearable electronic devices. However, the brittle nature of small molecules in most high-efficiency OSCs consisting of polymer and small molecule encourages easy formation of cracks in the photoactive film under deformation. Here, the vertical composition distribution of the active layer has been well optimized through sequential blade coating to realize highly deformable while efficient OSC. The optimized morphology exhibits distinct donor-rich and homogenous region distributed along the vertical direction in the bulk. The donor-rich region provides sufficient chain entanglements and strong interfaces beneficial for mechanical robustness of film, while homogeneously mixed region offers continuous interpenetrating network to maintain high device through-put, resulting in superior efficiency of 14.4% with high crack-onset strain (COS) of 30.5%. This efficiency versus COS combination is much higher than the best combination reported in all polymer systems (COS of 15.9% and efficiency of 11.1%). To the best of our knowledge, it is the highest COS value achieved in polymer-small molecule systems. As a result, the rational control over vertical stratification demonstrated here would guide researchers in the development of innovative wearable electronics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Cyclic strain enhances the early stage mineral nucleation and the modulus of demineralized bone matrix

The adaptive response of bones to mechanical loading is essential for musculoskeletal development. Despite the importance of collagen in bone mineralization, little is known about how cyclic strain influences physicochemical responses of collagen, especially at the early stage of mineralization when the levels of strain are higher than those in mature bones. The findings in this study show that, without any cell-mediated activity, cyclic strain increases nucleation rates of calcium phosphate (CaP) nanocrystals in highly-organized collagen matrices. The cyclic strain enhances the transport of mineralization fluids with nucleation precursors into the matrix, thus forming more CaP nanocrystals and increasing the elastic modulus of the collagen matrix. The results also suggest that the multiscale spatial distribution of nanocrystals in the fibrous collagen network determines tissue-level mechanical properties more critically than the total mineral content. Furthermore, by linking nano- and micro-scale observations with tissue-level mechanical properties, we provide new insights into designing better biomaterials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Adaptive Hierarchical Cyber Attack Detection and Localization in Active Distribution Systems

Development of a cyber security strategy for the active distribution systems is challenging due to the inclusion of distributed renewable energy generations. Here this paper proposes an adaptive hierarchical cyber attack detection and localization framework for distributed active distribution systems via analyzing electrical waveforms. Cyber attack detection is based on a sequential deep learning model, via which even minor cyber attacks can be identified. The two-stage cyber attack localization algorithm first estimates the cyber attack sub-region, and then localize the specified cyber attack within the estimated subregion. We propose a modified spectral clustering-based network partitioning method for the hierarchical cyber attack ‘coarse’ localization. Next, to further narrow down the cyber attack location, a normalized impact score based on waveform statistical metrics is proposed to obtain a ‘fine’ cyber attack location by characterizing different waveform properties. Finally, compared with classical and state-of-art methods, a comprehensive quantitative evaluation with two case studies shows promising estimation results of the proposed framework.

42 ENGINEERING↗
DOE OSTI2020

Discrete Fracture Network Modeling to Estimate Upscaled Parameters for the Topopah Spring, Lava Flow, and Tiva Canyon Aquifers at Pahute Mesa, Nevada National Security Site

This report describes the results of Discrete Fracture Network (DFN) simulations for the Topopah Spring Aquifer (TSA), Lava Flow Aquifer, and Tiva Canyon Aquifer (TCA), at Pahute Mesa on the Nevada National Security Site (NNSS), formerly the Nevada Test Site. The research focuses on calculating upscaled groundwater flow and contaminant transport parameters using DFNs generated according to fracture characteristics observed in the TSA, LFA and TCA at Pahute Mesa. The highly fractured and heterogeneous nature of these aquifers makes them candidates for stochastic DFN modeling of radionuclide transport on a small scale with subsequent upscaling. One hundred independent DFN realizations are generated for each aquifer, and the upscaled parameters for continuum simulations of subsurface flow and transport in fractured media at Pahute Mesa are calculated. Our goal is to implement a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, such as channelization of flow and transport along a few well connected, large fractures. Additionally, to simulate advective and advective-diffusive transport through the fracture networks, the Time Domain Random Walk (TDRW) approach is applied to account for matrix diffusion into a finite half-space. Moreover, a novel approach to calculate dynamic (active) fracture surface area to reflect flow channeling is implemented. This work will improve the representation of radionuclide transport processes in largescale, regulatory-focused models by providing estimates of hard-to-measure flow and contaminant transport parameters at large scales. In this report, we (1) show recent results of flow and transport simulations on multiple DFN realizations of the TSA, LFA, TCA; (2) discuss the resulting distributions of estimated upscaled parameters; (3) describe the estimation of upscaled parameters for an equivalent parallel-plate continuum model and (4) present a comparison between simulated transport from the equivalent continuum model and an actual DFN.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Learning interpretable surface elasticity properties from bulk properties via neural network equation learners

Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness. However their analytical expressions are typically difficult to derive from atomistic data, and depend strongly on modeling choices. This work presents a neural network-based equation learner which combines customized activation functions and connection-based pruning to discover parsimonious, closed-form equations for surface elasticity from atomistic simulations. Applying the method to seven face-centered cubic (FCC) metals, our equation learner uncovers interpretable equations that describe both low-Miller index and high-Miller index surface properties, capturing long-tail property distributions accurately. The discovered expressions are decoupled into two components: a universal, geometry-driven orientation function, and material-specific baseline coefficients. We find that lower-order properties such as surface tension are fundamentally geometry dependent, while higher-order properties such as surface stress and elasticity show more complex geometry and material dependence. We also relate material dependent coefficients to bulk properties, forming a clear map from bulk material properties to surface elasticity. Overall, this approach demonstrates that interpretable neurosymbolic machine learning can bridge the gap between atomistic simulations and physical laws, enabling the discovery of generalizable structure–property relationships for materials science phenomena such as surface elasticity.

Equation learning↗
DOE OSTI2022

Risk-Based Dispatch Bound Calculator

This calculator outputs time-varying lower and upper bounds (matrices), called dispatch bounds, for the controllable portions of the power injections at each node in a distribution network to guarantee that the voltage magnitudes stay within prescribed bounds with at least a given probability for any set of power injections that are within their dispatch bounds. The calculator is meant to be a tool for a central controller of a distribution network to set dispatch bounds for each node that allows each node to independently decide their actual power injection within their dispatch bound. The user can choose whether to assume the forecast errors of the uncontrollable power injections are gaussian or are worst-case (distributionally robust). The user can choose whether the dispatch bounds include the controllable reactive power or just the active power under a constant power factor assumption.

Comden, Joshua↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for inverse problems: Determining material properties for heterogeneous systems

Here, we determine spatially varying discontinuous material properties using a domain-decomposition based physics-informed neural networks (PINNs) framework named the Adaptive Interface-PINNs or AdaI-PINNs (Roy et al., 2024). We propose the use of distinct neural networks for the field variables and material properties within each material, utilizing adaptive activation functions. While the neural networks across different materials share the same weights and biases, their activation functions are uniquely tailored using a hyperparameter that influences the slope of the activation function. The proposed framework is tested on several one-dimensional and two-dimensional benchmark examples, and its performance is compared with conventional PINNs and existing domain-decomposition PINNs frameworks, namely, the Multi-domain physics-informed neural network (M-PINN), and the eXtended physics-informed neural networks (XPINNs). The results demonstrate that the proposed approach can determine randomly distributed discontinuous material properties with an L 2 error of $\mathscr{O}$ (10 -3 ) for the material property and the root-mean-square error of $\mathscr{O}$ (10 -3 ) for the primary variable while the other approaches yield errors that are approximately two orders of magnitude larger (that is, $\mathscr{O}$ (10 -1 )). Moreover, the spatial distribution of material properties obtained using the proposed framework is in close agreement with the true distribution, whereas the other approaches fare much worse. Additionally, the proposed approach is approximately 40% faster than its competitors, indicating its potential as a robust alternative for solving inverse problems in heterogeneous materials.

36 MATERIALS SCIENCE↗