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At least 109 records · Page 6

Support for the 66th International Conference on Electron, Ion, and Photon Beam Technologies and Nanofabrication (Final Report)

This project aimed to enable student participation in the 66th International Conference on Electron, Ion, and Photon Beam Technologies and Nanofabrication (EIPBN). EIPBN, affectionately known as “3-Beams,” is the premier gathering of scientists and engineers who are dedicated to electron, ion and photon lithography, imaging, and analysis; nanofabrication process technologies; atomically precise fabrication; related emerging technologies; and their applications in a broad spectrum of fields. It is where top researchers from academia, government laboratories, and industries from around the world meet to present and discuss recent trends and future innovations in these technologies. The goal of the conference is to advance knowledge by enabling the exchange of information concerning advanced and emerging nanofabrication and nanomanufacturing topics and how they enable traditional and novel applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

In-Situ Process Monitoring Evaluation and Demonstration using Advanced Characterization with Laser Powder Bed Systems

Oak Ridge National Laboratory’s (ORNL) Manufacturing Demonstration Facility (MDF) worked with EOS Group to evaluate the current in-situ sensor capabilities of an EOS M290 Laser Powder Bed Fusion machine. The M290 was fitted with a 1 Mega-Pixel (MP) grayscale visible-light camera and a 5 MP temporally integrated (TI) near-infrared (NIR) camera. One print from stainless steel (SS) 316 and two from Inconel 625 (IN625) were performed where data including in-situ imaging and a machine log file were captured. These data were subsequently analyzed using a Dynamic Multi-Scale Segmentation Convolutional Neural Network (DMSCNN) trained on user defined classes and correlated to as-printed flaws, in the form of porosity, discovered in X-Ray Computed Tomography (XCT). In Phase I, two indications were detected in-situ and spatially correlated to stochastic lack-of-fusion flaws discovered using XCT. In Phase II, using these links from in-situ signatures to XCT flaw populations, a second neural network (NN) was trained to create a Voxelized Property Prediction Model (VPPM) to predict porosity percentages within the part using only features garnered from the in-situ data from two IN625 complex geometries. The VPPM was able to accurately predict porosity values for IN625 parts with an R 2 value of 0.764.

36 MATERIALS SCIENCE↗

In-Situ Process Monitoring Evaluation and Demonstration using Advanced Characterization with Laser Powder Bed Systems

Oak Ridge National Laboratory’s (ORNL) Manufacturing Demonstration Facility (MDF) worked with EOS Group to evaluate the current in-situ sensor capabilities of an EOS M290 Laser Powder Bed Fusion machine. The M290 was fitted with a 1 Mega-Pixel (MP) grayscale visible-light camera and a 5 MP temporally integrated (TI) near-infrared (NIR) camera. One print from stainless steel (SS) 316 and two from Inconel 625 (IN625) were performed where data including in-situ imaging and a machine log file were captured. These data were subsequently analyzed using a Dynamic Multi-Scale Segmentation Convolutional Neural Network (DMSCNN) trained on user defined classes and correlated to as-printed flaws, in the form of porosity, discovered in X-Ray Computed Tomography (XCT). In Phase I, two indications were detected in-situ and spatially correlated to stochastic lack-of-fusion flaws discovered using XCT. In Phase II, using these links from in-situ signatures to XCT flaw populations, a second neural network (NN) was trained to create a Voxelized Property Prediction Model (VPPM) to predict porosity percentages within the part using only features garnered from the in-situ data from two IN625 complex geometries. The VPPM was able to accurately predict porosity values for IN625 parts with an R 2 value of 0.764.

36 MATERIALS SCIENCE↗

Online thermal profile prediction for large format additive manufacturing: A hybrid CNN-LSTM based approach

Large format additive manufacturing (LFAM) is an advanced 3D printing technique that efficiently fabricates large-scale components through a layer-by-layer extrusion and deposition process. Accurate surface layer temperature monitoring is essential to prevent manufacturing failures and ensure final product quality. Traditional physics-based offline approaches for simulating thermal behavior are often inefficient and complex, posing challenges on real-time, in-situ monitoring. Here, to address this, we propose a data-driven hybrid CNN-LSTM model to predict sequential thermal images of arbitrary length using real-time infrared thermal imaging. In this approach, a Convolutional Neural Networks (CNN) is trained offline to capture spatial features, reduce dimensional complexity, and enhance time efficiency, while a stacked Long Short-Term Memory (LSTM) is applied online to capture temporal information for improved prediction of future thermal behavior in subsequent printing layers. Model performance is evaluated using MSE, SSIM, and PSNR metrics and is benchmarked against stacked LSTM and convolutional LSTM models, demonstrating superior accuracy and applicability. Additionally, to mitigate noise from moving extruders and gantry backgrounds in thermal images, a fine-tuned semantic segmentation model is implemented offline to extract printing geometry, enabling precise temperature tracking along the tool path for further thermal analysis. The frameworks developed in this study significantly advance temperature monitoring, thermal analysis, and in-situ manufacturing control for LFAM, bridging the gap between theoretical modeling and practical application.

Geometry extraction↗

Anisotropic Turbulent Flows Observed in Above-the-loop-top Regions during Solar Flares

Abstract Solar flare above-the-loop-top (ALT) regions are vital for understanding solar eruptions and fundamental processes in plasma physics. Recent advances in three-dimensional (3D) magnetohydrodynamic (MHD) simulations have revealed unprecedented details on turbulent flows and MHD instabilities in flare ALT regions. Here, for the first time, we examine the observable anisotropic properties of turbulent flows in ALT by applying a flow-tracking algorithm on narrow-band extreme-ultraviolet images that are observed from the face-on viewing perspective. First, the results quantitatively confirm the previous observation that vertical motions dominate and that the anisotropic flows are widely distributed in the entire ALT region with the contribution from both upflows and downflows. Second, the anisotropy shows height-dependent features, with the most substantial anisotropy appearing at a certain middle height in ALT, which agrees well with the MHD modeling results where turbulent flows are caused by Rayleigh–Taylor-type instabilities in the ALT region. Finally, our finding suggests that supra-arcade downflows (SADs), the most prominently visible dynamical structures in ALT regions, are only one aspect of turbulent flows. Among these turbulent flows, we also report the antisunward-moving underdense flows that might develop due to MHD instabilities, as suggested by previous 3D flare models. Our results indicate that the entire flare fan displays group behavior of turbulent flows where the observational bright spikes and relatively dark SADs exhibit similar anisotropic characteristics.

Xie, Xiaoyan (ORCID:0009000705827807)↗

Contaminant Investigation and Pre‐Processing Opportunities for Textile‐To‐Textile Recycling

Millions of metric tons of textiles are landfilled or incinerated each year in the United States, with less than 1% of textiles recycled into new clothing or fabrics. To counter this trend, a growing number of companies and researchers are exploring how a circular economy can be applied to support textile‐to‐textile recycling. A significant barrier they face comes down to quickly and efficiently extracting pure feedstock material from post‐consumer garments that feature a mix of natural and synthetic fibers. Textile recyclers prefer pure feedstocks, as working with mixed sources typically means lower throughput, higher risk of equipment failure, and diminished business margins. To facilitate a circular economy for textiles, methods, and technologies are needed that can efficiently separate out materials and contaminants from end‐of‐life textiles to increase the flow of pure feedstocks to recyclers. This paper summarizes findings from interviews with a cross section of textile recyclers and from a review of literature to define basic feedstock requirements. In addition to our qualitative research, we deconstruct a bale of post‐consumer textiles and analyze them using computer‐vision imaging, Fourier transform infrared spectroscopy (FTIR), and machine learning. The resulting data are used to set system‐level design inputs for an automated contaminant removal system to process post‐consumer clothing into appropriate feedstocks for recycling. To set the system's levels for automated real‐time near‐infrared analysis, we identify the minimum percentage of primary material that any single garment in a load of used clothing must contain for the average of the full output stream to meet the target purity levels of recyclers. Here, the envisioned automated system can also address undesirable trace materials that might contaminate the processed stream by using imaging cameras coupled with artificial intelligence to identify sections of clothing for de‐trimming. Proof‐of‐concept machine learning algorithms are evaluated to locate and identify trims or garment areas with hidden contaminant materials. Integrating these methods into automated textile cutting systems can provide a cost‐effective means for increasing feedstock purity from used clothing, which can advance circularity for textiles by helping recyclers to reach production volumes and quality targets that were not possible solely with manual dismantling operations.

Parsons, Ryan [Rochester Institute of Technology, ↗

Direct Observations of Solute Dispersion in Rocks With Distinct Degree of Sub‐Micron Porosity

Abstract The transport of chemical species in rocks is affected by their structural heterogeneity to yield a wide spectrum of local solute concentrations. To quantify such imperfect mixing, advanced methodologies are needed that augment the traditional breakthrough curve analysis by probing solute concentration within the fluids locally. Here, we demonstrate the application of asynchronous, multimodality imaging by X‐ray computed tomography (XCT) and positron emission tomography (PET) to the study of passive tracer experiments in laboratory rock cores. The four‐dimensional concentration maps measured by PET reveal specific signatures of the transport process, which we have quantified using fundamental measures of mixing and spreading. We observe that the extent of solute spreading correlate strongly with the strength of subcore‐scale porosity heterogeneity measured by XCT, while dilution is enhanced in rocks containing substantial sub‐micron porosity. We observe that the analysis of different metrics is necessary, as they can differ in their sensitivity to the strength and forms of heterogeneity. The multimodality imaging approach is uniquely suited to probe the fundamental difference between spreading and mixing in heterogeneous media. We propose that when multi‐dimensional data is available, mixing and spreading can be independently quantified using the same metric. We also demonstrate that one‐dimensional transport models have limited predictive ability toward the internal evolution of the solute concentration, when the model is solely calibrated against the effluent breakthrough curves. The data set generated in this study can be used to build realistic digital rock models and to benchmark transport simulations that account deterministically for rock property heterogeneity.

Kurotori, Takeshi [Department of Chemical Engineer↗

Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials: Part II Resveratrol Exemplar

This SAND report summarizes work supported by an Engineering Sciences Research Foundation (ESRF) Lab Directed Research and Development (LDRD) project entitled “Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials.” This SAND report is written in two parts with Part 1 discusses recrystallization of our explosive exemplar and Part 2 summarizing our work with recrystallization of resveratrol. We have studied resveratrol recrystallization with a multiscale approach combining experiments, modeling and simulation. At the single crystal scale, microscopy experiments illuminate crystal time-dependent growth rates using advanced image analysis. Bench scale experiments were carried out to look at growth of multiple particles in a small reactor creating thousands of particles and analyzing the results with microscopy and μCT. For the modeling we combine kinetic Monte Carlo (kMC) models with subscale information from density functional theory (DFT) or molecular dynamics. This work is discussed in Part 1 and can also be found in a paper from the project discussing a coarse-grained kMC model specifically developed for resveratrol. For well-mixed systems, we have population balance equations (PBE) linked with species mass conservation forming a set of ordinary differential equations that can be solved quickly. For more complicated geometries, such as the vat crystallization used throughout the complex, a coupled computational fluid dynamic (CFD)/PBE method was developed to account for gradients in temperature and concentration and differences in crystallization rates throughout the domain. These simulations are more complex and require high performance computing. We present results for two cases: 5% seed fast cool with parameters fit to the well-mixed case and 5% seed slow cool using the same parameters. We show reasonable agreement with experiments though are particles are significantly larger than the experiments.

36 MATERIALS SCIENCE↗

In situ electron microscopy: atomic-scale dynamics of metal oxidation and corrosion

Corrosion degrades metals through complex microscopic processes that traditional methods often fail to capture. In-situ transmission electron microscopy (TEM) bridges this gap by providing real-time atomic-scale imaging of oxidation and corrosion dynamics. Gas-phase TEM uncovers critical oxidation mechanisms like oxide nucleation and alloying effects, while liquid-phase TEM tracks corrosion initiation. Coupled with emerging techniques like ultrafast direct electron detection cameras, these advancements promise unprecedented resolution in understanding material degradation.

36 MATERIALS SCIENCE↗

SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications

This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.

Venturelli, Davide↗

Techno-economics of hydrocarbon fuel production and recyclables recovery from landfill-destined municipal solid waste: AI-enhanced materials recovery facility design

Sustainable aviation fuels (SAF) production from cellulosic paper fractions of municipal solid waste (MSW) destined for landfills has strong potential to advance environmental, social, and economic sustainability across the aviation and waste sectors. This study proposes an artificial intelligence-enabled material recovery facility (AI-MRF) design to efficiently characterize, separate, process, and convert recovered paper waste from MSW into intermediate chemicals and SAF. The AI-MRF, designed to process 233,091 metric tons of MSW annually, integrates smart manufacturing technologies including AI, visual and hyperspectral imaging, multi-sensor data, and traditional sorting systems. Well-characterized and sorted cellulosic paper waste was utilized for chemical and fuel production scenarios, while clean plastics, metals, and glass were considered for recycling. Conversion of paper waste into intermediate sugars achieved a net present value (NPV) of up to $\$67$ million. For sugar-to-SAF production scenarios, the minimum fuel selling price (MFSP) was calculated at $\$6.11$ per gasoline gallon equivalent (GGE) when excluding recyclable revenue, and $\$4.03$ per GGE when halving recyclable revenue. The MFSP was further reduced to $\$1.96$ per GGE when accounting for SAF sales and recyclables. Nationally, this approach could yield about 2 billion GGE of hydrocarbon fuel annually from available MSW in the United States.

09 BIOMASS FUELS↗

Patch-Based Convolutional Neural Networks for Multiple Microstructural Features Detection in FIB-SEM Micrographs of Irradiated Nuclear Fuel

Focused ion beam scanning electron microscopy (FIB-SEM) tomography has increasingly been utilized for acquiring three-dimensional (3D) microstructure features at the sub-micron scale in irradiated nuclear materials. This technique involves sequential ion beam slicing followed by electron beam imaging and compositional mapping using energy dispersive spectroscopy (EDS). Despite its growing use, several challenges persist. These include the time-intensive nature of data collection of EDS data, difficulties in distinguishing between various microstructures, and issues with image alignment. These challenges currently limit the broader application of FIB-SEM tomography in the field. To overcome these limitations, we propose using convolutional neural networks (CNNs) to automate microstructure identification in SEM images. Our study introduces a new framework for identifying microstructures in irradiated U-10Zr (wt. %) metallic fuel with limited annotated data. The framework includes the creation of a reliable annotated dataset with paired SEM and ground truth data from EDS maps, the applications of CNNs for microstructure identification, and the validation of model performance. Specifically, we employed the Segment Anything Model (SAM) to align SEM images with corresponding EDS maps and focused ion beam (FIB) tomography SEM data. We evaluate several models, including Patch-based U-Net, Attention U-Net, and Residual U-Net, finding that patch-based U-Net exhibits superior segmentation performance and consistency. This approach reduces reliance on EDS detectors and aids in accelerating nuclear material analysis process, highlighting the potential of advanced deep learning techniques to improve microstructural understanding in nuclear material. This is the first framework to integrate SAM and Patch-based CNN models for semantic segmentation of irradiated nuclear materials, with potential applicability to other tomography datasets.

36 - MATERIALS SCIENCE↗

High precision monitoring of outgassing species in model EUV photoresists with a cavity ring-down spectrometer

Extreme ultraviolet (EUV) photoresists play a pivotal role in advancing nanopatterning technologies by balancing image quality and sensitivity. The outgassing behavior of photoresist thin films under EUV and deep ultraviolet (DUV) exposure reveals chemical details relevant to their performance. This study focuses on utilizing an analytical technique not previously used in photolithography, the tabletop cavity ring-down spectrometer, to investigate outgassing dynamics in EUV photoresists, enabling precise chemical identification and deeper insights into resist processing. The spectrometer’s enhanced laser path length (~20 km) and broadband absorption capabilities in the CH overtone region allow for sensitive and temporally resolved detection of outgassed species. Using a model resist comprising a polymer matrix with a photoacid generator and quencher, we analyzed the influence of time delays between exposure and Post-Exposure Bake (PEB) as well as storage under varying environmental conditions. Suppression of isobutylene outgassing and thickness loss was observed with extended delays between exposure and PEB, potentially linked to water absorption and acid deactivation. The technique proved highly effective in distinguishing subtle chemical differences between processing stages. Delay times and their environmental conditions, particularly humidity, reduce outgassing and thickness loss of photoresists during PEB, suggesting decreased acid-driven deprotection. This can potentially impact sensitivity, defectivity, and roughness of resist patterns, necessitating precise monitoring and control.

Lüttgenau, Bernhard↗

Spatiotemporal dynamics of fast electron heating in solid-density matter via XFEL

Abstract High-intensity, short-pulse lasers are crucial for generating energetic electrons that produce high-energy-density (HED) states in matter, offering potential applications in igniting dense fusion fuels for fast ignition laser fusion. High-density targets heated by these electrons exhibit spatially non-uniform and highly transient conditions, which have been challenging to characterize due to limitations in diagnostics that provide simultaneous high spatial and temporal resolution. Here, we employ an X-ray Free Electron Laser (XFEL) to achieve spatiotemporally resolved measurements at sub-micron and femtosecond scales on a solid-density copper foil heated by laser-driven fast electrons. Our X-ray transmission imaging reveals the formation of a solid-density hot plasma localized to the laser spot size, surrounded by Fermi degenerate, warm dense matter within a picosecond, and the energy relaxation occurring within the hot plasma over tens of picoseconds. These results validate 2D particle-in-cell simulations incorporating atomic processes and provide insights into the energy transfer mechanisms beyond current simulation capabilities. This work significantly advances our understanding of rapid fast electron heating and energy relaxation in solid-density matter, serving as a key stepping stone towards efficient high-density plasma heating and furthering the fields of HED science and inertial fusion energy research using intense, short-pulse lasers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-precision monitoring of outgassing species in model extreme ultraviolet photoresists with a cavity ring-down spectrometer

Background Extreme ultraviolet (EUV) photoresists play a pivotal role in advancing nanopatterning technologies by balancing image quality and sensitivity. The outgassing behavior of photoresist thin films under EUV and deep ultraviolet (DUV) exposure reveals chemical details relevant to their performance. Aim Here, we focus on utilizing an analytical technique not previously used in photolithography, the tabletop cavity ring-down spectrometer, to investigate outgassing dynamics in EUV photoresists, enabling precise chemical identification and deeper insights into resist processing. Approach The spectrometer’s enhanced laser path length (∼ 20 km) and broadband absorption capabilities in the C–H overtone region allow for sensitive and temporally resolved detection of mixtures of outgassed species. Using a model resist comprising a polymer matrix with a photoacid generator and quencher, we analyzed the influence of time delays between exposure and post-exposure bake (PEB) as well as storage under varying environmental conditions. Results Suppression of isobutylene outgassing and thickness loss was observed with extended delays between exposure and PEB, potentially linked to water absorption and acid deactivation. The technique proved highly effective in distinguishing subtle chemical differences between processing stages. Conclusions Delay times and their environmental conditions, particularly humidity, reduce outgassing and thickness loss of photoresists during PEB, suggesting decreased acid-driven deprotection. This can potentially impact sensitivity, defectivity, and roughness of resist patterns, necessitating precise monitoring and control.

Extreme ultraviolet photoresists↗

Distinguishing isotropic and anisotropic signals for X-ray total scattering using machine learning

Understanding structure–property relationships is essential for advancing technologies based on thin films. X-ray pair distribution function (PDF) analysis can access relevant atomic structure details spanning local-, mid- and long-range structure. While X-ray PDF has been adapted for thin films on amorphous substrates, measurements on single-crystal substrates are necessary to accurately determine structure origins for some thin film materials, especially those for which the substrate changes the accessible structure and properties. However, when measuring films on single-crystal substrates, high-intensity anisotropic Bragg spots saturate 2D detector images, overshadowing the thin films' isotropic scattering signal. This renders previous data processing methods for films on amorphous substrates unsuitable for films on single-crystal substrates. To address this measurement need, we developed IsoDAT2D, an innovative data processing approach using unsupervised machine learning algorithms. The program combines dimensionality reduction and clustering algorithms to separate thin film and single-crystal substrate X-ray scattering signals. We use SimDAT2D , a program we developed to generate simulated thin film data, to validate IsoDAT2D . Here we also use IsoDAT2D to isolate X-ray total scattering signal from a thin film on a single-crystal substrate. The resulting PDF data are compared with similar data processed using previous methods, especially substrate subtraction for single-crystal and amorphous substrates. PDF data from IsoDAT2D -identified X-ray total scattering data are significantly better than from single-crystal substrate subtraction, but not as reliable as PDF data from amorphous substrate subtraction. With IsoDAT2D , there are new opportunities to expand PDF to a wider variety of thin films, including those on single-crystal substrates, with which new structure–property relationships can be elucidated to enable fundamental understanding and technological advances.

36 MATERIALS SCIENCE↗

Understanding Formation of Irradiation-Induced Defects through 4D-STEM, Electron Tomography, and WBDF-STEM

A major challenge in advancing nuclear materials for next-generation fission and proposed fusion reactors is to comprehensively understand the formation of irradiation-induced defects. Here it is essential to correlate the evolution of irradiation-induced defects and the degradation of mechanical properties, as they collectively dictate the material's lifespan and ensure nuclear safety. Scanning transmission electron microscopy (STEM) based techniques have emerged as indispensable tools for irradiation-induced defect characterization, offering high spatial resolution imaging and chemical analysis, such as electron energy loss spectroscopy (EELS) and energy dispersive X-ray spectroscopy (EDXS). These techniques have been effectively used to obtain an atomic-scale view of the defect structure. Recent advances in electron microscopy, particularly in 4D-STEM, offer detailed insight into microstructural evolution by capturing full 2D diffraction patterns at every pixel position. Using high-speed direct electron detectors, this technology generates a four-dimensional dataset, overcoming the limitations of traditional STEM imaging.

36 MATERIALS SCIENCE↗

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗