Diffusion Model Research Articles

Degradation generation and prediction based on machine learning methods: A comparative study

In engineering practice, degradation analysis often suffers from the small-sample problem. To this end, several generative models are developed to expand the degradation data, based on which both the original data and the synthetic data are used to train neural networks for degradation prediction. However, these methods are rarely compared with each other, and the performances of competitive candidates are not explored. Given this, this paper reviews some machine learning-based methods and performs a comparison among them. Particularly, a segmented sampling method is proposed and the diffusion model is introduced for degradation generation. Results of both numerical simulations and case studies show that none of these methods can perform best in all cases, yet making use of synthetic data improves the predictive performance. Overall, the time-series generative adversarial network and the segmented sampling method are recommended for degradation generation, and the gated recurrent unit network is recommended for prediction.

Fractional Diversity Entropy: A Vibration Signal Measure to Assist a Diffusion Model in the Fault Diagnosis of Automotive Machines

Real-world vibration signal acquisition of automotive machines often results in imbalanced sample sets due to restricted test conditions, adversely impacting fault diagnostic accuracy. To address this problem, we propose fractional diversity entropy (FrDivEn) and incorporate it into the classifier-guided diffusion model (CGDM) to synthesize high-quality samples. Additionally, we present a corresponding imbalanced fault diagnostic method. This method first converts vibration data to Gramian angular field (GAF) image samples through GAF transformation. Then, FrDivEn is mapped to the gradient scale of CGDM to trade off the diversity and fidelity of synthetic samples. These synthetic samples are mixed with real samples to obtain a balanced sample set, which is fed to the fine-tuned pretrained ConvNeXt for fault diagnosis. Various sample synthesizers and fault classifiers were combined to conduct imbalanced fault diagnosis experiments across bearing, gearbox, and rotor datasets. The results indicate that for the three datasets, the diagnostic accuracies of the proposed CGDM using FrDivEn at an imbalance ratio of 40:1 are 91.22%, 87.90%, and 98.89%, respectively, which are 7.32%, 11.59%, and 3.48% higher than that of the Wasserstein generative adversarial network (WGAN), respectively. The experimental results across the three datasets validated the validity and generalizability of the proposed diagnostic method.

Understanding the Kinetics of Cation Insertion-Coupled Electron Transfer in Thin Film Electrodes from Cyclic Voltammetry

Cyclic voltammetry is a powerful technique for probing the electrochemical kinetics of energy storage materials. However, interpretation of the cyclic voltammetry kinetics of such materials has been limited by the application of analytical solutions initially developed for ion blocking electrodes, whereby mass transport is limited to semi-infinite diffusion in the electrolyte medium. Here, we utilize established numerical simulation models for finite diffusion coupled with experimental results of a model insertion electrode to demonstrate the relationship between solid-state diffusion and cyclic voltammetry current, peak potential, and capacity. This simulation is publicly available.1 We show that the cyclic voltammetry response of thin film electrode materials undergoing solid-solution ion insertion without significant Ohmic polarization can be explained with finite diffusion. Specifically, we investigate the kinetic behavior of Li+ insertion-coupled electron transfer into thin films of orthorhombic Nb2O5. We observe a general trend in the b-value, a descriptive parameter derived from the relation ip=avb between peak current ip and scan rate v. We find that both in simulation and experiment, we can tune the b-value response between the theoretically limiting values of 0.5 and 1 based on the solid-state diffusion characteristics of the thin film and the experimental timescale. We also show that b-values below 0.5 are possible, and arise due to a combined effect of the potential window of the experiment and confined diffusion. Our findings show the power of a simple 1D finite-diffusion model for predicting the kinetic response of an electrode undergoing ion-coupled electron transfer, and help to inform on how the scan rate selection in voltammetry experiments affects the observed kinetic behavior. https://github.com/mchagnot/Numerical_CV_Sim_1D_Diffusion

(Battery Student Slam 8 Award Winner) Multi-Clustered Lithium Diffusion in Single-Crystalline NMC Battery Particles

Understanding the diffusion dynamics of lithium within solid-state electrodes is pivotal for developing high-performance batteries. In this context, layered oxides were utilized as a promising cathode material due to their high energy density and fast intraparticle lithium diffusivity. Despite advancements in material composition, coating, and doping, the understanding of intraparticle lithium diffusion has long been described by Fick's law. Conventionally, lithium diffusion is assumed to generate a monotonic lithium concentration gradient within solid-solution single-crystalline battery materials during cycling. This raises fundamental questions about diffusion in layered oxides; (1) Can the diffusion of Li in solids be interpreted as Fickian diffusion, similar to diffusion in gases or liquids, even though it involves structural and phase evolution throughout the battery cycle? and, (2) Does the fast diffusivity (10-11-10-9 cm2/s) support the homogenization of Li?In this study, we address these questions surrounding lithium diffusion in layered oxide by utilizing operando scanning transmission X-ray microscopy. We revealed the formation of mobile Li-dense/-dilute nano-domains within individual single-crystalline LiNi1/3Mn1/3Co1/3O2 (scNMC) during battery cycles. We term this phenomenon ‘multi-clustered lithium diffusion’, distinguishing our findings from the conventionally suggested Fickian diffusion model in solid-solution materials. These domains persist for at least 4 hours during relaxation, accompanied by locally residing strained domains, as confirmed by Bragg coherent diffraction imaging (BCDI), within a single particle. We believe these domains arise due to the compensation of localized chemical potential gradients that are generated by the sustained presence of strain within the battery particles during cycling.While maintaining integrity of Li-dense/-dilute domain at various C-rates, STXM result further show that Li-dilute domains maintain during the discharging. Given the lower concentration of Li at insertion boundaries, which could lower the surface charge transfer impedance of the system, Li-dilute domains facilitate lithium transport by functioning as low-resistance pathways. Through a comprehensive analysis of electrical impedance spectroscopy (EIS), STXM imaging and finite element analysis (FEA), we showed that controlling the local domain fraction is crucial for controlling the overpotential during subsequent charging. Our study introduces new insights into nanoscale solid-state diffusion, thereby enabling the fabrication of high-performance batteries. Figure 1

Leveraging Visual Language Model and Generative Diffusion Model for Zero-Shot SAR Target Recognition

Simulated data play an important role in SAR target recognition, particularly under zero-shot learning (ZSL) conditions caused by the lack of training samples. The traditional SAR simulation method is based on manually constructing target 3D models for electromagnetic simulation, which is costly and limited by the target’s prior knowledge base. Also, the unavoidable discrepancy between simulated SAR and measured SAR makes the traditional simulation method more limited for target recognition. This paper proposes an innovative SAR simulation method based on a visual language model and generative diffusion model by extracting target semantic information from optical remote sensing images and transforming it into a 3D model for SAR simulation to address the challenge of SAR target recognition under ZSL conditions. Additionally, to reduce the domain shift between the simulated domain and the measured domain, we propose a domain adaptation method based on dynamic weight domain loss and classification loss. The effectiveness of semantic information-based 3D models has been validated on the MSTAR dataset and the feasibility of the proposed framework has been validated on the self-built civilian vehicle dataset. The experimental results demonstrate that the first proposed SAR simulation method based on a visual language model and generative diffusion model can effectively improve target recognition performance under ZSL conditions.

Cold SegDiffusion: A novel diffusion model for medical image segmentation

Medical image segmentation is crucial in accurately identifying and delineating regions of interest in medical images, which can inform the diagnosis and treatment of various diseases. Therefore, developing high-performance computer-aided diagnosis systems for medical image segmentation has become a prominent focus within computer vision. With the development of deep learning, diffusion models have exhibited remarkable performance in medical image segmentation tasks. However, traditional segmentation diffusion models typically employ random Gaussian noise to generate segmentation masks, resulting in non-unique segmentation masks that fail to guarantee the reproducibility of segmentation results. To tackle this issue, this paper introduces a novel method, Cold SegDiffusion, for general medical image segmentation based on the diffusion model. In this method, medical image segmentation is conceptualized as a denoising problem. The segmentation masks covering medical images serve as input for the segmentation encoder, addressing the challenge of generating non-unique masks due to noise randomness. Additionally, the contrast enhancement module is designed to translate features into the frequency domain, addressing the issues of low contrast and boundary disappearance in medical images. Furthermore, the suggested conditional cross-attention module utilizes the conditional encoder and cross-attention weights to enhance important features of the segmentation encoder output, improving the network’s capacity to focus on target regions. The proposed method is validated across three medical image segmentation datasets with different modalities. Experimental results demonstrate that Cold SegDiffusion outperforms mainstream segmentation methods. The code is available at https://github.com/TimesXY/Cold-SegDiffusion.

DGGI: Deep Generative Gradient Inversion with diffusion model

Federated learning is a privacy-preserving distributed framework that facilitates information fusion and sharing among different clients, enabling the training of a global model without exposing raw data. However, the gradient inversion attack that can reconstruct the training data via gradients has posed a significant threat. Prior attack approaches have demonstrated the efficacy of gradient inversion on low-resolution datasets with small batch sizes, which is impractical in real scenarios. To tackle this issue, this paper proposes an innovative and practical gradient inversion method, namely Deep Generative Gradient Inversion (DGGI), which employs the prior knowledge of diffusion models to enhance reconstruction performance on high-resolution datasets and larger batch sizes. Furthermore, a novel group consistency regularization term that constrains the distance between reconstruction and alignment images has been developed to address the issue of spatial variations caused by pre-trained diffusion model. Experiments conducted on both natural and medical image datasets demonstrate that our DGGI method outperforms state-of-the-art baselines in image reconstruction metrics. Furthermore, our approach achieves pixel-level reconstruction and causes leakage of privacy information, even at larger batch sizes or under various defenses, which can aid in the exploration of latent security concerns within information fusion models.

PRECISION: A Physics-Constrained and Noise-Controlled Diffusion Model for Photon Counting Computed Tomography.

Recently, the use of photon counting detectors in computed tomography (PCCT) has attracted extensive attention. It is highly desired to improve the quality of material basis image and the quantitative accuracy of elemental composition, particularly when PCCT data is acquired at lower radiation dose levels. In this work, we develop a physics-constrained and noise-controlled diffusion model, PRECISION in short, to address the degraded quality of material basis images and inaccurate quantification of elemental composition mainly caused by imperfect noise model and/or hand-crafted regularization of material basis images, such as local smoothness and/or sparsity, leveraged in the existing direct material basis image reconstruction approaches. In stark contrast, PRECISION learns distribution-level regularization to describe the feature of ideal material basis images via training a noise-controlled spatial-spectral diffusion model. The optimal material basis images of each individual subject are sampled from this learned distribution under the constraint of the physical model of a given PCCT and the measured data obtained from the subject. PRECISION exhibits the potential to improve the quality of material basis images and the quantitative accuracy of elemental composition for PCCT.

Controllable Seismic Velocity Synthesis Using Generative Diffusion Models

AbstractAccurate seismic velocity estimations are vital to understanding Earth's subsurface structures, assessing natural resources, and evaluating seismic hazards. Machine learning‐based inversion algorithms have shown promising performance in regional (i.e., for exploration) and global velocity estimations, while their effectiveness hinges on access to large and diverse training data sets whose distributions generally cover the target solutions. Additionally, enhancing the precision and reliability of velocity estimation also requires incorporating prior information, for example, geological classes, well logs, and subsurface structures, but current statistical or neural network‐based methods are not flexible enough to handle such multimodal information. To address both challenges, we propose to use conditional generative diffusion models for seismic velocity synthesis in which we readily incorporate those priors. This approach enables the generation of seismic velocities that closely match the expected target distribution, offering data sets informed by both expert knowledge and measured data to support training for data‐driven geophysical methods. We demonstrate the flexibility and effectiveness of our method through training diffusion models on the OpenFWI data set under various conditions, including class labels, well logs, reflectivity images, and the combination of these priors. The performance of the approach under out‐of‐distribution conditions further underscores its generalization ability, showcasing its potential to provide tailored priors for velocity inverse problems and create specific training data sets for machine learning‐based geophysical applications.

Diffusion mechanism of quick-setting slurry in water-rich fractured rock mass based on circle-outburst diffusion model

Grouting is the most commonly used methods in dealing with water inrush issue in mine and tunnel engineering. In order to better predict the grouting effect, research on slurry diffusion mechanism became a hotspot for scholars. At present, the mainstream theoretical model used to study the slurry diffusion mechanism are the circle diffusion model and the modified ones in plane plate fracture. However, these models cannot explain the “contradiction” between the rapid setting characteristics of quick-setting slurry and the continuous long-term injection of slurry in grouting engineering, which cannot accurately predict the grouting pressure or grouting diffusion range. Therefore, a “circle-outburst diffusion model” which can explain the above “contradiction” was proposed in this paper. Based on the new model, stepwise algorithms were developed to predict the grouting pressure and slurry diffusion range. By means of conducting fracture grouting simulation test and collecting grouting pressure data in an actual grouting project, the new model was verified and the slurry diffusion mechanism was studied. Comparison results indicate that the new model can reveal the intrinsic reason for the irregular diffusion phenomenon of the slurry and forecast the outburst moment accurately. The circle diffusion stage and outburst diffusion stage elaborated in the new “circle-outburst diffusion model” were consistent with the staged characteristics of the grouting process presented in the grouting simulating test. Differences between theoretical and experimental pressure value were within 10 %, indicating a high degree of consistency. The number and distribution of outburst diffusion points determine slurry diffusion form and significantly influence the diffusion range. The grouting pressure and the length of slurry flow path increase nonlinearly with time in each diffusion stage. It is hoped that the new model can provide a theoretical basis for the study of diffusion mechanism of quick-setting slurry.

Copper leaching from ultrasonically treated milled waste printed circuit boards: investigation of parameters optimization and kinetics.

Waste printed circuit boards (WPCBs) encompass abundant metals (gold, silver, and copper), along with other harmful materials including brominated epoxy resins, plastics, and heavy metals (lead, mercury, and cadmium). Direct burning and landfilling of WPCBs may cause severe health issues and impair the environment. Therefore, sustainable treatment of WPCBs is necessary to recover valuable metals and remove hazardous materials before disposal. The present work investigates the separation of copper-rich metallic fractions from the WPCBs by the combination of hammer milling and ultrasonic irradiation. Initially, discarded mobile phone PCBs are pre-processed and shortened into 1 × 1 cm2. Downscaled WPCBs are fed into the hammer mill to obtain the fine ground powder. The Powdered WPCBs are further processed through ultrasonic treatment to acquire metal-rich fraction. XRD, SEM-EDS, and ICP/AAS analysis revealed that the current technique can efficiently separate the metal-rich fraction without using toxic solvents. Results show the enhancement of copper fraction from 42.73 to 87 wt. % after ultrasonic treatment of WPCBs ground powder. Further, nitric acid leaching has been implemented to metal-rich fractions, and the parameters have been optimized for copper leaching with the assistance of response surface methodology (RSM) of the design of experiments (DOE). Quantitative dissolution (98.96%) of copper occurred using 3.5M nitric acid within 3h at 30°C with 50 GPL pulp density and 500rpm agitation speed. Finally, the kinetics of the leaching process were studied to conform the kinetics model. Moreover, the activation energy for diffusion (19.075kJ/mole) and reaction kinetics model (13.29kJ/mole) has also been calculated. The low energy consumption due to room temperature pre-treatment and effective leaching ensures the industrial feasibility of the proposed process.

Metal implant segmentation in CT images based on diffusion model

BackgroundComputed tomography (CT) is widely in clinics and is affected by metal implants. Metal segmentation is crucial for metal artifact correction, and the common threshold method often fails to accurately segment metals.PurposeThis study aims to segment metal implants in CT images using a diffusion model and further validate it with clinical artifact images and phantom images of known size.MethodsA retrospective study was conducted on 100 patients who received radiation therapy without metal artifacts, and simulated artifact data were generated using publicly available mask data. The study utilized 11,280 slices for training and verification, and 2,820 slices for testing. Metal mask segmentation was performed using DiffSeg, a diffusion model incorporating conditional dynamic coding and a global frequency parser (GFParser). Conditional dynamic coding fuses the current segmentation mask and prior images at multiple scales, while GFParser helps eliminate high-frequency noise in the mask. Clinical artifact images and phantom images are also used for model validation.ResultsCompared with the ground truth, the accuracy of DiffSeg for metal segmentation of simulated data was 97.89% and that of DSC was 95.45%. The mask shape obtained by threshold segmentation covered the ground truth and DSCs were 82.92% and 84.19% for threshold segmentation based on 2500 HU and 3000 HU. Evaluation metrics and visualization results show that DiffSeg performs better than other classical deep learning networks, especially for clinical CT, artifact data, and phantom data.ConclusionDiffSeg efficiently and robustly segments metal masks in artifact data with conditional dynamic coding and GFParser. Future work will involve embedding the metal segmentation model in metal artifact reduction to improve the reduction effect.

Modeling of effect of fly ash amount on microstructure and chloride diffusivity of blended fly ash-cement systems

Reasonable utilization of industrial fly-ash wastage in concrete engineering has been regarded as an effective way to reduce carbon emissions. By adding the reasonable dosage of fly ash to cement paste, the compactness and microstructure characteristics of the blended cement systems can be significantly improved, thereby effectively enhancing the durability of concrete structures. The vector hydration model of blended fly ash-cement systems with the interference effects of different hydration layers of fly ash and cement particles, the solubility equilibrium of solid phases and the electrical neutrality of the pore solution involved is established. By fully comparing with the experimental data of hydration degree, capillary porosity and CH content, the accuracy of the developed hydration model is verified. Based on the hydration model, the effect of fly ash content on the concentration of different ions and pH in the pore solution with curing time is discussed. Additionally, the evolution characteristic of hydration degree, capillary porosity and CH content with curing time at different fly ash content is also analyzed. Based on the reconstructed microstructure of blended systems, the rolling sweep (RS) technique is used to determine the pore size distribution of capillary pores. The effect of fly ash content on cumulative pore size distribution and differential pore size distribution at different curing time is quantitatively evaluated and discussed. By utilizing the first-passage cube, the dual-probability-Brownian motion method is constructed to predict the chloride diffusivity of blended cement systems. After diffusion model is verified by multi-group experimental data, the optimal dosage of fly ash at different water-binder ratio is calculated, which can provide theoretical guidance for practical applications in concrete engineering.

Adaptive Truncation Threshold Determination for Multimode Fiber Single-Pixel Imaging

Truncated singular value decomposition (TSVD) is a popular recovery algorithm for multimode fiber single-pixel imaging (MMF-SPI), and it uses truncation thresholds to suppress noise influences. However, due to the sensitivity of MMF relative to stochastic disturbances, the threshold requires frequent re-determination as noise levels dynamically fluctuate. In response, we design an adaptive truncation threshold determination (ATTD) method for TSVD-based MMF-SPI in disturbed environments. Simulations and experiments reveal that ATTD approaches the performance of ideal clairvoyant benchmarks, and it corresponds to the best possible image recovery under certain noise levels and surpasses both traditional truncation threshold determination methods with less computation—fixed threshold and Stein’s unbiased risk estimator (SURE)—specifically under high noise levels. Moreover, target insensitivity is demonstrated via numerical simulations, and the robustness of the self-contained parameters is explored. Finally, we also compare and discuss the performance of TSVD-based MMF-SPI, which uses ATTD, and machine learning-based MMF-SPI, which uses diffusion models, to provide a comprehensive understanding of ATTD.

Determining a time‐varying potential in time‐fractional diffusion from observation at a single point

AbstractWe discuss the identification of a time‐dependent potential in a time‐fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by leveraging the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results.

Microstructural brain assessment in late-life depression and apathy using diffusion MRI multi-compartments models and tractometry

Late-life depression (LLD) is both common and disabling and doubles the risk of dementia onset. Apathy might constitute an additional risk of cognitive decline but clear understanding of its pathophysiology is lacking. While white matter (WM) alterations have been assessed using diffusion tensor imaging (DTI), this model cannot accurately represent WM microstructure. We hypothesized that a more complex multi-compartment model would provide new biomarkers of LLD and apathy. Fifty-six individuals (LLD n = 35, 26 females, 75.2 ± 6.4 years, apathy evaluation scale scores (41.8 ± 8.7) and Healthy controls, n = 21, 16 females, 74.7 ± 5.2 years) were included. In this article, a tract-based approach was conducted to investigate novel diffusion model biomarkers of LLD and apathy by interpolating microstructural metrics directly along the fiber bundle. We performed multivariate statistical analysis, combined with principal component analysis for dimensional data reduction. We then tested the utility of our framework by demonstrating classically reported from the literature modifications in LDD while reporting new results of biological-basis of apathy in LLD. Finally, we aimed to investigate the relationship between apathy and microstructure in different fiber bundles. Our study suggests that new fiber bundles, such as the striato-premotor tracts, may be involved in LLD and apathy, which bring new light of apathy mechanisms in major depression. We also identified statistical changes in diffusion MRI metrics in 5 different tracts, previously reported in major cognitive disorders dementia, suggesting that these alterations among these tracts are both involved in motivation and cognition and might explain how apathy is a prodromal phase of degenerative disorders.

Pointwise estimates on the fundamental solution to nonlocal diffusion equation

In this article we study the pointwise behavior of the fundamental solution S ( t , x ) to the nonlocal diffusion model u t = D ( J ∗ u − u ) on R , S ( t , x ) can be written as e − Dt δ ( x ) + S 0 ( t , x ) , where S 0 ( t , x ) is called the regularizing part. Under some conditions on J and its Fourier transform J ^ , we obtain some new pointwise estimates on S 0 ( t , x ) . Then we apply our results to study the spatial dynamics of the nonlocal diffusion population model in a shifting environment considered in Li et al. [Spatial dynamics of a nonlocal dispersal population model in a shifting environment. J Nonlinear Sci. 2018;28:1189–1219]. In our study the convolution kernel J can be assumed to be more general, i.e. not necessarily of compact support, also the proof is greatly simplified. It is our believe that these pointwise estimates possess their own interest in further studying nonlocal diffusion models.

Toward Smart Ultrasound Image Augmentation to Advance Tumor Treatment Monitoring: Exploring the Potential of Diffusion Generative Model

Abstract Medical imaging is a crucial tool in clinics to monitor tumor treatment progress. In practice, many imaging tools (such as magnetic resonance imaging (MRI) and computed tomography (CT) scans) are in general costly and may also expose patients to radiation, leading to potential side effects. Recent studies have demonstrated that ultrasound imaging, which is safe, low-cost, and easy to access, can monitor the drug delivery progress in solid tumors. However, the noisy nature of ultrasound images and the high-level uncertainty of cancer disease progression are still challenging in ultrasound-based tumor treatment monitoring. To overcome these barriers, this work presents a comparative study to explore the potential advantages of the emerging diffusion generative models against the commonly applied state-of-the-art generative models. Namely, the denoising diffusion models (DDMs), against the generative adversarial networks (GAN), and variational auto-encoders (VAE), are used for analyzing the ultrasound images through image augmentation. These models are evaluated based on their capacity to augment ultrasound images for exploring the potential variations of tumor treatment monitoring. The results across different cases indicate that the denoising diffusion implicit models (DDIM)/kernel inception distance (KID)-inception score (IS) model leveraged in this work outperforms the other models in the study in terms of similarity, diversity, and predictive accuracy. Therefore, further investigation of such diffusion generative models could be considered as they can potentially serve as a great predictive tool for ultrasound image-enabled tumor treatment monitoring in the future.

Production of Industrial-Grade Monoclinic Lead Chromate (PbCrO4) from Indigenous Chromite ore for Paint Pigment Utilization

Decades of use have proven that lead chromate (PbCrO4) powder is an excellent paint pigment material. Unfortunately, practically this entire superb chromate compound used for decorative systems, protective systems, and mass dyeing of paper and polymer materials is conventionally made using inorganic synthetic chromium salts. In this study, we reported a promising simple, low-cost lead chromate production route derived from chromite ore from Nigeria. The Nigerian chromite ore was roasted in a 1:1 NaOH salt and then leached with water at 60°C. Lead nitrate was added to the leached liquor to further co-precipitate it. The resulting precipitate was then cleaned in ethanol and oven dried for ten hours at 80°C. The experimental results showed that lead ion concentration, temperature and flow rate have large influence on lead chromate precipitation, and the precipitation data fit a diffusion model. The activation energy of lead precipitation obtained was 4.76 kJ/mol, and the reaction order was 0.873 nearly one in relation to the concentration of lead ion. Additionally, XRD, FT-IR, and SEM/EDS comparative investigation of the properties established which favourable paint pigment performance similar to that of commercial industrial lead chromate powder in a range of all established physicochemical properties clarified the developing direction of research on lead chromate synthesis from Chromite leached liquor.

Molecular relaxation by reverse diffusion with time step prediction

Abstract Molecular relaxation, finding the equilibrium state of a non-equilibrium structure, is an essential component of computational chemistry to understand reactivity. Classical force field (FF) methods often rely on insufficient local energy minimization, while neural network FF models require large labeled datasets encompassing both equilibrium and non-equilibrium structures. As a remedy, we propose MoreRed, molecular relaxation by reverse diffusion, a conceptually novel and purely statistical approach where non-equilibrium structures are treated as noisy instances of their corresponding equilibrium states. To enable the denoising of arbitrarily noisy inputs via a generative diffusion model, we further introduce a novel diffusion time step predictor. Notably, MoreRed learns a simpler pseudo potential energy surface (PES) instead of the complex physical PES. It is trained on a significantly smaller, and thus computationally cheaper, dataset consisting of solely unlabeled equilibrium structures, avoiding the computation of non-equilibrium structures altogether. We compare MoreRed to classical FFs, equivariant neural network FFs trained on a large dataset of equilibrium and non-equilibrium data, as well as a semi-empirical tight-binding model. To assess this quantitatively, we evaluate the root-mean-square deviation between the found equilibrium structures and the reference equilibrium structures as well as their energies.